Measurement of the Branching Fraction for D^+ to K^- pi^+ pi^+

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中国物理学会年秋季会议资料.ppt

Early theories: 0.9-1.3 Measurements: smaller Recent theories:0.5-0.7
experiment and theoretical prediction
Motivation
(3770) is thought to decay almost entirely to pure DDbar, but there is large
|Vcs | [|Vcd|]
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Search for some exclusive non-DDbar decays
BES observed 12 signal events for the decay (3770) non D D measured the branching fraction to be
BF ( (3770) J / ) (0.34 0.14 0.09)%
CLEO confirmed BES observation of the decay, and measured the branching fractions to be

B → πρ, πω decays in perturbative QCDapp roach

Digital Object Identiﬁer (DOI)10.1007/s100520100878Eur.Phys.J.C 23,275–287(2002)T HE E UROPEANP HYSICAL J OURNAL CB →πρ,πωde cays in pe rturbative QCDapproachC.-D.L¨u 1,2,3,M.-Z.Yang 1,2,31CCAST (World Laboratory),P.O.Box 8730,Beijing 100080,P.R.China 2Institute of High EnergyPhy sics,CAS,P.O.Box 918(4),Beijing 100039,P.R.China 3Physics Department,Hiroshima University,Higashi-Hiroshima 739-8526,JapanReceived:5November 2001/Published online:8February2002–c Springer-Verlag /Societ`a Italiana di Fisica 2002Abstract.We calculate the branching ratios and CP -asymmetries for B 0→π+ρ−,B 0→ρ+π−,B +→ρ+π0,B +→π+ρ0,B 0→π0ρ0,B +→π+ωand B 0→π0ωdecays,in the perturbative QCD approach.In this approach,we calculate non-factorizable and annihilation type contributions,in addition to the usualfactorizable contributions.Our result is in agreement with the branching ratio of B 0/¯B0→π±ρ∓,B ±→π±ρ0,π±ωmeasured bythe CLEO and BABAR collaborations.We also predict large CP -asymmetries in these decays.These channels are useful to determine the CKM angle φ2.1IntroductionThe rare decays of the B -mesons are getting more and more interesting,since they are useful for the search of CP -violation and sensitive to new physics.The recent measurement of B →πρand πωdecays by the CLEO Collaboration [1]aroused more discussions on these decays [2].The B →πρ,πωdecays which are helpful for the de-termination of the Cabbibo–Kobayashi–Maskawa (CKM)unitarity triangle φ2have been studied in the factoriza-tion approach in detail [3,4].In this paper,we would like to study the B →πρand πωdecays in the perturba-tive QCD approach (PQCD),where we can calculate the non-factorizable contributions as corrections to the usual factorization approach.In the B →πρ,πωdecays,the B -meson is heavy,sit-ting at rest.It decays into two light mesons with large mo-menta.Therefore the light mesons are moving very fast in the rest frame of the B -meson.In this case,the short dis-tance hard process dominates the decay amplitude.The reasons can be ordered as:ﬁrst,because there are not many resonances near the energy region of the B mass,it is reasonable to assume that the ﬁnal state interaction is not important in two-body B decays.Second,with the ﬁnal light mesons moving very fast,there must be a hard gluon to kick the light spectator quark (almost at rest)in the B -meson to form a fast moving pion or light vector meson.So the dominant diagram in this theoretical pic-ture is the one with a hard gluon from the spectator quark connecting with the other quarks in the four quark oper-ator of the weak interaction.There are also soft (soft and collinear)gluon exchanges between the quarks.Summing over those leading soft contributions gives a Sudakov formMailing addressfactor which suppresses the dominance of the soft con-tribution.This makes the PQCD reliable in calculating the non-leptonic decays.With the Sudakov resummation,we can include the leading double logarithms for all loop diagrams,in association with the soft contribution.Un-like the usual factorization approach,the hard part of the PQCD approach consists of six quarks rather than four.We thus call it the case of six-quark operators or six-quark eﬀective theory.Applying the six-quark eﬀective theory to B -meson decays,we need meson wave functions for the hadronization of quarks into mesons.All the collinear dy-namics is included in the meson wave functions.In this paper,we calculate the B →πand B →ρform factors,which are input parameters used in the factoriza-tion approach.The form factor calculations can give severe restrictions to the input meson wave functions.We also calculate the non-factorizable contributions and the anni-hilation type diagrams,which are diﬃcult to calculate in the factorization approach.We found that this type of di-agrams gives dominant contributions to the strong phases.The strong phase in this approach can also be calculated directly,without ambiguity.In the next section,we will brieﬂy introduce our method of PQCD.In Sect.3,we per-form the perturbative calculations for all the channels.We give the numerical results and discussions in Sect.4.Fi-nally Sect.5is a short summary.2The frameworkThe three scale PQCD factorization theorem has been de-veloped for non-leptonic heavy meson decays [5].The fac-torization formula is given by the typical expressionC (t )×H (x,t )×Φ(x )276 C.-D.L¨u,M.-Z.Yang:B→πρ,πωdecays in perturbative QCD approach×exp−s(P,b)−2t1/bd¯µ¯µγq(αs(¯µ)),(1)where C(t)are the corresponding Wilson coeﬃcients,Φ(x) are the meson wave functions.The quark anomalous di-mensionγq=−αs/πdescribes the evolution from scale t to1/b.Non-leptonic heavy meson decays involve three scales: the W-boson mass m W,at which the matching conditions of the eﬀective Hamiltonian is deﬁned,the typical scale t of a hard sub-amplitude,which reﬂects the dynamics of heavy quark decays,and the factorization scale1/b, with b the conjugate variable of the parton transverse mo-menta.The dynamics below the1/b scale is regarded as being completely non-perturbative,and can be parame-terized into meson wave functions.Above the scale1/b, PQCD is reliable and radiative corrections produce two types of large logarithms:ln(m W/t)and ln(tb).The for-mer are summed by the renormalization group equations to give the leading logarithm evolution from m W to the t scale contained in the Wilson coeﬃcients C(t),while the latter are summed to give the evolution from the t scale down to1/b,shown as the last factor in(1).There exist also double logarithms ln2(P b)from the overlap of collinear and soft divergences,P being the dom-inant light-cone component of a meson momentum.The resummation of these double logarithms leads to a Su-dakov form factor exp[−s(P,b)],which suppresses the long distance contributions in the large b region,and vanishes as b>1/ΛQCD.This factor improves the applicability of PQCD.For the detailed derivation of the Sudakov form factors,see[6,7].Since all logarithm corrections have been summed by renormalization group equations,the above factorization formula does not depend on the renormal-ization scaleµ.With all the large logarithms resummed,the remaining ﬁnite contributions are absorbed into a hard sub-ampli-tude H(x,t).The H(x,t)is calculated perturbatively us-ing the four quark operators together with the spectator quark,connected by a hard gluon.When the end-point region(x→0,1)of the wave function is important for the hard amplitude,the corresponding large double loga-rithmsαs ln2x shall appear in the hard amplitude H(x,t), which should be resummed to give a jet function S t(x). This technique is the so-called threshold resummation[8]. The threshold resummation form factor S t(x)vanishes as x→0,1,which eﬀectively suppresses the end-point be-havior of the hard amplitude.This suppression will be-come important when the meson wave function remains constant at the end-point region.For example,the twist-3 wave functionsφPπandφtπare such kinds of wave func-tions;they can be found in the numerical section of this paper.The typical scale t in the hard sub-amplitude is around(ΛM B)1/2.It is chosen as the maximum value of those scales which appear in the six-quark action.This is to diminish theα2s corrections to the six-quark amplitude. The expressions of the scale t in diﬀerent sub-amplitudes will be derived in the next section and the formula is shown in the appendix.2.1Wilson coeﬃcientsFirst we begin with the weak eﬀective Hamiltonian H eﬀfor the∆B=1transitions:H eﬀ=G F√2V ub V∗ud(C1O u1+C2O u2)−V tb V∗td10i=3C i O i.(2) We specify below the operators in H eﬀfor b→d:O u1=¯dαγµLuβ·¯uβγµLbα,O u2=¯dαγµLuα·¯uβγµLbβ,O3=¯dαγµLbα·q¯q βγµLq β,O4=¯dαγµLbβ·q¯q βγµLq α,O5=¯dαγµLbα·q¯q βγµRq β,O6=¯dαγµLbβ·q¯q βγµRq α,O7=32¯dαγµLbα·qe q ¯q βγµRq β,O8=32¯dαγµLbβ·qe q ¯q βγµRq α,O9=32¯dαγµLbα·qe q ¯q βγµLq β,O10=32¯dαγµLbβ·qe q ¯q βγµLq α.(3)Hereαandβare the SU(3)color indices;L and R are the left-and right-handed projection operators with L= (1−γ5),R=(1+γ5).The sum over q runs over the quarkﬁelds that are active at the scaleµ=O(m b),i.e., (q {u,d,s,c,b}).The PQCD approach works well for the leading twist approximation and leading double logarithm summation. For the Wilson coeﬃcients,we will also use the leading logarithm summation for the QCD corrections,although the next-to-leading order calculations already exists in the literature[9].This is the consistent way to cancel the ex-plicitµdependence in the theoretical formulae.If the scale m b<t<m W,then we evaluate the Wil-son coeﬃcients at a t scale using the leading logarithm running equations[9]in Appendix B of[10].In numerical calculations,we useαs=4π/[β1ln(t2/Λ(5)QCD2)]which is the leading order expression withΛ(5)QCD=193MeV,de-rived forΛ(4)QCD=250MeV.Hereβ1=(33−2n f)/12,with the appropriate number of active quarks n f.n f=5when the scale t is larger than m b.If the scale t<m b,then we evaluate the Wilson co-eﬃcients at the t scale using the formulae in Appendix C of[10]for four active quarks(n f=4)(again in leading logarithm approximation).C.-D.L¨u,M.-Z.Yang:B→πρ,πωdecays in perturbative QCD approach2772.2Wave functionsIn the resummation procedure,the B-meson is treated asa heavy-light system.In general,the B-meson light-conematrix element can be decomposed as[11,12]1 0d4z(2π)4e i k1·z 0|¯bα(0)dβ(z)|B(p B)=−i√2N c(p B+m B)γ5×φB(k1)−n−v√2¯φB(k1)βα,(4)where n=(1,0,0T),and v=(0,1,0T)are the unit vec-tors pointing to the plus and minus directions,respec-tively.From the above equation,one can see that there are two Lorentz structures in the B-meson distribution amplitudes.They obey the following normalization condi-tions:d4k1 (2π)4φB(k1)=f B2√2N c,d4k1(2π)4¯φB(k1)=0.(5)In general,one should consider both these two Lorentz structures in calculations of B-meson decays.However,it can be argued that the contribution of¯φB is numerically small[13];thus its contribution can be neglected.There-fore,we only consider the contribution of the Lorentz structureΦB=1√2N c(p B+m B)γ5φB(k1)(6)in our calculation.We keep the same input as in the other calculations in this direction[10,13,14]and it is also easier for comparing with other approaches[12,15].Throughout this paper,we use the light-cone coordinates to write the four momentum as(k+1,k−1,k⊥1).In the next section,we will see that the hard part is always independent of one of the k+1and/or k−1,if we make some approximations.The B-meson wave function is then a function of the variablesk−1(or k+1)and k⊥1,φB(k−1,k⊥1)=d k+1φ(k+1,k−1,k⊥1).(7)Theπ-meson is treated as a light-light system.In the B-meson rest frame,the pion is moving very fast,and one of the k+1or k−1is zero which depends on the deﬁnition of the z axis.We consider a pion moving in the minus direction in this paper.The pion distribution amplitude is deﬁned by[16]π−(P)|¯dα(z)uβ(0)|0=i√2N c1dx e i xP·zγ5Pφπ(x)+m0γ5φP(x)−m0σµνγ5Pµzνφσ(x)6βα.(8)For theﬁrst and second term in the above equation,wecan easily get the projector of the distribution amplitudein the momentum space.However,for the third term weshould make some eﬀort to transfer it into the momentumspace.By using integration by parts for the third term,after a few steps,(8)can beﬁnally changed toπ−(P)|¯dα(z)uβ(0)|0=i√2N c1dx e i xP·zγ5Pφπ(x)+m0γ5φP(x)+m0[γ5(v n−1)]φtπ(x)βα,(9)whereφtπ(x)=(1/6)(d/x)φσ(x),and the vector v is par-allel to theπ-meson momentum pπ.m0=m2π/(m u+m d)is a scale characterized by chiral perturbation theory.InB→πρdecays,theρ-meson is only longitudinally polar-ized.We only consider its wave function in longitudinalpolarization[13,17]:ρ−(P, L)|¯dα(z)uβ(0)|0=1√2N c1dx e i xP·zpρφtρ(x)+mρφρ(x)+mρφsρ(x).(10)The second term in the above equation is the leading twistwave function(twist-2),while theﬁrst and third terms aresub-leading twist(twist-3)wave function.The transverse momentum k⊥is usually convenientlyconverted to the b parameter by a Fourier transforma-tion.The initial conditions ofφi(x),i=B,π,are of non-perturbative origin,satisfying the normalization1φi(x,b=0)d x=12√6f i,(11)with f i the meson decay constant.3Perturbative calculationsIn the previous section we have discussed the wave func-tions and Wilson coeﬃcients of the factorization formulain(1).In this section,we will calculate the hard part H(t).This part involves the four quark operators and the nec-essary hard gluon connecting the four quark operator andthe spectator quark.Since theﬁnal results are expressedas integrations of the distribution function variables,wewill show the whole amplitude for each diagram includingwave functions.Similar to the B→ππdecays[10],there are8typesof diagrams contributing to the B→πρdecays,which areshown in Fig.1.Let usﬁrst calculate the usual factorizablediagrams a and b.The operators O1,O2,O3,O4,O9,andO10are(V−A)(V−A)currents,and the sum of theiramplitudes is given byF e=8√2πC F G F fρmρm2B( ·pπ)278 C.-D.L¨u ,M.-Z.Yang:B →πρ,πωdecays in perturbative QCDapproachFig.1a–h.Diagrams contributing to the B →πρdecays (diagram a and b contribute to the B →πform factor)× 1d x 1d x 2∞b 1d b 1b 2d b 2φB (x 1,b 1)×(1+x 2)φA π(x 2,b 2)+r π(1−2x 2) φP π(x 2,b 2)+φσπ(x 2,b 2) αs (t 1e )×h e (x 1,x 2,b 1,b 2)exp[−S ab (t 1e )]+2r πφP π(x 2,b 2)αs (t 2e )h e (x 2,x 1,b 2,b 1)×exp[−S ab (t 2e )],(12)where r π=m 0/m B =m 2π/[m B (m u +m d )];C F =4/3is a color factor.The function h e ,the scales t i e and the Sudakov factors S ab are displayed in the appendix.In the above equation,we do not include the Wilson coeﬃcients of the corresponding operators,which are process depen-dent.They will be shown later in this section for diﬀerent decay channels.The diagrams in F ig.1a,bare also the di-agrams for the B →πform factor F B →π1.Therefore wecan extract F B →π1from (12).We haveF B →π1(q 2=0)=F e√2G F f ρm ρ( ·p π).(13)The operators O 5,O 6,O 7,and O 8have the structure of (V −A )(V +A ).In some decay channels,some of these operators contribute to the decay amplitude in a factoriz-able way.Since only the vector part of the (V +A )current contributes to the vector meson production,π|V −A |B ρ|V +A |0 = π|V −A |B ρ|V −A |0 ,(14)the result of these operators is the same as (12).In some other cases,we need to do a Fierz transformation for these operators to get the right color structure for the factoriza-tion to work.In this case,we get (S −P )(S +P )operatorsfrom (V −A )(V +A )ones.Because neither the scalar northe pseudo-scalar density give contributions to the vector meson production,i.e. ρ|S +P |0 =0,we getF P e =0.(15)For the non-factorizable diagrams c and d,all threemeson wave functions are involved.The integration of b 3can be performed easily using the δfunction δ(b 3−b 1),leaving only the integration of b 1and b 2.For the (V −A )(V −A )operators the result isM e =−323√3πC F G F m ρm 2B ( ·p π)× 10d x 1d x 2d x 3 ∞0b 1d b 1b 2d b 2φB (x 1,b 1)×x 2 φA π(x 2,b 1)−2r πφσπ(x 2,b 1) ×φρ(x 3,b 2)h d (x 1,x 2,x 3,b 1,b 2)exp[−S cd (t d )].(16)For the (V −A )(V +A )operators the formula is diﬀerent:M P e =643√3πC F G F m 2ρm B ( ·p π)× 10d x 1d x 2d x 3 ∞0b 1d b 1b 2d b 2φB (x 1,b 1)×r π(x 3−x 2)× φP π(x 2,b 1)φt ρ(x 3,b 2)+φσπ(x 2,b 1)φs ρ(x 3,b 2) −r π(x 2+x 3)× φP π(x 2,b 1)φs ρ(x 3,b 2)+φσπ(x 2,b 1)φt ρ(x 3,b 2) +x 3φA π(x 2,b 1) φt ρ(x 3,b 2)−φsρ(x 3,b 2) ×h d (x 1,x 2,x 3,b 1,b 2)exp[−S cd (t d )].(17)Comparing with the expression of M e in (16),the (V −A )(V +A )type result M Pe is suppressed by m ρ/m B .C.-D.L¨u ,M.-Z.Yang:B →πρ,πωdecays in perturbative QCD approach 279For the non-factorizable annihilation diagrams e andf,again all three wave functions are involved.The inte-gration of b 3can be performed easily using the δfunction δ(b 3−b 2).Here we have two kinds of contribution,which are diﬀerent.M a is the contribution containing the oper-ator of type (V −A )(V −A ),and M Pa is the contribution containing the operator of type (V −A )(V +A ):M a =323√3πC F G F m ρm 2B ( ·p π)× 10d x 1d x 2d x 3 ∞0b 1d b 1b 2d b 2φB (x 1,b 1)× x 2φA π(x 2,b 2)φρ(x 3,b 2)+r πr ρ(x 2−x 3)× φP π(x 2,b 2)φt ρ(x 3,b 2)+φσπ(x 2,b 2)φs ρ(x 3,b 2) +r πr ρ(x 2+x 3)× φσπ(x 2,b 2)φt ρ(x 3,b 2)+φP π(x 2,b 2)φsρ(x 3,b 2)×h 1f (x 1,x 2,x 3,b 1,b 2)exp[−S ef (t 1f )]−x 3φA π(x 2,b 2)φρ(x 3,b 2)+r πr ρ(x 3−x 2)× φP π(x 2,b 2)φt ρ(x 3,b 2)+φσπ(x 2,b 2)φs ρ(x 3,b 2) +r πr ρ(2+x 2+x 3)φP π(x 2,b 2)φs ρ(x 3,b 2)−r πr ρ(2−x 2−x 3)φσπ(x 2,b 2)φtρ(x 3,b 2)×h 2f (x 1,x 2,x 3,b 1,b 2)exp[−S ef (t 2f )] ,(18)M P a=−323√3πC F G F m ρm 2B ( ·p π)× 10d x 1d x 2d x 3 ∞0b 1d b 1b 2d b 2φB (x 1,b 1)× x 2r πφρ(x 3,b 2) φP π(x 2,b 2)+φσπ(x 2,b 2) −x 3r ρφA π(x 2,b 2)φt ρ(x 3,b 2)+φs ρ(x 3,b 2)×h 1f (x 1,x 2,x 3,b 1,b 2)exp[−S ef (t 1f )]+ (2−x 2)r πφρ(x 3,b 2) φP π(x 2,b 2)+φσπ(x 2,b 2) −r ρ(2−x 3)φA π(x 2,b 2) φt ρ(x 3,b 2)+φsρ(x 3,b 2)×h 2f (x 1,x 2,x 3,b 1,b 2)exp[−S ef (t 2f )] ,(19)where r ρ=m ρ/m B .The factorizable annihilation dia-grams g and h involve only the πand ρwave functions.There are also two kinds of decay amplitudes for these two diagrams.F a is for (V −A )(V −A )type operators,and F P a is for (S −P )(S +P )type operators:F a =8√2C F G F πf B m ρm 2B ( ·p π)× 1d x 1d x 2 ∞0b 1d b 1b 2d b 2×x 2φA π(x 1,b 1)φρ(x 2,b 2)−2(1−x 2)r πr ρφP π(x 1,b 1)φtρ(x 2,b 2)+2(1+x 2)r πr ρφP π(x 1,b 1)φsρ(x 2,b 2)×αs (t 1e )h a (x 2,x 1,b 2,b 1)exp[−S gh (t 1e )]−x 1φA π(x 1,b 1)φρ(x 2,b 2)+2(1+x 1)r πr ρφP π(x 1,b 1)φs ρ(x 2,b 2)−2(1−x 1)r πr ρφσπ(x 1,b 1)φsρ(x 2,b 2)×αs (t 2e )h a (x 1,x 2,b 1,b 2)exp[−S gh (t 2e )],(20)F P a=16√2C F G F πf B m ρm 2B ( ·p π)× 10d x 1d x 2 ∞0b 1d b 1b 2d b 2×2r πφP π(x 1,b 1)φρ(x 2,b 2)+x 2r ρφAπ(x 1,b 1)×φs ρ(x 2,b 2)−φt ρ(x 2,b 2)×αs (t 1e )h a (x 2,x 1,b 2,b 1)exp[−S gh (t 1e )]+ x 1r π φP π(x 1,b 1)−φσπ(x 1,b 1) φρ(x 2,b 2)+2r ρφA π(x 1,b 1)φsρ(x 2,b 2)×αs (t 2e )h a (x 1,x 2,b 1,b 2)exp[−S gh (t 2e )] ,(21)In the above equations,we have used the assumptionthat x 1 x 2,x 3.Since the light quark momentum frac-tion x 1in the B -meson is peaked at the small x 1re-gion,while the quark momentum fraction x 2of the pion is peaked around 0.5,this is not a bad approximation.The numerical results also show that this approximation makes very little diﬀerence in the ﬁnal result.After us-ing this approximation,all the diagrams are functions of k −1=x 1m B /(21/2)of the B -meson only,independent ofthe variable k +1.Therefore the integration of (7)is per-formed safely.If we exchange the πand ρin Fig.1,the result will be diﬀerent for some diagrams because this will switch the dominant contribution from the B →πform factor to the B →ρform factor.The new diagrams are shown in Fig.2.Inserting (V −A )(V −A )operators,the corresponding amplitude for F ig.2a,bisF eρ=8√2πC F G F f πm ρm 2B ( ·p π)(22)× 10d x 1d x 2 ∞0b 1d b 1b 2d b 2φB (x 1,b 1)× (1+x 2)φρ(x 2,b 2)+(1−2x 2)r ρφt ρ(x 2,b 2)+φs ρ(x 2,b 2)280 C.-D.L¨u ,M.-Z.Yang:B →πρ,πωdecays in perturbative QCDapproachFig.2a–h.Diagrams contributing to the B →πρdecays (diagram a and b contribute to the B →ρform factor A B →ρ)×αs (t 1e )h e (x 1,x 2,b 1,b 2)exp[−S ab (t 1e )]+2r ρφs ρ(x 2,b 2)αs (t 2e )h e (x 2,x 1,b 2,b 1)exp[−S ab (t 2e )].These two diagrams are also responsible for the calculationof the B →ρform factors.The form factor relative to theB →πρdecays is A B →ρ0,which can be extracted from (22):A B →ρ0(q 2=0)=F eρ√2G F f πm ρ( ·p π).(23)For (V −A )(V +A )operators,F ig.2a,bgiveF Peρ=−16√2πC F G F f πm ρr πm 2B ( ·p π)× 10d x 1d x 2 ∞0b 1d b 1b 2d b 2φB (x 1,b 1)× φρ(x 2,b 2)−r ρx 2φt ρ(x 2,b 2)+(2+x 2)r ρφs ρ(x 2,b 2)×αs (t 1e )h e (x 1,x 2,b 1,b 2)exp[−S ab (t 1e )]+ x 1φρ(x 2,b 2)+2r ρφs ρ(x 2,b 2) ×αs (t 2e )h e (x 2,x 1,b 2,b 1)exp[−S ab (t 2e )] .(24)For the non-factorizable diagrams in Fig.2c,d the result isM eρ=−323√3πC F G F m ρm 2B ( ·p π)× 10d x 1d x 2d x 3 ∞0b 1d b 1b 2d b 2φB (x 1,b 1)×x 2 φρ(x 2,b 2)−2r ρφt ρ(x 2,b 2) ×φA π(x 3,b 1)h d (x 1,x 2,x 3,b 1,b 2)×exp[−S cd (t d )].(25)For the non-factorizable annihilation diagrams e and f,we have M aρfor (V −A )(V −A )operators and M Paρfor (V −A )(V +A )operators.M aρ=323√3πC F G F m ρm 2B ( ·p π)× 10d x 1d x 2d x 3 ∞0b 1d b 1b 2d b 2φB (x 1,b 1)× exp[−S ef (t 1f )]×x 2φA π(x 3,b 2)φρ(x 2,b 2)+r πr ρ(x 2−x 3)× φP π(x 3,b 2)φt ρ(x 2,b 2)+φσπ(x 3,b 2)φs ρ(x 2,b 2)+r πr ρ(x 2+x 3)φσπ(x 3,b 2)φtρ(x 2,b 2)+φP π(x 3,b 2)φsρ(x 2,b 2)h 1f (x 1,x 2,x 3,b 1,b 2)−x 3φA π(x 3,b 2)φρ(x 2,b 2)+r πr ρ(x 3−x 2)× φP π(x 3,b 2)φt ρ(x 2,b 2)+φσπ(x 3,b 2)φs ρ(x 2,b 2) −r πr ρ(2−x 2−x 3)φσπ(x 3,b 2)φt ρ(x 2,b 2)+r πr ρ(2+x 2+x 3)φP π(x 3,b 2)φsρ(x 2,b 2)×h 2f (x 1,x 2,x 3,b 1,b 2)exp[−S ef (t 2f )],(26)M P aρ=M Pa .(27)For the factorizable annihilation diagrams g and hF aρ=−F a ,(28)F Paρ=−F P a ,(29)If the ρ-meson is replaced by the ω-meson in Figs.1and2,the formulas will be the same,except for replacing f ρby f ωand φρby φω.C.-D.L¨u ,M.-Z.Yang:B →πρ,πωdecays in perturbative QCD approach 281In the language of the above matrix elements for dif-ferent diagrams (12)–(29),the decay amplitude for B 0→π+ρ−can be written M (B 0→π+ρ−)=F eρ ξu13C 1+C 2−ξt C 4+13C 3+C 10+13C 9−F Peρξt C 6+13C 5+C 8+13C 7+M eρ[ξu C 1−ξt (C 3+C 9)]+M a ξu C 2−ξt C 4−C 6+12C 8+C 10−M aρξt C 3+C 4−C 6−C 8−12C 9−12C 10−M Paρξt C 5−12C 7 +F a ξu C 1+13C 2−ξt −13C 3−C 4−32C 7−12C 8+53C 9+C 10+F Pa ξt 13C 5+C 6−16C 7−12C 8 ,(30)where ξu =V ∗ub V ud ,ξt =V ∗tb V td .The Ci s should be cal-culated at the appropriate scale t using the equations in the appendices of [10].The decay amplitude of thecharge conjugate decay channel B 0→ρ+π−is the same as (30)except replacing the CKM matrix elements ξu to ξ∗u and ξt to ξ∗t under the deﬁnition of charge conjugationC |B 0 =−|¯B 0 .We haveM (B 0→ρ+π−)=F e ξu 13C 1+C 2−ξt C 4+13C 3+C 10+13C 9+M e [ξu C 1−ξt (C 3+C 9)]−M Pe ξt [C 5+C 7]+M aρ ξu C 2−ξt C 4−C 6+12C 8+C 10−M a ξt C 3+C 4−C 6−C 8−12C 9−12C 10−M Pa ξt C 5−12C 7 +F a ξu −C 1−13C 2−ξt 13C 3+C 4+32C 7+12C 8−53C 9−C 10−F Pa ξt 13C 5+C 6−16C 7−12C 8 .(31)The decay amplitude for B 0→π0ρ0can be written as−2M (B 0→π0ρ0)=F e ξu C 1+13C 2−ξt −13C 3−C 4+32C 7+12C 8+53C 9+C 10+F eρ ξu C 1+13C 2−ξt−13C 3−C 4−32C 7−12C 8+53C 9+C 10+F Peρξt 13C 5+C 6−16C 7−12C 8+M e ξu C 2−ξt −C 3−32C 8+12C 9+32C 10+M eρ ξu C 2−ξt −C 3+32C 8+12C 9+32C 10−(M a +M aρ)[ξu C 2−ξt C 3+2C 4−2C 6−12C 8−12C 9+12C 10+(M P e +2M Pa )ξt C 5−12C 7.(32)The decay amplitude for B +→ρ+π0can be written as √2M (B +→ρ+π0)=(F e +2F a ) ξu13C 1+C 2−ξt 13C 3+C 4+C 10+13C 9+F eρ ξu C 1+13C 2−ξt −13C 3−C 4−32C 7−12C 8+C 10+53C 9−F Peρξt −13C 5−C 6+12C 8+16C 7+M eρ ξu C 2−ξt −C 3+32C 8+12C 9+32C 10+(M e +M a −M aρ)[ξu C 1−ξt (C 3+C 9)]−M P e ξt [C 5+C 7]−2F Pa ξt 13C 5+C 6+13C 7+C 8 .(33)The decay amplitude for B +→π+ρ0can be written as√2M (B +→π+ρ0)=F e ξu C 1+13C 2−ξt −13C 3−C 4+32C 7+12C 8+53C 9+C 10+(F eρ−2F a ) ξu13C 1+C 2−ξt 13C 3+C 4+13C 9+C 10−(F P eρ−2F Pa )ξt 13C 5+C 6+13C 7+C 8+M e ξu C 2−ξt −C 3−32C 8+12C 9+32C 10+(M eρ−M a +M aρ)[ξu C 1−ξt (C 3+C 9)]+M Pe ξt C 5−12C 7.(34)282 C.-D.L¨u ,M.-Z.Yang:B →πρ,πωdecays in perturbative QCD approachFrom (30)–(34),we can verify that the isospin relation M (B 0→π+ρ−)+M (B 0→π−ρ+)−2M (B 0→π0ρ0)=√2M (B +→π0ρ+)+√2M (B +→π+ρ0)(35)holds exactly in our calculations.The decay amplitude for B +→π+ωcan also be writ-ten as an expression of the above F i and M i ,but one should remember replacing f ρby f ωand φρby φω√2M (B +→π+ω)=F e ξu C 1+13C 2 −ξt73C 3+53C 4+2C 5+23C 6+12C 7+16C 8+13C 9−13C 10+F eρ ξu 13C 1+C 2 −ξt 13C 3+C 4+13C 9+C 10−F Peρξt 13C 5+C 6+13C 7+C 8+M e ξu C 2−ξtC 3+2C 4−2C 6−12C 8−12C 9+12C 10+(M eρ+M a +M aρ)[ξu C 1−ξt (C 3+C 9)]−(M P a +M P aρ)ξt [C 5+C 7]−M Pe ξt C 5−12C 7.(36)The decay amplitude for B 0→π0ωcan be written as2M (B 0→π0ω)=F e ξu −C 1−13C 2−ξt−73C 3−53C 4−2C 5−23C 6−12C 7−16C 8−13C 9+13C 10+F eρ ξu C 1+13C 2−ξt −13C 3−C 4−32C 7−12C 8+53C 9+C 10+F Peρξt C 6+13C 5−16C 7−12C 8+M e −ξu C 2−ξt−C 3−2C 4+2C 6+12C 8+12C 9−12C 10+M eρ ξu C 2−ξt −C 3+32C 8+12C 9+32C 10+(M a +M aρ)ξu C 2−ξt −C 3−32C 8+12C 9+32C 10+(M P e +2M Pa )ξt C 5−12C 7.(37)4Numerical calculations and discussions of resultsIn the numerical calculations we useΛ(f =4)MS=0.25GeV ,f π=130MeV ,f B =190MeV ,m 0=1.4GeV ,f ρ=f ω=200MeV ,f T ρ=f T ω=160MeV ,M B =5.2792GeV ,M W =80.41GeV .(38)Note that for simplicity we use the same value for f ρ(f Tρ)and f ω(f Tω).This also makes it easy for us to see the major diﬀerence for the two mesons in B decays.In principle,the decay constants can be a little diﬀerent.For the light meson wave function,we neglect the b dependent part,which is not important in the numerical analysis.We use the wave function for φA πand the twist-3wave functions φP πand φtπfrom [16]:φA π(x )=3√6f πx (1−x )(39)× 1+0.44C 3/22(2x −1)+0.25C 3/24(2x −1),φP π(x )=f π2√6(40)×1+0.43C 1/22(2x −1)+0.09C 1/24(2x −1) ,φt π(x )=f π2√6(1−2x ) 1+0.55(10x 2−10x +1) .(41)The Gegenbauer polynomials are deﬁned byC 1/22(t )=12(3t 2−1),C 1/24(t )=18(35t 4−30t 2+3),C 3/22(t )=32(5t 2−1),C 3/24(t )=158(21t 4−14t 2+1),(42)whose coeﬃcients correspond to m 0=1.4GeV.In the B →πρ,πωdecays,it is the longitudinal polarization of the ρand ω-meson which contributes to the decay ampli-tude.Therefore we choose the wave function of the ρ-and ω-meson similar to the pion case in (39)and (41)[17]:φρ(x )=φω(x )=3√6f ρx (1−x ) 1+0.18C 3/22(2x −1) ,(43)φt ρ(x )=φtω(x )=f T ρ2√6 3(2x −1)2+0.3(2x −1)2× 5(2x −1)2−3+0.21[3−30(2x −1)2+35(2x −1)4],(44)φs ρ(x )=φsω(x )(45)=32√6f Tρ(1−2x ) 1+0.76(10x 2−10x +1) .。

Measurement of the Branching Fractions and CP Asymmetries of B--D0(cp)K- Decays with the Ba

a r X i v :h e p -e x /0408082v 1 17 A u g 2004B A B A R -CONF-04/039SLAC-PUB-10655Measurement of the Branching Fractions and CP Asymmetries of B −→D 0(CP )K −Decays with the B A B A R Detector The B A B A R Collaboration February 7,2008Abstract We present a study of B −→D 0(CP )K −decays,where D 0(CP )is reconstructed in ﬂavor (K −π+),CP -even (K −K +,π−π+)and CP -odd (K 0S π0)eigenstates,based on a sample of about 214million Υ(4S )→BB (B −→D 0K −)/B (B −→D 0π−)=0.87±0.14(stat)±0.06(syst),R −≡B (B −→D 0CP −K −)/B (B −→D 0CP −π−)B (B −→D 0CP +K −)+B (B +→D 0CP +K +)=0.40±0.15(stat)±0.08(syst)B(B−→D0CP−K−)−B(B+→D0CP−K+)A CP−≡Work supported in part by Department of Energy contract DE-AC03-76SF00515.The B A B A R Collaboration,B.Aubert,R.Barate,D.Boutigny,F.Couderc,J.-M.Gaillard,A.Hicheur,Y.Karyotakis,J.P.Lees,V.Tisserand,A.ZghicheLaboratoire de Physique des Particules,F-74941Annecy-le-Vieux,FranceA.Palano,A.PompiliUniversit`a di Bari,Dipartimento di Fisica and INFN,I-70126Bari,ItalyJ.C.Chen,N.D.Qi,G.Rong,P.Wang,Y.S.ZhuInstitute of High Energy Physics,Beijing100039,ChinaG.Eigen,I.Ofte,B.StuguUniversity of Bergen,Inst.of Physics,N-5007Bergen,NorwayG.S.Abrams,A.W.Borgland,A.B.Breon,D.N.Brown,J.Button-Shafer,R.N.Cahn,E.Charles, C.T.Day,M.S.Gill,A.V.Gritsan,Y.Groysman,R.G.Jacobsen,R.W.Kadel,J.Kadyk,L.T.Kerth,Yu.G.Kolomensky,G.Kukartsev,G.Lynch,L.M.Mir,P.J.Oddone,T.J.Orimoto,M.Pripstein,N.A.Roe,M.T.Ronan,V.G.Shelkov,W.A.WenzelLawrence Berkeley National Laboratory and University of California,Berkeley,CA94720,USAM.Barrett,K.E.Ford,T.J.Harrison,A.J.Hart,C.M.Hawkes,S.E.Morgan,A.T.Watson University of Birmingham,Birmingham,B152TT,United KingdomM.Fritsch,K.Goetzen,T.Held,H.Koch,B.Lewandowski,M.Pelizaeus,M.SteinkeRuhr Universit¨a t Bochum,Institut f¨u r Experimentalphysik1,D-44780Bochum,GermanyJ.T.Boyd,N.Chevalier,W.N.Cottingham,M.P.Kelly,tham,F.F.WilsonUniversity of Bristol,Bristol BS81TL,United KingdomT.Cuhadar-Donszelmann,C.Hearty,N.S.Knecht,T.S.Mattison,J.A.McKenna,D.Thiessen University of British Columbia,Vancouver,BC,Canada V6T1Z1A.Khan,P.Kyberd,L.TeodorescuBrunel University,Uxbridge,Middlesex UB83PH,United KingdomA.E.Blinov,V.E.Blinov,V.P.Druzhinin,V.B.Golubev,V.N.Ivanchenko,E.A.Kravchenko,A.P.Onuchin,S.I.Serednyakov,Yu.I.Skovpen,E.P.Solodov,A.N.YushkovBudker Institute of Nuclear Physics,Novosibirsk630090,RussiaD.Best,M.Bruinsma,M.Chao,I.Eschrich,D.Kirkby,nkford,M.Mandelkern,R.K.Mommsen,W.Roethel,D.P.StokerUniversity of California at Irvine,Irvine,CA92697,USAC.Buchanan,B.L.HartﬁelUniversity of California at Los Angeles,Los Angeles,CA90024,USAS.D.Foulkes,J.W.Gary,B.C.Shen,K.WangUniversity of California at Riverside,Riverside,CA92521,USAD.del Re,H.K.Hadavand,E.J.Hill,D.B.MacFarlane,H.P.Paar,Sh.Rahatlou,V.SharmaUniversity of California at San Diego,La Jolla,CA92093,USAJ.W.Berryhill,C.Campagnari,B.Dahmes,O.Long,A.Lu,M.A.Mazur,J.D.Richman,W.Verkerke University of California at Santa Barbara,Santa Barbara,CA93106,USAT.W.Beck,A.M.Eisner,C.A.Heusch,J.Kroseberg,W.S.Lockman,G.Nesom,T.Schalk,B.A.Schumm,A.Seiden,P.Spradlin,D.C.Williams,M.G.WilsonUniversity of California at Santa Cruz,Institute for Particle Physics,Santa Cruz,CA95064,USAJ.Albert,E.Chen,G.P.Dubois-Felsmann,A.Dvoretskii,D.G.Hitlin,I.Narsky,T.Piatenko,F.C.Porter,A.Ryd,A.Samuel,S.YangCalifornia Institute of Technology,Pasadena,CA91125,USAS.Jayatilleke,G.Mancinelli,B.T.Meadows,M.D.SokoloﬀUniversity of Cincinnati,Cincinnati,OH45221,USAT.Abe,F.Blanc,P.Bloom,S.Chen,W.T.Ford,U.Nauenberg,A.Olivas,P.Rankin,J.G.Smith,J.Zhang,L.ZhangUniversity of Colorado,Boulder,CO80309,USAA.Chen,J.L.Harton,A.Soﬀer,W.H.Toki,R.J.Wilson,Q.ZengColorado State University,Fort Collins,CO80523,USAD.Altenburg,T.Brandt,J.Brose,M.Dickopp,E.Feltresi,A.Hauke,cker,R.M¨u ller-Pfeﬀerkorn, R.Nogowski,S.Otto,A.Petzold,J.Schubert,K.R.Schubert,R.Schwierz,B.Spaan,J.E.Sundermann Technische Universit¨a t Dresden,Institut f¨u r Kern-und Teilchenphysik,D-01062Dresden,GermanyD.Bernard,G.R.Bonneaud,F.Brochard,P.Grenier,S.Schrenk,Ch.Thiebaux,G.Vasileiadis,M.VerderiEcole Polytechnique,LLR,F-91128Palaiseau,FranceD.J.Bard,P.J.Clark,vin,F.Muheim,S.Playfer,Y.XieUniversity of Edinburgh,Edinburgh EH93JZ,United KingdomM.Andreotti,V.Azzolini,D.Bettoni,C.Bozzi,R.Calabrese,G.Cibinetto,E.Luppi,M.Negrini,L.Piemontese,A.SartiUniversit`a di Ferrara,Dipartimento di Fisica and INFN,I-44100Ferrara,ItalyE.TreadwellFlorida A&M University,Tallahassee,FL32307,USAF.Anulli,R.Baldini-Ferroli,A.Calcaterra,R.de Sangro,G.Finocchiaro,P.Patteri,I.M.Peruzzi,M.Piccolo,A.ZalloLaboratori Nazionali di Frascati dell’INFN,I-00044Frascati,ItalyA.Buzzo,R.Capra,R.Contri,G.Crosetti,M.Lo Vetere,M.Macri,M.R.Monge,S.Passaggio,C.Patrignani,E.Robutti,A.Santroni,S.TosiUniversit`a di Genova,Dipartimento di Fisica and INFN,I-16146Genova,ItalyS.Bailey,G.Brandenburg,K.S.Chaisanguanthum,M.Morii,E.WonHarvard University,Cambridge,MA02138,USAR.S.Dubitzky,ngeneggerUniversit¨a t Heidelberg,Physikalisches Institut,Philosophenweg12,D-69120Heidelberg,Germany W.Bhimji,D.A.Bowerman,P.D.Dauncey,U.Egede,J.R.Gaillard,G.W.Morton,J.A.Nash,M.B.Nikolich,G.P.TaylorImperial College London,London,SW72AZ,United KingdomM.J.Charles,G.J.Grenier,U.MallikUniversity of Iowa,Iowa City,IA52242,USAJ.Cochran,H.B.Crawley,msa,W.T.Meyer,S.Prell,E.I.Rosenberg,A.E.Rubin,J.YiIowa State University,Ames,IA50011-3160,USAM.Biasini,R.Covarelli,M.PioppiUniversit`a di Perugia,Dipartimento di Fisica and INFN,I-06100Perugia,ItalyM.Davier,X.Giroux,G.Grosdidier,A.H¨o cker,place,F.Le Diberder,V.Lepeltier,A.M.Lutz, T.C.Petersen,S.Plaszczynski,M.H.Schune,L.Tantot,G.WormserLaboratoire de l’Acc´e l´e rateur Lin´e aire,F-91898Orsay,FranceC.H.Cheng,nge,M.C.Simani,D.M.WrightLawrence Livermore National Laboratory,Livermore,CA94550,USAA.J.Bevan,C.A.Chavez,J.P.Coleman,I.J.Forster,J.R.Fry,E.Gabathuler,R.Gamet,D.E.Hutchcroft,R.J.Parry,D.J.Payne,R.J.Sloane,C.TouramanisUniversity of Liverpool,Liverpool L6972E,United KingdomJ.J.Back,1C.M.Cormack,P.F.Harrison,1F.Di Lodovico,G.B.Mohanty1Queen Mary,University of London,E14NS,United KingdomC.L.Brown,G.Cowan,R.L.Flack,H.U.Flaecher,M.G.Green,P.S.Jackson,T.R.McMahon,S.Ricciardi,F.Salvatore,M.A.WinterUniversity of London,Royal Holloway and Bedford New College,Egham,Surrey TW200EX,United KingdomD.Brown,C.L.DavisUniversity of Louisville,Louisville,KY40292,USAJ.Allison,N.R.Barlow,R.J.Barlow,P.A.Hart,M.C.Hodgkinson,ﬀerty,A.J.Lyon,J.C.WilliamsUniversity of Manchester,Manchester M139PL,United KingdomA.Farbin,W.D.Hulsbergen,A.Jawahery,D.Kovalskyi,e,V.Lillard,D.A.RobertsUniversity of Maryland,College Park,MD20742,USAG.Blaylock,C.Dallapiccola,K.T.Flood,S.S.Hertzbach,R.Koﬂer,V.B.Koptchev,T.B.Moore,S.Saremi,H.Staengle,S.WillocqUniversity of Massachusetts,Amherst,MA01003,USAR.Cowan,G.Sciolla,S.J.Sekula,F.Taylor,R.K.Yamamoto Massachusetts Institute of Technology,Laboratory for Nuclear Science,Cambridge,MA02139,USAD.J.J.Mangeol,P.M.Patel,S.H.RobertsonMcGill University,Montr´e al,QC,Canada H3A2T8zzaro,V.Lombardo,F.PalomboUniversit`a di Milano,Dipartimento di Fisica and INFN,I-20133Milano,ItalyJ.M.Bauer,L.Cremaldi,V.Eschenburg,R.Godang,R.Kroeger,J.Reidy,D.A.Sanders,D.J.Summers,H.W.ZhaoUniversity of Mississippi,University,MS38677,USAS.Brunet,D.Cˆo t´e,P.TarasUniversit´e de Montr´e al,Laboratoire Ren´e J.A.L´e vesque,Montr´e al,QC,Canada H3C3J7H.NicholsonMount Holyoke College,South Hadley,MA01075,USAN.Cavallo,2F.Fabozzi,2C.Gatto,L.Lista,D.Monorchio,P.Paolucci,D.Piccolo,C.Sciacca Universit`a di Napoli Federico II,Dipartimento di Scienze Fisiche and INFN,I-80126,Napoli,ItalyM.Baak,H.Bulten,G.Raven,H.L.Snoek,L.WildenNIKHEF,National Institute for Nuclear Physics and High Energy Physics,NL-1009DB Amsterdam,The NetherlandsC.P.Jessop,J.M.LoSeccoUniversity of Notre Dame,Notre Dame,IN46556,USAT.Allmendinger,K.K.Gan,K.Honscheid,D.Hufnagel,H.Kagan,R.Kass,T.Pulliam,A.M.Rahimi,R.Ter-Antonyan,Q.K.WongOhio State University,Columbus,OH43210,USAJ.Brau,R.Frey,O.Igonkina,C.T.Potter,N.B.Sinev,D.Strom,E.TorrenceUniversity of Oregon,Eugene,OR97403,USAF.Colecchia,A.Dorigo,F.Galeazzi,M.Margoni,M.Morandin,M.Posocco,M.Rotondo,F.Simonetto,R.Stroili,G.Tiozzo,C.VociUniversit`a di Padova,Dipartimento di Fisica and INFN,I-35131Padova,ItalyM.Benayoun,H.Briand,J.Chauveau,P.David,Ch.de la Vaissi`e re,L.Del Buono,O.Hamon,M.J.J.John,Ph.Leruste,J.Malcles,J.Ocariz,M.Pivk,L.Roos,S.T’Jampens,G.Therin Universit´e s Paris VI et VII,Laboratoire de Physique Nucl´e aire et de Hautes Energies,F-75252Paris,FranceP.F.Manfredi,V.ReUniversit`a di Pavia,Dipartimento di Elettronica and INFN,I-27100Pavia,ItalyP.K.Behera,L.Gladney,Q.H.Guo,J.PanettaUniversity of Pennsylvania,Philadelphia,PA19104,USAC.Angelini,G.Batignani,S.Bettarini,M.Bondioli,F.Bucci,G.Calderini,M.Carpinelli,F.Forti, M.A.Giorgi,A.Lusiani,G.Marchiori,F.Martinez-Vidal,3M.Morganti,N.Neri,E.Paoloni,M.Rama,G.Rizzo,F.Sandrelli,J.WalshUniversit`a di Pisa,Dipartimento di Fisica,Scuola Normale Superiore and INFN,I-56127Pisa,ItalyM.Haire,D.Judd,K.Paick,D.E.WagonerPrairie View A&M University,Prairie View,TX77446,USAN.Danielson,P.Elmer,u,C.Lu,V.Miftakov,J.Olsen,A.J.S.Smith,A.V.TelnovPrinceton University,Princeton,NJ08544,USAF.Bellini,G.Cavoto,4R.Faccini,F.Ferrarotto,F.Ferroni,M.Gaspero,L.Li Gioi,M.A.Mazzoni,S.Morganti,M.Pierini,G.Piredda,F.Safai Tehrani,C.VoenaUniversit`a di Roma La Sapienza,Dipartimento di Fisica and INFN,I-00185Roma,ItalyS.Christ,G.Wagner,R.WaldiUniversit¨a t Rostock,D-18051Rostock,GermanyT.Adye,N.De Groot,B.Franek,N.I.Geddes,G.P.Gopal,E.O.Olaiya Rutherford Appleton Laboratory,Chilton,Didcot,Oxon,OX110QX,United KingdomR.Aleksan,S.Emery,A.Gaidot,S.F.Ganzhur,P.-F.Giraud,G.Hamel de Monchenault,W.Kozanecki, M.Legendre,G.W.London,B.Mayer,G.Schott,G.Vasseur,Ch.Y`e che,M.ZitoDSM/Dapnia,CEA/Saclay,F-91191Gif-sur-Yvette,FranceM.V.Purohit,A.W.Weidemann,J.R.Wilson,F.X.YumicevaUniversity of South Carolina,Columbia,SC29208,USAD.Aston,R.Bartoldus,N.Berger,A.M.Boyarski,O.L.Buchmueller,R.Claus,M.R.Convery,M.Cristinziani,G.De Nardo,D.Dong,J.Dorfan,D.Dujmic,W.Dunwoodie,E.E.Elsen,S.Fan, R.C.Field,T.Glanzman,S.J.Gowdy,T.Hadig,V.Halyo,C.Hast,T.Hryn’ova,W.R.Innes, M.H.Kelsey,P.Kim,M.L.Kocian,D.W.G.S.Leith,J.Libby,S.Luitz,V.Luth,H.L.Lynch,H.Marsiske,R.Messner,D.R.Muller,C.P.O’Grady,V.E.Ozcan,A.Perazzo,M.Perl,S.Petrak, B.N.Ratcliﬀ,A.Roodman,A.A.Salnikov,R.H.Schindler,J.Schwiening,G.Simi,A.Snyder,A.Soha,J.Stelzer,D.Su,M.K.Sullivan,J.Va’vra,S.R.Wagner,M.Weaver,A.J.R.Weinstein, W.J.Wisniewski,M.Wittgen,D.H.Wright,A.K.Yarritu,C.C.YoungStanford Linear Accelerator Center,Stanford,CA94309,USAP.R.Burchat,A.J.Edwards,T.I.Meyer,B.A.Petersen,C.RoatStanford University,Stanford,CA94305-4060,USAS.Ahmed,M.S.Alam,J.A.Ernst,M.A.Saeed,M.Saleem,F.R.WapplerState University of New York,Albany,NY12222,USAW.Bugg,M.Krishnamurthy,S.M.SpanierUniversity of Tennessee,Knoxville,TN37996,USAR.Eckmann,H.Kim,J.L.Ritchie,A.Satpathy,R.F.SchwittersUniversity of Texas at Austin,Austin,TX78712,USAJ.M.Izen,I.Kitayama,X.C.Lou,S.YeUniversity of Texas at Dallas,Richardson,TX75083,USAF.Bianchi,M.Bona,F.Gallo,D.GambaUniversit`a di Torino,Dipartimento di Fisica Sperimentale and INFN,I-10125Torino,ItalyL.Bosisio,C.Cartaro,F.Cossutti,G.Della Ricca,S.Dittongo,S.Grancagnolo,nceri,P.Poropat,5L.Vitale,G.VuagninUniversit`a di Trieste,Dipartimento di Fisica and INFN,I-34127Trieste,ItalyR.S.PanviniVanderbilt University,Nashville,TN37235,USASw.Banerjee,C.M.Brown,D.Fortin,P.D.Jackson,R.Kowalewski,J.M.Roney,R.J.SobieUniversity of Victoria,Victoria,BC,Canada V8W3P6H.R.Band,B.Cheng,S.Dasu,M.Datta,A.M.Eichenbaum,M.Graham,J.J.Hollar,J.R.Johnson,P.E.Kutter,H.Li,R.Liu,A.Mihalyi,A.K.Mohapatra,Y.Pan,R.Prepost,P.Tan,J.H.vonWimmersperg-Toeller,J.Wu,S.L.Wu,Z.YuUniversity of Wisconsin,Madison,WI53706,USAM.G.Greene,H.NealYale University,New Haven,CT06511,USA1INTRODUCTIONA theoretically clean measurement of the angleγ=arg(−V ud V∗ub/V cd V∗cb)can be obtained from the study of B−→D(∗)0K(∗)−decays by exploiting the interference between the b→c¯u s and b→u¯c s decay amplitudes[1].The method originally proposed by Gronau,Wyler and London is based on the interference between B−→D0K−and B−→D0decay to CP eigenstates.We deﬁne the ratios R and R CP±of Cabibbo-suppressed to Cabibbo-favored branching fractionsR(CP±)≡B(B−→D0(CP±)K−)+B(B+→B(B−→D0(CP±)π−)+B(B+→B(B−→D0CP±K−)+B(B+→D0CP±K+).(2)Neglecting the D0−D0π−)/A(B−→D0π−)of the amplitudes of the B−→D0K−)/A(B−→D0K−)|is the magnitude of the ratio of the amplitudes for the processes B−→B pairs collected with the B A B A R detector at the PEP-II asymmetric-energy B factory.The B A B A R detector is described in detail elsewhere[2].Charged-particle tracking is provided by aﬁve-layer silicon vertex tracker(SVT)and a40-layer drift chamber(DCH).For charged-particle identiﬁcation,ionization energy loss in the DCH and SVT,and Cherenkov radia-tion detected in a ring-imaging device(DIRC)are used.Photons are identiﬁed by the electromag-netic calorimeter(EMC),which comprises6580thallium-doped CsI crystals.These systems are mounted inside a1.5-T solenoidal superconducting magnet.The segmentedﬂux return,including endcaps,is instrumented with resistive plate chambers(IFR)for muon and K0Lidentiﬁcation.We use the GEANT[3]software to simulate interactions of particles traversing the detector,taking into account the varying accelerator and detector conditions.3ANALYSIS METHODWe reconstruct B−→D0h−decays,where the prompt track h−is a kaon or a pion.Reference to the charge-conjugate state is implied here and throughout the text unless otherwise stated.Candidates for D0are reconstructed in the CP-even eigenstatesπ−π+and K−K+,in the CP-odd eigenstate K0Sπ0,and in the non-CPﬂavor eigenstate K−π+.K0Scandidates are selected in theπ−π+channel.The prompt particle h−is required to have momentum greater than1.4GeV/c.Particle IDinformation from the drift chamber and,when available,from the DIRC must be consistent with the kaon hypothesis for the K meson candidate in all D0modes and with the pion hypothesis for theπ±meson candidates in the D0→π−π+mode.For the prompt track to be identiﬁed as a pion or a kaon,we require that at leastﬁve Cherenkov photons are detected to insure a good measurement of the Cherenkov angle.We reject a candidate track if its Cherenkov angle is not within3σof the expected value for either the kaon or pion mass hypothesis.We also reject candidate tracks that are identiﬁed as electrons by the DCH and the EMC or as muons by the DCH and the IFR.Photon candidates are clusters in the EMC that are not matched to any charged track,have a raw energy greater than30MeV and lateral shower shape consistent with the expected pattern of energy deposit from an electromagnetic shower.Photon pairs with invariant mass within the range 115–150MeV/c2(∼3σ)and total energy greater than200MeV are consideredπ0candidates. To improve the momentum resolution,theπ0candidates are kinematicallyﬁt with their mass constrained to the nominalπ0mass[4].Neutral kaons are reconstructed from pairs of oppositely charged tracks with the invariant mass within10MeV(∼3σ)from the nominal K0mass.We also require that the ratio between theﬂight length distance in the plane transverse to the beams direction and its uncertainty is greater than 3.The invariant mass of a D0candidate,m(D0),must be within3σof the D0mass.The D0mass resolutionσis about7.5MeV in the K−π+,K−K+andπ−π+modes,and about21MeV in the π0mode.Selected D0candidates areﬁtted with a constraint to the nominal D0mass.K0SWe reconstruct B meson candidates by combining a D0candidate with a track h−.For the K−π+mode,the charge of the track h−must match that of the kaon from the D0me-son decay.We select B meson candidates by using the beam-energy-substituted mass m ES=rejects more than90%of the continuum background while retaining77%of the signal in the K−π+, K−K+and K0π0modes and65%in theπ−π+channel.SMultiple B−→D0h−candidates are found in about4%of the events for the K0Sπ0and in less than1%of the events for the other D0decays.In these events aχ2is constructed from m(π0)(for K0Sπ0only),m(D0),and m ES and only the candidate with the smallestχ2is retained.The total reconstruction eﬃciencies,based on simulated signal events,are about33%(K−π+),28%(K−K+), 26%(π−π+)and17%(K0Sπ0).The main contributions to the BB events,in which the prompt track is either a pion or a kaon.The input variables to theﬁt are∆E and a particle identiﬁcation probability for the prompt track based on the Cherenkov angleθC,the momentum p and the polar angleθof the track.The extended likelihood function L is deﬁned asL=exp −M i=1n i N j=1 M i=1n i P i(∆E,θC; αi) ,(3)where N is the total number of observed events.The M functions P i(∆E,θC; αi)are the probability density functions(PDFs)for the variables∆E,θC,given the set of parameters αi.Since these two quantities are suﬃciently uncorrelated,their probability density functions are evaluated as a product P i=P i(∆E; αi)×P i(θC; αi).The∆E distribution for B−→D0K−signal events is parametrized with a Gaussian function. The∆E distribution for B−→D0π−is parametrized with the same Gaussian used for B−→D0K−with a relative shift of the mean,computed event by event as a function of the prompt track momentum,arising from the wrong mass assignment to the prompt track.The oﬀset and width of the Gaussian are keptﬂoating in theﬁt and are determined from data together with the yields.The∆E distribution for the continuum background is parametrized with a linear function whose slope is determined from oﬀ-resonance data.The∆E distribution for the B4PHYSICS RESULTS AND SYSTEMATIC STUDIESThe results of theﬁt are summarized in Table1.Figure1shows the distributions of∆E for the K−π+,CP+and CP−modes after enhancing the B→D0K purity by requiring that the prompt track be consistent with the kaon hypothesis.This requirement is about95%eﬃcient for the B−→D0K−signal while retaining only4%of the B−→D0π−candidates.The projection of a likelihoodﬁt,modiﬁed to take into account the tighter selection criteria,is overlaid in theﬁgure. Table1:Results of the B−→D0K−and B−→D0π−yields from the maximum-likelihoodﬁt on data.D0mode N(B→D0π)N(B→D0K)N(B−→D0K−)N(B+→K−π+11930±120897±34441±24456±25K0Sπ01248±4076+13−1246+10−930+9−8The double ratios R±are computed by scaling the ratios of the numbers of B−→D0K−and B−→D0π−mesons by correction factors(ranging from0.997to1.020depending on the D0mode) that account for small diﬀerences in the eﬃciency between the B−→D0K−and B−→D0π−selec-tions,estimated with simulated signal samples.The results are listed in Table2.The direct CP asymmetries A CP±for the B±→D0CP±K±decays are calculated from the measured yields of positive and negative charged meson decays and the results are reported in Table2.Table2:Measured double branching fraction ratios R±and CP asymmetries A CP±for diﬀerent D0decay modes.Theﬁrst error is statistical,the second is systematic.D0decay mode R CP/R A CPK−K+0.92±0.16±0.070.43±0.16±0.09π−π+0.70±0.29±0.090.27±0.40±0.09CP-even combined0.87±0.14±0.060.40±0.15±0.08The uncertainties in the branching fractions of the channels contributing to the B[6]Belle Collaboration,K.Abe et al.,Phys.Rev.D6*******(2002);B A B A R Collaboration,B.Aubert et al.,hep-ex/0308065,submitted to Phys.Rev.Lett..[7]B A B A R Collaboration,B.Aubert et al.,Phys.Rev.Lett.92202002(2004).Figure1:∆E distributions of B−→D0h−candidates,where a charged kaon mass hypothesis is assumed for h.Events are enhanced in B−→D0K−purity by requiring the Cherenkov angle of the track h to be within2σof the kaon hypothesis.Top:B−→D0[K−π+]K−;middle:B−→π0]K−.Solid curves represent projections of D0CP+[K−K+,π−π+]K−;bottom:B−→D0CP−[K0Sthe maximum likelihoodﬁt;dashed-dotted,dotted and dashed curves represent the B→D0K,B→D0πand background contributions.。

Measurement of the Branching Fractions of $Lambda_{c}^{+}to pbar{K}n(pi)$

$Measurement of the Branching Fractions of $Lambda_{c}^{+}to pbar{K}n(pi)$$

a rXiv:h ep-e x /97912v11Sep1997CLNS 97/1502CLEO 97-18Measurement of the Branching Fractions of Λ+c →p K 0,p K 0π0,all measured relative to pK −π+.The relative branching fractions are 0.67±0.04±0.11,0.46±0.02±0.04,0.52±0.04±0.05,and 0.66±0.05±0.07respectively.M.S.Alam,1S.B.Athar,1Z.Ling,1A.H.Mahmood,1H.Severini,1S.Timm,1F.Wappler,1A.Anastassov,2J.E.Duboscq,2D.Fujino,2,∗K.K.Gan,2T.Hart,2 K.Honscheid,2H.Kagan,2R.Kass,2J.Lee,2M.B.Spencer,2M.Sung,2A.Undrus,2,†R.Wanke,2A.Wolf,2M.M.Zoeller,2B.Nemati,3S.J.Richichi,3W.R.Ross,3P.Skubic,3 M.Bishai,4J.Fast,4J.W.Hinson,4N.Menon,ler,4E.I.Shibata,4I.P.J.Shipsey,4M.Yurko,4L.Gibbons,5S.Glenn,5S.D.Johnson,5Y.Kwon,5,‡S.Roberts,5E.H.Thorndike,5C.P.Jessop,6K.Lingel,6H.Marsiske,6M.L.Perl,6 D.Ugolini,6R.Wang,6X.Zhou,6T.E.Coan,7V.Fadeyev,7I.Korolkov,7Y.Maravin,7 I.Narsky,7V.Shelkov,7J.Staeck,7R.Stroynowski,7I.Volobouev,7J.Ye,7M.Artuso,8 A.Eﬁmov,8M.Goldberg,8D.He,8S.Kopp,8G.C.Moneti,8R.Mountain,8S.Schuh,8 T.Skwarnicki,8S.Stone,8G.Viehhauser,8X.Xing,8J.Bartelt,9S.E.Csorna,9V.Jain,9,§K.W.McLean,9S.Marka,9R.Godang,10K.Kinoshita,i,10P.Pomianowski,10 S.Schrenk,10G.Bonvicini,11D.Cinabro,11R.Greene,11L.P.Perera,11G.J.Zhou,11B.Barish,12M.Chadha,12S.Chan,12G.Eigen,ler,12C.O’Grady,12M.Schmidtler,12J.Urheim,12A.J.Weinstein,12F.W¨u rthwein,12D.W.Bliss,13G.Masek,13H.P.Paar,13S.Prell,13V.Sharma,13D.M.Asner,14J.Gronberg,14T.S.Hill,nge,14S.Menary,14R.J.Morrison,14H.N.Nelson,14T.K.Nelson,14C.Qiao,14J.D.Richman,14D.Roberts,14A.Ryd,14M.S.Witherell,14R.Balest,15B.H.Behrens,15W.T.Ford,15H.Park,15J.Roy,15J.G.Smith,15J.P.Alexander,16C.Bebek,16B.E.Berger,16K.Berkelman,16K.Bloom,16D.G.Cassel,16H.A.Cho,16D.S.Crowcroft,16M.Dickson,16P.S.Drell,16K.M.Ecklund,16R.Ehrlich,16A.D.Foland,16P.Gaidarev,16B.Gittelman,16S.W.Gray,16D.L.Hartill,16B.K.Heltsley,16P.I.Hopman,16J.Kandaswamy,16P.C.Kim,16D.L.Kreinick,16 T.Lee,16Y.Liu,16G.S.Ludwig,16N.B.Mistry,16C.R.Ng,16E.Nordberg,16M.Ogg,16,∗∗J.R.Patterson,16D.Peterson,16D.Riley,16A.Soﬀer,16B.Valant-Spaight,16C.Ward,16 M.Athanas,17P.Avery,17C.D.Jones,17M.Lohner,17C.Prescott,17J.Yelton,17J.Zheng,17G.Brandenburg,18R.A.Briere,18A.Ershov,18Y.S.Gao,18D.Y.-J.Kim,18 R.Wilson,18H.Yamamoto,18T.E.Browder,19F.Li,19Y.Li,19J.L.Rodriguez,19T.Bergfeld,20B.I.Eisenstein,20J.Ernst,20G.E.Gladding,20G.D.Gollin,20 R.M.Hans,20E.Johnson,20I.Karliner,20M.A.Marsh,20M.Palmer,20M.Selen,20 J.J.Thaler,20K.W.Edwards,21A.Bellerive,22R.Janicek,22D.B.MacFarlane,22P.M.Patel,22A.J.Sadoﬀ,23R.Ammar,24P.Baringer,24A.Bean,24D.Besson,24D.Coppage,24C.Darling,24R.Davis,24N.Hancock,24S.Kotov,24I.Kravchenko,24N.Kwak,24S.Anderson,25Y.Kubota,25S.J.Lee,25J.J.O’Neill,25S.Patton,25R.Poling,25T.Riehle,25V.Savinov,25and A.Smith251State University of New York at Albany,Albany,New York122222Ohio State University,Columbus,Ohio432103University of Oklahoma,Norman,Oklahoma730194Purdue University,West Lafayette,Indiana479075University of Rochester,Rochester,New York146276Stanford Linear Accelerator Center,Stanford University,Stanford,California94309 7Southern Methodist University,Dallas,Texas752758Syracuse University,Syracuse,New York132449Vanderbilt University,Nashville,Tennessee3723510Virginia Polytechnic Institute and State University,Blacksburg,Virginia24061 11Wayne State University,Detroit,Michigan4820212California Institute of Technology,Pasadena,California9112513University of California,San Diego,La Jolla,California9209314University of California,Santa Barbara,California9310615University of Colorado,Boulder,Colorado80309-039016Cornell University,Ithaca,New York1485317University of Florida,Gainesville,Florida3261118Harvard University,Cambridge,Massachusetts0213819University of Hawaii at Manoa,Honolulu,Hawaii9682220University of Illinois,Champaign-Urbana,Illinois6180121Carleton University,Ottawa,Ontario,Canada K1S5B6and the Institute of Particle Physics,Canada22McGill University,Montr´e al,Qu´e bec,Canada H3A2T8and the Institute of Particle Physics,Canada23Ithaca College,Ithaca,New York1485024University of Kansas,Lawrence,Kansas6604525University of Minnesota,Minneapolis,Minnesota55455Since theﬁrst observation of the lowest lying charmed baryon,theΛ+c,there have been many measurements made of its exclusive decay channels.As it is diﬃcult to measure the production cross-section of theΛ+c baryons,decay rates are typically presented as branching ratios relative toΛ+c→pK−π+,the most easily observed decay channel.However,fewer than half of theΛ+c hadronic decays are presently accounted for.Measurement of these modes is of practical as well as theoretical interest.Here,we present measurements of the branching fractions ofΛ+c into pK−π+π0,p K0π+π−,and pE2beam−m2Λc is the scaled momentum of theΛ+c candidate.Approximately 60%ofΛ+c baryons from cK0candidates were identiﬁed in their decay K0s→π+π−,by reconstructing a secondary vertex from the intersection of two oppositely charged tracks in the r−φplane. The invariant mass of theMode MC Width(MeV)SignalK0191025±40 pK0π027774±52 TABLE I.The number ofΛ+c’s found with x p(Λc)>0.5D∗+→K−π+π+decays that were identiﬁed topologically.The reconstruction eﬃciency of theΛ+c decays has some dependence on the resonant substructure of these states.In the case of the pK−π+mode,the Monte-Carlo generator produced a mixture of non-resonant three-body decay together with∆++K−and pK0→K0s and K0s→π=π−branching fractions.We have considered many possible sources of systematic error in the measurement.The main contributors to the systematic uncertainty came from the following sources:1)Un-certainties in theﬁtting procedures,which were estimated by looking at the changes in the yields using diﬀerent orders of polynomial background and diﬀerent signal widths(15%in the case of pK−π+π0,but much smaller for the other modes),2)uncertainties due to the unknown mix of resonant substructure in the multi-body decays(up to3%depending on the mode),3)uncertainties due toπ0ﬁnding(5%),K0sﬁnding(5%)and trackﬁnding(1%), and4)uncertainties in the reconstruction eﬃciency due to the particle identiﬁcation criteria for protons and kaons(4%).These uncertainties have been added in quadrature to obtain the total systematic uncertainty for each mode,taking into account the fact that many of these tend to cancel in a measurement of ratios of branching fractions.There are three main types of quark decay diagrams that contribute toΛ+c decays.The simplest method is the simple spectator diagram in which the virtual W+fragments inde-pendently of the spectator quark.The second method involves the quark daughters of the W+combining with the remaining quarks.The third method,W-exchange,involves the W+ combining with the initial d quark.Unfortunately all the decay modes under investigation here can proceed by more than one of these decay diagrams,and their decay rates are not amenable to calculation.In conclusion,we have measured new branching fractions of theΛ+c into4decay modes, measured relative to the normalizing modeΛ+c→pK−π+.The results for three of these modes are in agreement with,and more accurate than,previous measurements.We have made theﬁrst measurement of the decay rate ofΛ+c→pMode Relative Eﬃciency B/B(pK−π+)Previous MeasurementsK00.2180.46±0.02±0.040.44±0.07±0.05[4]0.55±0.17±0.14[6]0.62±0.15±0.03[7]pK0π00.1150.66±0.05±0.07TABLE II.The measured relative branching fractionsREFERENCES[1]Y.Kubota et al.,Nucl.Inst.and Methods A320,66(1992).[2]R.Brun et al.,CERN/DD/EE/84-11.[3]Review of Particle Properties,R.Barnett et al.,Phys.Rev.D541(1996).[4]P.Avery et al.,Phys.Rev.D43,3499(1991)[5]S.Barlag et al.,Z.Phys.C48,29(1990).[6]J.Anjos et al.,Phys.Rev.D41,801(1990).[7]H.Albrecht et al.,Phys.Lett.B207,109(1988).IVeM5/stnevEIMass (GeV)FIG.1.Invariant mass plots for the5diﬀerent decay modes of theΛ+c。

Charmless Three-body Decays of B Mesons

Abstract
An exploratory study of charmless 3-body decays of B mesons is presented using a simple model based on the framework of the factorization approach. The nonresonant contributions arising from B → P1 P2 transitions are evaluated using heavy meson chiral perturbation theory (HMChPT). The momentum dependence of nonresonant amplitudes is assumed to be in the exponential form e−αNR pB ·(pi +pj ) so that the HMChPT results are recovered in the soft meson limit pi , pj → 0. In addition, we have identiﬁed another large source of the nonresonant signal in the matrix elements 0 of scalar densities, e.g. KK |s ¯s|0 , which can be constrained from the decay B → KS KS KS or B − → K − KS KS . The intermediate vector meson contributions to 3-body decays are identiﬁed through the vector current, while the scalar meson resonances are mainly associated with the scalar density. Their eﬀects are described in terms of the Breit-Wigner formalism. Our main results are: (i) All KKK modes are dominated by the nonresonant background. The predicted branching ratios of K + K − KS (L) , K + K − K − and K − KS KS modes are consistent with the data within errors. (ii) Although the penguin-dominated B 0 → K + K − KS decay is subject to a potentially signiﬁcant tree pollution, its eﬀective sin 2β is very similar to that of the KS KS KS mode. However, direct CP asymmetry of the former, being of order −4%, is more prominent than the latter. (iii) For 0 B → Kππ decays, we found sizable nonresonant contributions in K − π + π − and K π + π − modes, in agreement with the Belle measurements but larger than the BaBar result. (iv) Time-dependent CP asymmetries in KS π 0 π 0 , a purely CP -even state, and KS π + π − , an admixture of CP -even and CP -odd components, are studied. (v) The π + π − π 0 mode is found to have a rate larger than π + π − π − even though the former involves a π 0 in the ﬁnal state. They are both dominated by resonant ρ contributions. (vi) We have computed the resonant contributions to 3-body decays and determined the rates for the quasi-two-body decays B → V P and B → SP . The predicted ρπ, f0 (980)K and f0 (980)π rates are in agreement with the data, while the calculated φK, K ∗ π, ρK ∗ (1430)π are in general too small compared to experiment. (vii) Sizable direct CP asymmetry and K0 is found in K + K − K − and K + K − π − modes.

Vub from Exclusive Semileptonic B to pi Decays

a School
arXiv:hep-ph/0703284v2 17 May 2007
Abstract
We use Omn` es representations of the form factors f+ and f0 for exclusive semileptonic B → π decays, paying special attention to the treatment of the B∗ pole and its effect on f+ . We apply them to combine experimental partial branching fraction information with theoretical calculations of both form factors to extract |Vub |. The precision we achieve is competitive with the inclusive determination and we do not ﬁnd a signiﬁcant discrepancy between our result, |Vub | = (3.90 ± 0.32 ± 0.18) × 10−3 , and the inclusive world average value, (4.45 ± 0.20 ± 0.26) × 10−3 [1].
SHEP–0710
|Vub| from Exclusive Semileptonic B → π Decays
Jonathan M Flynna and Juan Nievesb
of Physics and Astronomy, University of Southampton Highﬁeld, Southampton SO17 1BJ, UK b Departay Nuclear, Universidad de Granada, E–18071 Granada, Spain

Measurement of branching fractions for the inclusive Cabibbo-favored ~K0(892) and Cabibbo-s

$Measurement of branching fractions for the inclusive Cabibbo-favored ~K0(892) and Cabibbo-s$

M. G. Zhao10, P. P. Zhao1, W. R. Zhao1, X. J. Zhao1, Y. B. Zhao1, H. Q. Zheng11, J. P. Zheng1,
L. S. Zheng1, Z. P. Zheng1, X. C. Zhong1, B. Q. Zhou1, G. M. Zhou1, L. Zhou1, N. F. Zhou1, K. J. Zhu1,
R. Y. Li1, S. M. Li1, W. D. Li1, W. G. Li1, X. L. Li8, X. Q. Li10, Y. L. Li4, Y. F. Liang14, H. B. Liao6, C. X. Liu1,
F. Liu6, Fang Liu16, H. H. Liu1, H. M. Liu1, J. Liu11, J. B. Liu1, J. P. Liu17, R. G. Liu1, Z. A. Liu1, Z. X. Liu1,
X. Tang1, N. Tao16, Y. R. Tian15, G. L. Tong1, D. Y. Wang1, J. Z. Wang1, K. Wang16, L. Wang1, L. S. Wang1,
M. Wang1, P. Wang1, P. L. Wang1, S. Z. Wang1, W. F. Wang1d, Y. F. Wang1, Z. Wanenan Normal University, Xinxiang 453002, P.R. China
6 Huazhong Normal University, Wuhan 430079, P.R. China
7 Hunan University, Changsha 410082, P.R. China

B Decays at BABAR

a r X i v :h e p -e x /0308069v 1 28 A u g 20031Presented at QCD 02:High Energy Physics International Conference in Quantum Chromodynamics,Montpellier,France,2-9Jul 2002.Nucl.Phys.B (Proc.Suppl.)121(2003)239-248SLAC-PUB-10138B Decays at B A B A RJ.J.Back a ∗aPhysics Department,Queen Mary,University of London,Mile End Road,London,E14NS,UK (on behalf of the B A B A R Collaboration)We present branching fraction and CP asymmetry results for a variety of B decays based on up to 56.4fb −1collected by the B A B A R experiment running near the Υ(4S )resonance at the PEP-II e +e −B -factory.1.The B A B A R DetectorThe results presented in this paper are based on an integrated luminosity of up to 56.4fb −1collected at the Υ(4S )resonance with the B A B A R detector [1]at the PEP-II asymmetric e +e −col-lider at the Stanford Linear Accelerator Center.Charged particle track parameters are measured by a ﬁve-layer double-sided silicon vertex tracker and a 40-layer drift chamber located in a 1.5-T magnetic ﬁeld.Charged particle identiﬁcation is achieved with an internally reﬂecting ring imag-ing Cherenkov detector (DIRC)and from the av-erage d E/d x energy loss measured in the track-ing devices.Photons and π0s are detected with an electromagnetic calorimeter (EMC)consisting of 6580CsI(Tl)crystals.An instrumented ﬂux return (IFR),containing multiple layers of re-sistive plate chambers,provides muon and long-lived hadron identiﬁcation.2.B Decay ReconstructionThe B meson candidates are identiﬁed kine-matically using two independent variables.Theﬁrst is ∆E =E ∗−E ∗beam ,which is peaked at zero for signal events,since the energy of the B candi-(E ∗2beam −p ∗2B ),where p ∗Bis the momentum of the B meson in the Υ(4S )rest frame,and must be close to the nominal B mass [5].The resolution of m ES is dominated by the beam energy spread and is approximately 2.5MeV /c 2.Several of the B modes presented here havedecays that involve neutral pions (π0)and K 0S particles.Neutral pion candidates are formed by combining pairs of photons in the EMC,with re-quirements made to the energies of the photons and the mass and energy of the π0.Table 1shows these requirements for various decay modes,aswell as the selection requirements for K 0S candi-dates,which are made by combining oppositely charged pions.Signiﬁcant backgrounds from light quark-antiquark continuum events are suppressed using various event shape variables which exploit the diﬀerence in the event topologies in the centre-of-mass frame between background events,which have a di-jet structure,and signal events,which tend to be rather spherical.One example is thecosine of the angle θ∗T between the thrust axis of the signal B candidate and the thrust axis of the2Table1Selection requirements forπ0and K0Scandidates for various B decay modes(h=K/π).Eγis the minimum photon energy and mπ0and Eπ0the mass and energy,respectively,ofπ0candidates.Themass of the K0S is m K0S,the opening angle between the K0Smomentum and its line-of-ﬂight isφK0S,thetransverseﬂight distance of the K0S from the primary event vertex is d K0Sandτ/σK0Sis the K0Slifetimedivided by its error.B→DK>70[124,144]>200————B→D(∗)D(∗)>30[115,155]>200[473,523]<200>2—B→hπ0>30[111,159]—————B→hK0———[487,509]——>5 B→φK(∗)———[487,510]<100—>3 B→ηh>50[120,150]—————B→ηK0>50[115,155]—[491,507]<40>2—B→η′K(∗)0———[488,508]———B→K∗γ>30[115,150]>200[489,507]———B→K(∗)ℓ+ℓ−———[480,498]—>1—33.B→DKThe decays B−→D0K−and B±→D0±K±,where D0±denotes the CP-even(+)or CP-oddstates(−)(D0±¯D0)/√B(B−→D0π−)=(8.31±0.35±0.13)%,(2)where theﬁrst error is statistical and the sec-ond error is systematic.This quantity has alsobeen measured by the CLEO and BELLE Col-laborations,where they get R=(5.5±1.4±0.5)%[7]and R=(7.9±0.9±0.6)%[8],re-spectively.Theory predicts,using factorisationand tree-level Feynman diagrams only,a valueR≈tan2θC(f K/fπ)2≈7.4%,whereθC is theCabibbo angle,and f K and fπare the mesondecay constants.For the CP-even mode D0+→K+K−we have measuredB(B−→D0+K−)+B(B+→D0+K+)R CP=B(B−→D0+K−)+B(B+→D0+K+)=0.15±0.24+0.07.(4)44.B→D(∗)D(∗)Time-dependent CP violating asymmetries in the decays B→D(∗)D(∗)can be used to measurethe CKM angleβ[9],in a way complimentary to measurements already made with decays such asB0→J/ψK0S[10].However,the vector-vector decay of B0→D∗+D∗−is not a pure CP eigen-state,which may cause a sizeable dilution to theCP violation that can be observed.In principle,a full time-dependent angular analysis can remove this dilution[11].We reconstruct exclusively the decays B0→D∗+D∗−and B0→D∗±D∓,where D∗±→D0π±or D±π0.Theﬁnal states we consider for the neutral D mesons are K−π+,K−π+π0, K−π+π−π+and K0Sπ+π−,while we consider theD+ﬁnal states K−π+π+,K0Sπ+and K−K+π+. B0candidates are reconstructed by performing a mass-constrainedﬁt to the D and D∗candi-dates.In the case when more than one B candi-date is found for an event,we chose the B candi-date in which the D and D∗mesons have invari-ant masses closest to their nominal values[5]. Signal events are required to satisfy|∆E|< 25MeV and5.273<m ES<5.285GeV/c2. Using a sample of22.7million BΓdΓ4(1−R t)sin2θtr+3B(B+→π+π0),(9)where B(B0→π0π0) CP=15m ES (GeV/c 2)E v e n t s /2 M e V /c2B A B AR5105.2 5.225 5.25 5.2755.3Figure 3.Distribution of m ES for B +→π+π0events in on-resonance data.The solid curve rep-resents the projection of the maximum likelihood ﬁt result,while the dotted curve represents the background contribution.Table 2Two-body charmless B decay branching frac-tions (B )and CP asymmetries (A CP )based on 56.4fb −1.Upper limits are given at the 90%conﬁdence level.π+π04.1+1.1+0.8−1.0−0.7−0.02+0.27−0.26±0.10K +π011.1+1.3−1.2±1.00.00±0.11±0.02π+K 017.5+1.8−1.7±1.8−0.17±0.10±0.02K +6.Three-body Charmless Charged B Decays The decays B +→h +h −h +,where h =πor K ,can be used to measure the angle γ[18].The ba-sic idea is that there can be interference between resonant and non-resonant amplitudes leading to direct CP violation.A Dalitz plot analysis can,in principle,give us information about all of the strong and weak phases in these decays.A ﬁrst step towards this goal is to measure the branch-ing fractions into the whole Dalitz plot.We can write these asB =1Bi S iBis the total number of B6Figure4.Unbinned Dalitz plots(with no back-ground subtraction or eﬃciency corrections)for B+→K+π−π+events in on-resonance sideband (top left)and signal(top right)data,and forB+→K+K−K+events in on-resonance side-band(bottom left)and signal(bottom right) data.Open charm contributions are not removed.measure(180±4±11)×10−6for the branch-ing fraction for the B−→D0π−control sample, which agrees with the previously measured value of(203±20)×10−6[5].7.B→φK(∗),φπThese modes are interesting because only pen-guin diagrams contribute to the decay amplitudes (mainly b→s¯s s),and the time-dependent CP asymmetry for the neutral mode B0→φK0S can be used to measure sin2β.Comparison with sin2βresults from charmonium modes will allow Table3Three-body charmless charged B decay branching fractions(×10−6)from B A B A R(51.5fb−1)and BELLE(29.1fb−1).π+π−π+8.5±4.0±3.6(<15)—K+π−π+59.2±4.7±4.955.6±5.8±7.7 K+K−π+2.1±2.9±2.0(<7)<21K+K−K+34.7±2.0±1.835.3±3.7±4.57 Table4Branching fractions(×10−6)for B→φK and B+→φπ+decays from B A B A R(56.3fb−1and20.7fb−1†), BELLE(21.6fb−1)and CLEO(9.1fb−1).φK+9.2±1.0±0.811.2+2.2−2.0±1.45.5+2.1−1.8±0.6φK08.7+1.7−1.5±0.98.9+3.4−2.7±1.0<12.3φK∗+9.7+4.2−3.4±1.7†<36<22.5φK∗08.7+2.5−3.7−1.7−2.1±1.1†13.0+6.4−5.2±2.111.5+4.5+1.8φπ+<0.6—<5Mode B(×10−5)A C PB0→K∗0γ4.23±0.40±0.22−0.05±0.09±0.01B+→K∗+γ3.83±0.62±0.22−0.04±0.13±0.01B(¯B→¯K∗γ)+B(B→K∗γ).(11)Theoretical expectations for the branching frac-tions are in agreement with the measured values.8Table 5Measured branching fractions (×10−6)for B decays with ηand η′mesons from the CLEO,BELLE and B A B A R collaborations.ηπ+1.2+2.8−1.2(<5.7)5.4+2.0−1.7±0.62.2+1.8−1.6±0.1(<5.2)†ηK +2.2+2.8−2.2(<6.9)5.3+1.8−1.5±0.63.8+1.8−1.5±0.2(<6.4)†ηK 00.0+3.2−0.0(<9.3)6.0+3.8−2.9±0.4(<12)†ηK ∗013.8+5.5−4.6±1.616.5+4.6−4.2±1.219.8+6.5−5.6±1.5†ηK ∗+26.4+9.6−8.2±3.326.5+7.8−7.0±3.022.1+11.1−9.2±3.2†η′K +80+10−9±778±6±967±5±5η′K 089+18−16±968±1046±6±4η′K ∗07.8+7.7−5.7(<24)4.0+3.5−2.4±1.0(<13)9) 2c (GeV/ES m)2c (GeV/ES m 2c E n t r i e s /3 M e V /Figure 6.Projections from the likelihood ﬁts of the K (∗)ℓ+ℓ−modes onto m ES for the signal re-gion −0.11<∆E <0.05GeV for electrons and −0.07<∆E <0.05GeV for muons.The dotted lines show the level of background,while the solid lines show the sum of the signal and background contributions.11.ConclusionsWe have shown a selection of results from the B A B A R experiment based on up to 56.4fb −1col-lected at the Υ(4S )resonance.We have made the following observations:•B →DK .We have measured the ratio of the branching fractions for B −→D 0K −and B −→D 0π−,as well as the CP asym-metry for the CP -even mode B −→D 0+K −,which is the ﬁrst step towards measuring γ.•B →D (∗)D (∗)decays,which can be used to measure β,have been fully reconstructed.We have a ﬁrst measurement of the CP -oddcontent of these decays.•We observe B +→π+π0for the ﬁrst time,which,with other two body charmless modes,can be used to extract the angle α.•Three-body charmless B decays.Signiﬁ-cant signals have been observed for B +→K +π−π+and B +→K +K −K +.A Dalitz plot analysis of these decays could give us information about the angle γ.•We have made observations of the decays B +→φK +and B 0→φK 0,and we also conﬁrm the rather large branching fractions of ηK ∗and η′K ﬁrst seen by CLEO,which presents a theoretical challenge.•Radiative penguin modes.We observe a sig-nal for B 0→Kℓ+ℓ−for the ﬁrst time.Many of the results are approaching the level of predictions from the Standard Model.We ob-serve no direct CP violation in several decays,which could indicate that (the diﬀerences be-tween)strong phases are small.We can expect many more fruitful searches and improvements to existing measurements in the near future.REFERENCES1.B A B A R Collaboration,B.Aubert et al.,“TheB A B A R Detector”,Nucl.Instr.and Meth.A 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核临界和辐射防护术语中英文对照

[Particle] fluence rate Energy fluence rate Particle radiance Energy radiance Energy imparted Linear energy Specific energy[imparted] Absorbed dose Absorbed dose rate kerma Kerma rate Exposure Exposure rate Decay constant Radioactive half-life Biological half-life Effective half-life Activity Surface activity Activity concentration Specific activity Air kerma rate constant Dose equicalent Dose equivalent Dose equivalent rate Adsorbed dose index Quality factor Dose equivalent indx Surface dose equivalent index Depth dose equivalent index Cross section Lethargy Attenuation coefficient Mass attenuation coefficient Mass energy transfer coefficient adsorption coefficient Mass energy adsorption coefficient Total mass stopping coefficient Linear energy transfer, LET
核临界术语临界的，临界中子反照率吸收剂量中子吸收临界事故报警系统 α 粒子 β 粒子曲率瞬发脉冲核闪变周期（T）指数柱体照射量几何良好易裂变核素易裂变系统核裂变裂变产物核闪变的裂变产额可裂变核素 γ 辐射戈瑞危险倒时数致电离辐射 “辐照” 辐射反应性非补偿反应性反射层反射层节省相对生物效应雷姆雷普危险度伦琴紧急停堆停堆机制 Critical,Criticality Albedo,neutron Absorbed dose Absorption,neutron Alarm system,criticality accident Alpha particle Beta particle buckling Burst,prompt Excursion period Exponential column exposure Favorable geometry Fissile nucleus Fissile system Fission,nuclear Fission products Fissionyield,excursion Fissionable nucleus Gamma radiation Gray (Gy) hazard inhour Ionizing radiation irradiation radiation reactivity Reactivity,uncompensated reflector Reflector savings (RBE) rem rep risk roentgen scram Shutdown mechanism

Hadronic B decays at BABAR

Invited talk presented at the XXXVIIth Rencontres de Moriond on QCD and Hadronic Interactions,
3/16/2002—3/23/2002, Les Arcs, France
Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 Work supported in part by Department of Energy contract DE-AC03-76SF00515.
The decay B → J/ψ φ, which has not yet been observed, is explained with the occurrence of cc¯dd¯ rescattering into a cc¯ss¯ state.
The above decay modes have been studied at BABAR. The η is reconstructed in γγ or π+π−π0 ﬁnal states and the η′ in the η(→ γγ)π+π− channel. The φ is reconstructed in the K+K− ﬁnal state. Table 1 shows the preliminary results 1 obtained from the analysis of 50.9 fb−1 of data recorded at the Υ (4S) resonance [6].
were performed by the CLEO Collaboration [9]. At BABAR, the decay B → ηcK is exclusively reconstructed, with the ηc decaying in KSK±π±,

$b to c$ Hadronic Decays

a r X i v :h e p -e x /9801028v 2 3 F eb 1998b →c HADRONIC DECAYSJORGE L.RODRIGUEZDepartment of Physics and Astronomy,University of Hawaii,2505Correa Road,Honolulu,Hawaii 96822,USAUniversity of Hawaii preprint UH 511-892-98A review of current experimental results on exclusive hadronic decays of bottom mesons to a single or double charmed ﬁnal state is presented.We concentrate on branching fraction measurements conducted at e +e −colliders at the Υ(4S )and at the Z 0resonance.The experimental results reported are then used in tests of theoretical model predictions,the determination of the QCD parameters a 1and a 2/a 1and tests of factorization.1IntroductionIn b →c hadronic hadronic transitions the spectator processes dominate.Other processes,such as the exchange or annihilation channels are suppressed relative to the spectator processes through form-factor suppression 1.Two classes of spectator processes are possible –internal and external spectator (See Fig.1)–each deﬁned by the quark-color arrangement of the ﬁnal state.In the factorization approximation three classes of spectator decays can be identiﬁed.In Class I or Class II decays,the quark conﬁguration of the ﬁnal states,neglecting ﬁnal-state rescattering,is possible only if the decay proceeds either through the external or internal diagram respectively.A third type of decay,Class III,the quark conﬁguration of the ﬁnal-states can be obtained via both diagrams.In this article I will describe the latest experimental results on the following hadronic two-body decays of the B meson:Class IClass IIClass IIIB 0→D (∗)+(nπ)−B 0→D (∗)0(nπ)0B −→D (∗)0(nπ)−B 0→D +J(nπ)−B −→D 0J (nπ)−B 0→D (∗)+D (∗)−sB −→D 0K −concentrating on the experimental techniques employed in measurements of branching fractions.I will also discuss some of the more important theoretical implications including tests of factorization and determination of the QCD parameters a 1and a 2/a 1.1qq___Internal spectator "Color-suppressed"qExternal spectatorFigure 1:Tree level decay diagrams dominant in two-body hadronic decays of B mesons.2Experimental ProgramsExcept for the B →J/ψK decays,measurements of hadronic decay rates of the B meson to charm have been performed exclusively in e +e −experiments.Decay rate measurements are dominated by experiments conducted at B ¯Bthreshold while experiments at higher energy have provide information on b lifetimes and on higher mass hadrons e.g.,B s ,Λb not accessible to experi-ments at B ¯Bthreshold.Recently,experiments at CERN have made contribu-tions to measurement of exclusive decays with a measurements from OPAL on ¯B0→D ∗+π−and ALEPH measurements of several B →DD s X,DDX and two-body D (∗)D (∗)s decays.In the next section I will brieﬂy describe the OPAL measurement as an example of the experimental method employed at the high energy e +e −experiments.I will then concentrate on recent measurements per-formed at CLEO II since they are the dominant contributors to measurements of exclusive hadronic decays of B d,u mesons.2.1Measurement of the branching fraction of ¯B0→D ∗+π−at OPAL The large sample of Z 0produced at LEP coupled with a reasonable partialwidth to b ¯b (6%)provides a signiﬁcant number of B ¯Bevents to examine.Un-fortunately the small branching fractions to any particular B decay mode and the large particle multiplicities involved present diﬃcult obstacles in exclusive reconstruction of hadronic B decays.Given these obstacles OPAL has a newmeasurement of ¯B0→D ∗+π−with their sample of 1.2×106hadronic Z 0decays.2Figure2:The invariant mass distribution of fully reconstructed B d mesons at OPAL.The dashed curve is theﬁt to data.It is a sum of two Gaussians plus a straight line.Theﬁrst Gaussian represents the signal the other the feed-down from the¯B0→D∗+ρ−decays.The straight line models the combinatoric background.The analysis6features a full reconstruction of the decay chain:aB0→D∗+π−;D∗+→D0π+;D0→K−π+where charged tracks are combined to form candidate particles.Each track in the event is identiﬁed as either a kaon or pion depending primarily on its energy loss in the jet chamber.Additional requirements on track transverse momentum and impact parameter are imposed.The invariant mass of the K−π+combination is required to be within90MeV of the nominal D0mass and the mass diﬀerence between the K−π+and(K−π+)π+combination is required to be within2MeV/c2of the known mass diﬀerence.The D0and D∗+candidates are formed separately for each jet and are then combined with other tracks in the jet to form a B d candidate.To reduce combinatorial backgrounds,a decay angle cut is imposed on the D0candidates and a helicity angle cut is imposed on the angular distribution of the decay products of the D∗+.The hard fragmentation of the b quark and its long lifetime are also ex-ploited to reduce combinatorial background.The momentum of the B d candi-date is required to exceed70%of the beam energy and the B d and D0decay vertices are required to be in the hemisphere centered around the B d momen-tum vector.After application of the selection criteria,11events are observed in the mass region between4.5and6.0GeV/c2,see Fig.2.To determine the event yield the m B distribution isﬁt to two-Gaussians plus a straight line.The second Gaussian takes into account the feed-down from¯B0→D∗+ρ−decays which have been miss-reconstructed as a¯B0→D∗+π−.This background peaksbelow the B d mass and isﬁxed in theﬁt to the value determined in a Monte Carlo simulation.Monte Carlo data is also used to determine the widths of both Gaussians.Theﬁt yields8.1±2.9events for the¯B0→D∗+π−and 2.9±1.9for the¯B0→D∗+ρ−mode at a mass of5.279±0.023GeV/c2.The branching fraction is estimated to be:B r(¯B0→D∗+π−)=(1.0±0.4±0.1)%The Standard Model value forΓbb/Γhad=0.217and the B d production fraction =0.38)are used6.This value is consistent with previous CLEO and (f BdARGUS results7and with current CLEO II results8.3Measurements at B¯B ThresholdThe large luminosity and clean environment typical at e+e−machines running at the B¯B threshold provide very large samples of B¯B events.For example, at CLEO the numbers of B¯B events collected from1994through1996was 3.1×106while ARGUS whose physics runs ended in1993,collected about 330,000B¯B pairs.The event topology at B¯B threshold is somewhat diﬀerent than at a ma-chine running on the Z0resonance.In particular,two characteristics diﬀer-entiate the reconstruction technique from that employed in the higher energy environment.First,signiﬁcantly larger backgrounds are encountered from con-tinuum processes.At B¯B threshold3/4of the total hadronic cross-section is from continuum events.Fortunately,this background is well behaved and can be accurately modeled by data taken below B¯B threshold;nevertheless,tech-niques must be employed to reduce the contribution from these backgrounds. Secondly,the fact that the B mesons are produced nearly at rest is exploited to improve signal identiﬁcation.Signal extraction is improved by replacing the energy of the reconstructed B meson with the energy of the beam which is typically known better by an order of magnitude than the reconstructed energy.In the following sections I will discuss new results from CLEO using the complete CLEO II data sample which consists of3.1fb−1taken at theΥ(4S).A smaller sample of1.4fb−1taken just below theΥ(4S)is also used to model the continuum background.These results have either been reported at conferences4Beam-constrained mass (GeV)E v e n t s /2M e VBeam-constrained mass (GeV)E v e n t s /2M e VFigure 3:The continuum-subtracted beam-constrained mass distributions for twelve B →D (∗)nπmodes.The hatched histograms shows the B ¯Bbackground spectrum,the open histograms is ﬁt to data by the sum of a Gaussian of plus the B ¯Bbackground distribution determined from Monte Carlo simulations.The data are the black squares with error bars.or have been recently published.All of the B branching fractions presented in Tables 1,2and 3have been rescaled to the D 0,D +,D ∗+and D ∗0branchingfractions used in Ref.[8].The D (∗)s branching fractions used are taken from Ref.[9].3.1Full Reconstruction of B →D (∗)(nπ)decays at CLEOCLEO has recently updated their branching fraction measurements of 22decay modes of the B d,u mesons.These have been released as conference reports 8,10.The analyses described here utilize the full reconstruction technique,similar to the method described in the previous section but optimized to exploit thekinematic properties unique to B ¯Bproduction from the decay of the Υ(4S ).Once again the goal is to maximize the number of B mesons by combining a selection of charged and neutral tracks into particle candidates which in turn are combined to reconstruct the B meson decay chain.The charmed candidates are formed from a selected sample of charged tracks and π0in the following decay modes:D ∗0→D 0π0D ∗+→D 0π+D 0→K −π+,K −π+π0,K −π+π−π+D +→K −π+π+.Invariant mass cuts are applied to the D 0and D −candidates and the D ∗,D 0mass diﬀerence is used to select D ∗+and D ∗0candidates.To reduce continuum background two quantities are used.The global event topology is exploited by cutting on the ratio of the 2nd to 1st Fox-Wolfram moment,selecting events above 0.5.Second,the sphericity angle θf5Table1:Branching Fractions for B→D(∗)(nπ)−Decay Modes23 Class I Decays Class III Decays Mode B r(%)Mode B r(%)Table2:Limits on Branching Fractions for¯B0→D(∗)0(nπ)0Decay Modes23Class II Decays@90%C.L.Mode B r(%)Mode B r(%)E v e n t s /.2 U n i t sBB ¯B0→D ∗+π−B −→D ∗0π−Figure 4:Projections of 2-D ﬁt to data for the variables cos(ΘB )and cos(ΘB ).The twoﬁgures on the left represent ¯B0→D ∗+π−decays the two on the right are for B −→D ∗0π−decays.The population of events in the non-physical region |cos(Θ)|>1.0is from mismeasured track combinations.Figure 4shows projections of a 2-dimensional χ2ﬁt to the data.The ﬁttingfunction consists of shapes for signal,continuum and B ¯Bbackground.The signal and B ¯Bbackground components were determined from Monte Carlo simulations while the continuum shape was modeled by oﬀ-resonance data.The overall normalization of the B ¯Bbackground component is allowed to vary in the ﬁt while the continuum component is ﬁxed.The ﬁtting functionused in the π−f π0ﬁt contains an additional component to accommodate thecontribution of the ¯B0→D ∗+π−decay where the D ∗+decays to D +π0.This is ﬁxed by the ¯B 0→D ∗+π−branching fraction determined in the π−f π+sﬁt.The measured branching fractions are:B (¯B0→D ∗+π−)=(2.81±0.11±0.21±0.05)×10−3B (B −→D ∗0π−)=(4.34±0.33±0.34±0.18)×10−3where the ﬁrst error is statistical the second is systematic and the third is due to the uncertainty in the D ∗branching fractions.These results are in excellent agreement with the results obtained by the full reconstruction technique.3.3B →D 0J (nπ)−decaysThe full and partial reconstruction techniques have been used by both CLEO and ARGUS to reconstruct decays of the B meson to excited L =1charmed8E v e n t s / 20 M e VM(D π) GeV/c2cos θ3Figure 5:Projections of 2-D ﬁt to data for the variables cos θ3and m D ∗+π−.The twoﬁgures on the left show the m D ∗+π−in diﬀerent regions of the cos θ3.The ﬁgures on the right show the projection of cos(θ3)in diﬀerent regions of m D ∗+π−.The data are the points with error bars.mesons.Published results exist only for the B −→D 01(2420)π−mode.For theB −→D 0J ρ−mode upper limits from CLEO II 15are available for the B −→D ∗2(2460)0ρ−and B →D 1(2420)0ρ−decays and from ARGUS a measurementof the sum over all D 0J has been reported 7.There are four excited states D (∗)J mesons with in a L =1orbital angularmomentum state.Two,the D ∗2(2460)and the D 1(2420)are narrow resonances which have been seen and their decays measured 7.Angular momentum and parity conservation place restrictions on the strong decay of these states.The D ∗2(2460)can decay via D-wave to either Dπor D ∗πwhile the D 1(2420)can decay to D ∗πvia S-wave or D-wave.Recently,CLEO II has reported new measurements on the D 1(2420)0π−and D ∗2(2460)0π−17using a partial reconstruction technique.The analysis follows the procedure outlined in Section 3.2.Once again the reconstruction of the decay depends on knowing the masses of the decay products,the beam-energy and the 4-momenta of the three pions,π1,π2,π3produced in the decaychain B →D 0J π1,D 0J →D ∗+π−2and D ∗→D +π3.In this analysis the mass of the D ∗+π−combination and the helicity angular distribution cos θ3are used to identify the signal.The variable θ3is deﬁned as the angle between the D 0and the direction of the D ∗in the D ∗rest frame and describes the helicity9Table3:Branching Fractions for B→D(∗)D∗+Decay Modes9,23sMode B r(%)Mode B r(%)means by which to probe a diﬀerent q2region than is possible with D(∗)+(nπ) decays.Measurements of B→D(∗)+sD(∗)rates together with measurementson the B→D∗+π−,ρ−rates allow the extraction of the f D s and f D∗s decayconstants1.Both CLEO and Argus9,7have measured B decays to Cabbibo allowed double charmﬁnal states.The CLEO II analysis reconstructs all eight decaymodes exclusively using several the three D0,one D+and several D s sub-channel decays.Only a subset consisting of2.04fb−1of the complete CLEO II on resonance data were used for this analysis.The values listed in Table3arethe published CLEO II values rescaled by the D and D∗branching fractions in Ref.[8].3.5B−→D0K−decaysA search for the Cabbibo suppressed decay to D0K−has been performed byCLEO II19.Interference between the b→c¯u s and b→u¯c s decay,which hadronize as B−→D0K−and B−→¯D0K−respectively can be used todetermine the CKM phase(γ)b.The analysis procedure features a full reconstruction technique but∆E is used extract the event yield.For this analysis particle ID is signiﬁcantlymore important because of the large background from the Cabbibo allowedB−→D0π−process.At CLEO,the current particle ID system cannot distin-guish with great certainty pions from kaons at high momentum.For exampleKπseparation at2.2GeV/c is less than2σwhereσis the diﬀerence between the expected and measured energy loss dE/dx due to speciﬁc ionization in the drift chamber.Fig.6shows the∆E distribution for the B−→D0K−with D0→K−π+,K−π+π0,K−π+π−π+combinations consistent with B produc-tion.The large background from misidentiﬁed B−→D0π−is seen to over-whelm the signal.The limit reported isB r(B−→D0K−)<4.4×10−4@90%C.L.4Test of FactorizationTheoretical models1,2,3,4,5of hadronic decays of heavy mesons invoke the fac-torization approximation to make deﬁnite predictions on decay rates to ex-clusive modes.Factorization is used in order to reduce the hadronic matrix elements to products of factorized matrix elements with one describing the creation of a hadron from the vacuum and the other describing the transitionFigure6:The distribution of the reconstructed energy minus the beam-energy for candidates the satisfy the full reconstruction selection algorithm.The data are the points,the solid hatched histogram is the signal the dashed histogram is assumed background,taken from the mass sidebands and theﬁt is shown by the open histogram.From left to right the D0→K−pi+,K−π+π0and K−3πmodes.of the B meson.The factorized B→D transition matrix element is equivalent to the matrix element encountered in semi-leptonic decays while the matrix element describing the creation of a meson from the vacuum is parameterized by the decay constant of the meson1.Some theoretical motivation exists,at least for decays with large energy re-lease,for the factorization hypothesis.These are based on“color transparency arguments”which postulate that a q¯q pair created in a point-like interaction will hadronize only after a time given by itsγfactor times a typical hadroniza-tion scale1.Thus in an energetic transition the hadronization of a light q¯q pair which travels together in the same direction will not occur until it is a signiﬁcant distance from the interaction region1.While this scenario describes decays such as B→D(∗)(nπ)−where nπis a light meson it does not apply to B→D(∗)D(∗)s decays where theγfactors are smaller.It remains to be seen if the factorization hypothesis holds for decays that occur at lower energy transfers.4.1Branching Fraction TestsTo test the factorization approximation we exploit the similarity between hadronic two-body decays and semi-leptonic decays.In semi-leptonic decays factorization is strictly obeyed since the leptonic current does not interact with the hadronic part.By taking the ratio of a hadronic decay rate to its semi-leptonic counterpart we can compare the experimental ratio to the theoretical expectation and thus performing a direct test of the factorization hypothesis3.12Table4:Test of Factorization:Comparison of R exp to R theo21,23q2R exp(GeV2)R theo(GeV2)d B rc2(µ)=1.04,where c1(µ)and c2(µ)are the Wilson coef-N cﬁcients calculated atµ=m b and1/N c=1/31.The semi-leptonic branching fraction is interpolated20from aﬁt to the diﬀerential branching fraction at the appropriate q2.The X h is a kinematic factor which depends on the masses of the hadrons and relevant form factors and is close to1.0.Table4shows a comparison between the experimental and the theoretical ratios for diﬀerent regions of q2.The agreement between data and theory is quite good in the low q2region suggesting that factorization works,at least for energetic Class I decays.5The Relative Sign and Amplitude of a1and a2Theoretical models based on the BSW approach relegate all short-distance QCD eﬀects into QCD parameters2,3,4.In two-body tree-level decays,two parameters,a1and a2multiply the dominant spectator contribution from the external and internal diagrams,respectively.They provide important clues into the role played by the strong interaction.For instance,the absolute value of the QCD parameters are sensitive to the factorization scale and additional long-distance contribution1.The latter being particularly true for the a2since it involves the diﬀerence between two small numbers.Also,the relative sign of a1and a2identiﬁes the kind of interference between the internal and external spectator diagrams.13To determine the values of a1and a2/a1we use the branching fraction measurements in Table1and3together with the theoretical predictions from the Neubert et al.model calculations3,1.Since the QCD parameters are ex-pected to be process independent1,at least for decays that occur at similar momentum scales,we perform a least squares to four of the D(∗)(nπ)decays, and a separateﬁt to the D(∗)D(∗)+sdecays.The results are:|a1|Dnπ=1.03±0.02±0.04±0.05|a1|DD s=1.01±0.05±0.12±0.05where theﬁrst error is statistical,the second is the systematic error c and the third is the error due to the uncertainty in the B lifetime/production ratio16.Consistent results are obtained using the Deandrea et al.model and the Nuebert and Stech“New Model”in Ref.[1].No process dependency is observed in the data.To determine the value and the relative sign a2/a1we form ratios of Class III to Class I branching fractions;again using the Neubert et al.model calcu-lations to extract the value from a least squaresﬁt to data.The value obtained from theﬁt was:a2f0τ0=1.14±0.14±0.13.The positive sign for a2/a1suggests that the internal and external decay amplitudes interfere constructively.This is in contrast to the situation in D decay where a negative sign implies destructive interference.The destructive interference in D decays is responsible for the longer lifetime of the charged D mesons which can proceed only through the external diagram.The positive sign of a2/a1seems to suggest a shorter lifetime for the charged B which is not observed in data.One possible explanation for this may be that constructive interference is only found in low multiplicity B decays which constitute a small fraction of the total hadronic width.It remains to be seen if this pattern persists for other B decays.6ConclusionsSigniﬁcant improvements in the precision of branching fraction measurements of exclusive hadronic B decays have been made in the recent past.This isprimarily due to the ever increasing statistics,particularly at B¯B threshold machines,and improvements in the analysis procedure.From these precise measurement we are now able to more accurately test theoretical predictions based on factorization.We showed in Table4a comparison between the ex-perimental results and theoretical predictions based on factorization.Weﬁnd that in energetic Class I transition the factorization hypothesis seems to be well supported by the data.It remains to be seen if factorization holds in the higher q2region and of the color-suppressed D(∗)0nπdecays.So far none of these color-suppressed decays have been observed.Also,the QCD param-eters a1and the a2/a1have been determined byﬁtting the data to model calculations.In Class III the relative sign of a2/a1was found to be positive indicating that the interference between internal and external decays diagrams is constructive.This fact provides additional insight into diﬀerences between the D and B decays which occur at diﬀerent factorization scales.7AcknowledgmentsI would like to thank those who participated or contributed to these analyses, in particular the CLEO II,and OPAL collaborations.I would also like to take this opportunity to thank Tom E.Browder and Sandip Pakvasa and their staﬀfor organizing an excellent Conference with a stimulating scientiﬁc program. References[1]M.Neubert and B.Stech,CERN preprint,CERN-TH/97-99,hep-ph/9705292,to appear in the Second Edition of Heavy Flavours by A.J.Buras and M.Linder(World Scientiﬁc)[2]M.Bauer,B.Stech and M.Wirbel,Z.Phys.C29,639(1985).[3]M.Neubert,V.Rieckert,B.Stech and Q.P.Xu in Heavy Flavours editedby A.J.Buras and H.Lindner,World Scientiﬁc,Singapore(1992). [4]A.Deandrea,N.Di Bartolomeo,R.Gatto and G.Nardulli,Phys.Lett.B318,549(1993).[5]C.Reader and N.Isgur,Phys.Rev.D47,1007(1993)[6]OPAL Collaboration,R.Akers Phys.Rev.Lett.B337,196(1994).[7]Review of Particle Properties,Phys.Rev.D54,(1996).[8]B.Barish,CLEO Collaboration,EPS Conference submission,EPS-339,CLEO CONF97-01(1997).In this paper ratios of D branching fractions were scaled by the B r(D0→K−π+)=0.0391±0.0008±0.0017[9]T.Bergfeld et al.,CLEO Collaboration,Phys.Rev.D53,4734(1996).In this paper ratios of the D s branching fractions were scaled byB r(D+s→φπ+)=0.035±0.004.15[10]D.W.Bliss,CLEO Collaboration,EPS Conference submission,EPS-338,CLEO CONF97-12(1997).[11]This numbers represents a weighted average of recent CLEO II resultsobtained from the full and partial reconstruction analyses described in Refs.[8]and[14].Since the measurement were conducted on the same experiment some of the systematic errors are correlated.In averaging the results these correlations were taken into account using the error matrix.[12]The non-resonantπ0π−component in D(∗)ρ−is small.It ranges fromless than2.5%to9.0%depending on the mode.For these modes we neglect non-resonant contributions.This analysis was performed in ref-erence15on approximately1/3of the current data sample.[13]The non-resonantπππandπρ0component in D(∗)a−1was found to beless than12%and24%in D0a1and D+a1decays at the90%Conﬁdence Level22.The event yields were corrected accordingly for the D(+,0)a−1 modes.In D∗a1the contributions from non-resonantπ−ρ0and D∗∗ρwere found to be less9.4%and10.6%respectively at the90%conﬁdence level15.We thus neglect non-resonant contributions to both D∗(+,0)a−1 modes.[14]G.Brandenburg et al.,CLEO Collaboration,submitted to PRL,hep-ex/9706019[15]M.S.Alam et al.,CLEO Collaboration,Phys.Rev.D50,43(1994).[16]B.Barish et al.,CLEO Collaboration,Phys.Rev.D51,1014(1995).[17]J.Gronberg et al.,CLEO Collaboration,ICHEP96Conference submis-sion,PA05-69,CLEO CONF96-25,(1996)[18]L.Montanet et al.,Phys.Rev.D50,1173(1994)[19]J.P.Alexander et al.,CLEO Collaboration,ICHEP96Conference sub-mission,PA05-68,CLEO CONF96-27,(1996)[20]T.E.Browder,K.Honscheid,D.Pedrini,Prog.Part.Nucl.Phys.35,81(1995)[21]I use the following decay constant and CKM matrix element inputs todetermine the R th ratios.For fπ=134±1MeV,fρ=210±5MeV, V ud=0.975±0.001,V cs=0.974±0.001.[22]J.L.Rodriguez,University of Florida Dissertation(1995).[23]The diﬀerence in the values listed and the numbers reported at theconference are due to recent CLEO II updates and a rescaling of previous results to D and D∗branching fraction used in Ref.[8].These numbers were not yet available in March1996.16。

Towards a measurement of $phi_3$

a r X i v :h e p -e x /0305026v 1 13 M a y 2003Presented at XXXVIII Rencontres De Moriond:Electroweak Interactions and Uniﬁed TheoriesLes Arcs,France,March 15–22,2003TOW ARDS A MEASUREMENT OF φ3S.K.SWAINDepartment of Physics and Astronomy,University of Hawaii at Manoa,Honolulu,HI,USAResults on the decays B −→D CP K −,¯B0→D (∗)0¯K (∗)0,B 0→D ∗∓π±and their charge conjugates using data collected at the Υ(4S )resonance with the Belle detector at the KEKB asymmetric e +e −storage ring are reported.The implications for the determination of the weak phase φ3are discussed.1B −→D CP K −The extraction of φ31,an angle of the Kobayashi-Maskawa triangle 2,is a challenging mea-surement even with modern high luminosity B factories.Recent theoretical work on B meson dynamics has demonstrated the direct accessibility of φ3using the process B −→DK −3,4.If the D 0is reconstructed as a CP eigenstate,the b →c and b →u processes interfere.This interference leads to direct CP violation as well as a characteristic pattern of branching frac-tions.However,the branching fractions for D meson decay modes to CP eigenstates are only of order 1%.Since CP violation through interference is expected to be small,a large numberof B decays is needed to extract φ3.Assuming the absence of D 0−¯D0mixing,the observables sensitive to CP violation that are used to extract the angle φ35are,A 1,2≡B (B −→D 1,2K −)−B (B +→D 1,2K +)1+r 2+2r cos δ′cos φ3R 1,2≡R D 1,2Figure1:∆E distributions for(a)B−→D fπ−,(b)B−→D f K−,(c)B−→D1π−,(d)B−→D1K−,(e)B−→D2π−and(f)B−→D2K−.Points with error bars are the data and the solid lines show theﬁt results. Table1:Signal yields,feed-acrosses and ratios of branching fractions.The errors on R D are statistical andsystematic,respectively.B(B−→D0π−)events events feed-acrosswhere the ratios R D1,2and R D0are deﬁned asB(B−→D1,2K−)+B(B+→D1,2K+)R D1,2=,B(B−→D0π−)+B(B+→¯D0π+)D1and D2are CP-even and CP-odd eigenstates of the neutral D meson,r denotes a ratio of amplitudes,r≡|A(B−→¯D0K−)/A(B−→D0K−)|,andδis their strong phase diﬀerence. Note that the asymmetries A1and A2have opposite signs.We reconstruct D0mesons in the following decay channels.For theﬂavor speciﬁc mode(denoted by D f),we use D0→K−π+8. For CP=+1modes,we use D1→K−K+andπ−π+while for CP=−1modes,we use D2→Table2:Yields,partial-rate charge asymmetries and90%C.L intervals for asymmetries.B±→D f K±165.4±14.5179.6±150.04±0.06±0.03−0.07<A f<0.15B±→D1K±22.1±6.125.0±6.50.06±0.19±0.04−0.26<A1<0.38B±→D2K±29.9±6.520.5±5.6−0.19±0.17±0.05−0.47<A2<0.11M bc (GeV/c2)E v e n t s /(0.002 G e V /c 2)∆E (GeV)E v e n t s /(0.01 G e V )Figure 2:∆E (left)and M bc (right)distributions for the ¯B0→D 0¯K (∗)0candidates.Points with errors represent the experimental data,hatched histograms show the D 0mass sidebands and curves are the results of the ﬁts.Table 3:Fit results,branching fractions or upper limits at 90%C.L and statistical signiﬁcances for ¯B0→¯D ∗0¯K (∗)0.¯B0→D 0¯K031.5+8.2−7.627.0+7.6−6.95.0+1.3−1.2±0.65.1σ¯B 0→D 0¯K ∗041.2+9.0−8.541.0+8.7−8.14.8+1.1−1.0±0.55.6σ¯B 0→D ∗0¯K 04.2+3.7−3.02.7+3.0−2.4<6.61.4σ¯B 0→D ∗0¯K ∗06.1+5.2−4.58.6+4.2−3.6<6.91.4σ¯B 0→¯D 0¯K ∗01.4+8.2−7.69.2+7.7−7.2<1.8−¯B 0→¯D∗0¯K ∗01.2+4.1−3.60.0+3.9−3.2<4.0−E 2beam−| p D + p h |2,where p D and p h are the momenta of D 0and K −/π−candidates and E beam is the beam energy in the c.m.frame.The second is the energy diﬀerence,∆E =E D +E h −E beam ,where E D is the energy of the D 0candidate,E h is the energy of the K −/π−candidate calculated from the measured momentum and assuming the pion mass,E h =-0.200.20.40.60.81∆z (µm)A (∆z )0.20.40.60.811.2050010001500200025003000Integrated luminosity (fb -1)δs i n (2φ1+φ3)30 fb -1KEKBJuly, 2001200 fb -1KEKB 20042000 fb -1Super-KEKBFigure 3:(Left)Distribution of the asymmetry,A (∆z ),as a function of ∆z for the data with the ﬁt curve overlaid.(Right)Error on sin(2φ1+φ3),as a function of integrated luminosity.15MeV /c 2and 25MeV /c 2of the nominal D 0mass,respectively.In each channel we further deﬁne a D 0mass sideband region,with width twice that of signal region.For the π0from the D 0→K −π+π0decay,we require that its momentum in the CM frame be greater than 0.4GeV /c in order to reduce combinatorial background.D ∗0mesons are reconstructed in the D ∗0→D 0π0decay mode.The mass diﬀerence between D ∗0and D 0candidates is requiredto be within 4MeV /c 2of the expected value.¯K∗0candidates are reconstructed from K −π+pairs with an invariant mass within 50MeV /c 2of the nominal ¯K∗0mass.We then combine D (∗)0candidates with K 0Sor ¯K ∗0to form B mesons.For the ﬁnal result using 78fb −1data,a simultaneous ﬁt to the ∆E distributions for the three D 0decay channels taking into account the corresponding detection eﬃciencies 10.The ﬁt result is shown in Fig.2.The signal yields from the ﬁtting and the branching fractions are shown in Table 3.3B 0−¯B0mixing with B 0(¯B 0)→D ∗∓π±partial reconstruction.Since both Cabibbo-favoured (B 0→D ∗−π+)and Cabibbo-suppressed (¯B0→D ∗−π+)decays contribute to the D ∗−π+ﬁnal state,a time-dependent analysis can be used to measure sin(2φ1+φ3).Since the ratio of amplitudes is expected to be small (∼0.02),the CP asymmetry will be hard to observe,but may be possible since the B 0→D ∗−π+decay rate is fairly large.A ﬁrst step towards this measurement is the extraction of the mixing parameter ∆m d from B 0→D ∗−π+.We use events with a partially reconstructed B 0(¯B0)→D ∗∓π±candidates and where the ﬂavor of the accompanying B meson is identiﬁed by the charge of the lepton from aB 0(¯B0)→X ∓l ±νdecay.The proper-time diﬀerence between the two B mesons is deter-mined from the distance between the two decay vertices (∆Z ).From a simultaneous ﬁt to the proper-time distributions for the same ﬂavor(SF)and opposite ﬂavor(OF)event samples,we measure the mass diﬀerence between the two mass eigenstates of the neutral B meson to be ∆m d =(0.509±0.017(stat )±0.020(sys ))ps −1.The result is obtained using 29.1fb −1data collected with Belle detector at KEKB.This is the ﬁrst direct measurement of ∆m d using the technique of partial reconstruction.Fig.3(left)shows the mixing asymmetry A (∆Z )as a func-tion of ∆Z whereA (∆Z )≡N OF (∆Z )−N SF (∆Z )AcknowledgmentsWe wish to thank the KEKB accelerator group for the excellent operation of the KEKB accel-erator.References1.Another naming convention,γ(=φ3),is also used in the literature.2.M.Kobayashi and T.Maskawa,Prog.Theor.Phys.49,652(1973).3.M.Gronau and D.Wyler,Phys.Lett.B265,172(1991);D.Atwood,I.Dunietz andA.Soni,Phys.Rev.Lett.78,3257(1997);4.M.Gronau,hep-ph/0211282;5.H.Quinn and A.I.Sanda,Euro.Phys.J.C15,626(2000);6.A.Bornheim et al.(CLEO Collab.),hep-ex/0302026,submitted to Phys.Rev.D.;7.A.Abashian et al.(Belle Collab.),Nucl.Instr.and Meth.A479,117(2002).8.Hereafter,the inclusion of the charge conjugate mode decay is implied unless otherwisestated.9.S.K.Swain and T.E.Browder et al.(Belle Collab.),hep-ex/0304032,submitted to Phys.Rev.D.;10.P.Krokovny et al.(Belle Collab.),Phys.Rev.Lett.90,141802(2003);11.Y.Zheng et al.(Belle Collab.),hep-ex/0211065,to appear in Phys.Rev.D.;12.K.Hagiwara et al.,Review of Particle Physics,Phys.Rev.D66,010001(2002);024********16M(π+π-) (GeV/c 2)E v e n t s / (1 M e V /c 2)024681012R vert (cm)E v e n t s / (2 c m )0246810121416cos θK*E v e n t s-202468101214M(K -π+) (GeV/c 2)E v e n t s / (10 M e V /c 2)05D *0K-00510D *0K-*0020D -0K-*0010-0.2-0.100.10.2D -*0K-*0∆E (GeV)E v e n t s /(0.01 G e V )。

Charmful Three-body Baryonic B decays

2
Institute of Physics, Academia Sinica, Taipei, Taiwan 115, R.O.C.
(Dated: June 6, 2008)
Abstract
We study the charmful three-body baryonic B decays with D (∗) or J/Ψ in the ﬁnal state. We ¯ 0 → np ¯ 0 → pp explain the measured rates of B ¯D ∗+ , B ¯D (∗)0 and B − → Λ¯ pJ/Ψ and predict the ¯ 0 → Λ¯ ¯ 0 → Σ0 p branching fractions of B pD ∗+ , B ¯D ∗+ , B − → Λ¯ pD 0 and B − → Λ¯ pD ∗0 to be of order (1.2, 1.1, 1.1, 3.9) × 10−5 , respectively. They are readily accessible to the B factories.
standing of the underlying mechanism for the threshold enhancement and the angular distribution in three-body decays. First, the aforementioned three features also manifest themselves the decay B → pp ¯D (∗) [25, 26], while the Dalitz plot of B → pp ¯D (∗) [26] with asymmetric ¯ ′ Mc . An enhancement at the low dibaryon mass has been seen, for example, in in B → BB

物理专业英语词汇

物理专业英语词汇Oo branch o 分支object 对象object distance 物距object point 物点object space 物空间objective 物镜objective glass 物镜objective lens 物镜objective prism 物端棱镜oblateness 扁率oblateness of the earth 地球偏率obliquity of the ecliptic 黄赤交角observable 可观测量observation 观测observer 观测员occupied level 满带能级ocean 海洋octahedron 八面体octal notation 八迸制表示octans 南极座octave 八度音octet 八重态octode 八极管octopole 八极octupole 八极octupole deformation 八极形变octupole magnet 八极磁铁octupole radiation 八极辐射ocular 接目透镜odd even mass effect 奇偶质量效应odd even nucleus 奇偶核odd odd nucleus 奇奇核odd parity 负宇称odd term 奇数项odometer 路程表oersted 奥斯特ohm 欧ohm's law 欧姆定律ohmic contact 欧姆接触ohmic heating 电阻加热ohmic resistance 欧姆电阻ohmmeter 欧姆计oil diffusion pump 油扩散泵oil drop experiment of millikan 密立根油滴实验oil immersion 浸油oil impregnated capacitor 油电容器oil sealed rotary vacuum pump 油密封式旋转真空泵okorokov effect 沃克罗柯夫效应olbers paradox 奥伯斯佯谬old style 旧历olive oil 橄榄油ombrometer 雨量器omega expansion 展开omega meson 介子omegatron 高频质谱仪omnitron 全能加速器on line 在线的on line control 在线控制on line isotope separator 在线同位素分离器on line measurement 在线测量on off action 开关酌one body approximation 单粒子近似one boson exchange force 单玻色子交换力one dimensional crystal 一维晶体one dimensional system 一维系one electron approximation 单电子近似one particle irreducible 单粒子不可约的one pion exchange force 单介子交换力onsager reciprocity theorem 昂萨格的互反定理oort constants 奥尔特常数opacity 不透迷opal glass 乳色玻璃opalescence 乳光open circuit 断路open cluster 疏散星团open cycle 开口循环open ended system 开端系open system 开放系open universe 开宇宙opera glass 观剧镜operating system 运算系统operation 运算operations research 运筹学operator 算子ophiuchus 蛇夫座optic axis 光轴optic mode 光学模optic nerve 视神经optical acoustic diffraction 光声衍射optical activity 旋光性optical analyser 光学检偏镜optical anisotropy 光学蛤异性optical anomaly 光学反常optical axis 光轴optical bench 光具座optical bistability 光双稳定性optical bistable device 光双稳定装置optical branching 光学分支optical breakdown 光哗optical calculation 光学计算optical center 光心optical character reader 光学文字读出机optical chirp 光学档脉冲optical communication 光学通信optical comparator 光学比较仪optical constant 光学常数optical density 光密度optical depth 光深optical disc 光盘optical disk 光盘optical distance 光程optical fiber 光学纤维optical filter 滤光片optical glass 光学玻璃optical harmonic generation 光谐波发生optical hologram 光学全息图optical homodyne spectroscopy 光零差光谱学optical illusion 光幻觉optical image 光学图象optical indicatrix 光学指标optical information processing 光学信息处理optical instrument 光学仪器optical integrated circuit 光学集成电路optical interference 光的干涉optical inversion system 光学转象系统optical isomer 旋光异构体optical isomerism 旋光异构optical libration 几何平动optical matched filter 光匹配滤光器optical memory 光存储器optical microscope 光学显微镜optical mixing 光混频optical model of nucleus 核的光学模型optical modulator 光灯器optical parametric amplification 光参量放大optical parametric effect 光参量效应optical parametric oscillation 光参量振荡optical parametric scattering 光参量散射optical path length 光程长度optical phase conjugation 光相位共轭optical phenomenon 光学现象optical pulse compression 光脉冲压缩optical pumping 光抽运optical pyrometer 光学高温计optical range finder 光学测距仪optical recording 光记录optical rectification 光学校正optical resonator 光谐振器optical rotatory dispersion 旋光色散optical rotatory power 旋光本领optical second harmonic generation 第二光谐波发生optical sensor 光学传感器optical shutter 光学快门optical spectrometer 光谱仪optical spectrum 光谱optical switch 光学开关optical system 光学系统optical theorem 光学定理optical thickness 光学厚度optical transistor 光敏晶体管optical waveguide 光波导optical wedge 光楔optically pumped laser 光泵激光器optically thick plasma 光学厚等离子体optically thin plasma 光学薄等离子体optics 光学optimal control 最佳控制optimization of energy usage 能源使用的最佳化optimum lattice 最佳晶格optoacoustic effect 光声效应optoelectronic technique 光电子技术optoelectronics 光电子学optogalvanic effect 光电偶效应optron 光导发光元件opw method 正交平面波法or circuit 或电路orbach process 奥巴克过程orbit 轨道orbit analysis 轨道分析orbit model 轨道模型orbit plane 轨道面orbit radius 轨道半径orbital 轨道函数orbital angular momentum 轨道角动量orbital diamagnetism 轨道抗磁性orbital electron 轨道电子orbital electron capture 轨道电子俘获orbital elements 轨道要素orbital frequency 轨道频率orbital magnetic moment 轨道磁矩orbital moment 轨道矩orbital motion 轨道运动orbital paramagnetism 轨道顺磁性orbital period 公转周期orbital plane 轨道面orbital precession 轨道旋进orbital quantum number 轨道量子数orbital velocity 轨道速度orbiting 轨道运动orbiting solar observatory 轨道太阳观测台orbitron gage 弹道规order 次order disorder ferroelectrics 有序无序铁电体order disorder transformation 有序无序转变order disorder transition 有序无序转变order of diffraction 衍射级order of interference 干涉级order of reflection 反射级order of symmetry 对称级order parameter 秩序参量ordered alloy 有序合金ordered and disordered structure 有序无序结构ordered lattice 有序晶格ordered structure 有序结构ordering energy 有序能ordinary rays 寻常射线ordinary wave 寻常波organic conductor 有机导体organic crystal 有机晶体organic metal 有机金属organic molecular beam epitaxy 有机分子束外延organic non linear optical material 有机非线性光学材料organic scintillator 有机闪烁体organic semiconductor 有机半导体organic superconductor 有机超导体organometal compound 有机金属化合物orientation 定位orientational polarization 定向极化oriented nuclei 定向核orifice 小孔origin of cosmic rays 宇宙线起源origin of elements 元素的起源origin of the earth 地球起源orion 猎户座orion nebula 猎户星云ornstein and zernike theory 奥豆坦泽尔尼克理论ornstein uhlenbeck's brownian motion 奥尔豆坦乌伦贝克布朗运动orr sommerfeld equation 奥尔拴菲方程orthicon 正析象管ortho ferrite 正铁氧体ortho para conversion 正态仲态转换ortho state 正态orthogonal functions 正交函数orthogonal group 正交群orthogonal matrix 正交矩阵orthogonal transformation 正交变换orthogonality 正交性orthogonalized plane wave method 正交平面波法orthohelium 正氦orthohydrogen 正氢orthonormal system 正交归一系orthonormality 正交归一性orthorhombic lattice 斜方晶格orthorhombic system 斜方晶系orthoscopic eyepiece 消畸变目镜oscillating circuit 振荡电路oscillating crystal method 回摆晶体法oscillating process 振荡过程oscillating universe 振动宇宙oscillation 振动oscillation energy 振荡能oscillation method 振荡方法oscillation mode 振荡模oscillation parameter 振荡参量oscillation photograph 振动晶体照相oscillation spectrum 振动谱oscillator 振子oscillator strength 振子强度oscillatory circuit 振荡电路oscillatory motion 振荡运动oscillistor 振荡晶体管oscillogram 波形图oscillograph 示波器oscilloscope 示波器osculating elements 密切要素osculating orbit 密切轨道osculating plane 密切平面osculating sphere 密切球面oseen approximation 奥森近似osmium 锇osmometer 渗压计osmose 渗透osmosis 渗透osmotic pressure 渗透压outgassing 除气output 输出output capacitance 输出电容output impedance 输出阻抗output transformer 输出变压器输出变换器overall efficiency 总效率overcharge 过充电overcooling 过冷overdamping 过阻尼overexposure 曝光过度overhauser effect 奥佛豪塞效应overheat 过热overheater 过热器overheating 过热overlap integral 重叠积分overload 过载overstability 过稳定性overtone 泛音overvoltage 过电压oxidation 氧化oxide cathode 氧化物阴极oxide coated cathode 氧化物阴极oxide superconductor 氧化物超导体oxygen 氧ozone layer 臭氧层Pp i n diode p i n 极管p i n junction p i n 结p n i p transistor p n i p 晶体管p n junction p n 结p n p junction p n p 结p n p n junction p n p n 结p n p n transistor p n p n 晶体管p p junction p p 结p type semiconductor p 型半导体p wave p 波pachymeter 测厚计packing 填塞packing effect 聚集效应packing fraction 聚集率packing loss 聚集效应padua model of the nucleon 核子的帕多瓦模型pair 偶pair annihilation 偶湮没pair correlation function 对相关函数pair creation 偶产生pair interaction 偶相互酌pair potential 对势pair production 偶产生pairing energy 对能pairing interaction 偶相互酌pairing rotation 对转动pairing vibration 对振动palaeo astrobiology 古天体生物学palaeomagnetism 古地磁学palaeovolcanology 古火山学paleobiogeochemistry 古生物地球化学palladium 钯panalyzor 多能分析仪panofsky ratio 帕诺夫斯基比panoramic lens 全景镜头panoramic telescope 全景望远镜paper capacitor 纸电容器paper chromatography 纸色谱法para state 仲态para statistics 仲统计法parabola 抛物线parabolic antenna 抛物面天线parabolic curve 抛物曲线parabolic orbit 抛物线轨道parabolic potential 抛物线势parabolic reflector 抛物面反射器parabolic type 抛物型paraboloid 抛物面paraboloid of revolution 回转抛物面paracrystal 仲晶paradox 佯谬parahelium 仲氦parahydrogen 仲氢parallactic angle 视差角parallactic ellipse 视差椭圆parallactic motion 视差动parallax 视差parallel circuit 并联电路parallel connection 并联parallel cut y 切割parallel displacement 平行位移parallel plate capacitor 平行板形电容器parallel plate condenser 平行板形电容器parallelogram of forces 力平行四边形paramagnet 顺磁体paramagnetic absorption 顺磁性吸收paramagnetic element 顺磁性元素paramagnetic material 顺磁物质paramagnetic relaxation 顺磁弛豫paramagnetic resonance 顺磁共振paramagnetic resonance absorption 顺磁共振吸收paramagnetic substance 顺磁物质paramagnetic susceptibility 顺磁磁化率paramagnetism 顺磁性paramagnon 顺磁振子parameter 参量parameter of state 态变数parametric amplifier 参量放大器parametric excitation 参量激发parametron 参数器parasitic ferromagnetism 寄生铁磁性parasitic oscillation 寄生振荡parasitic resonance 寄生共振paraterm 仲项paraxial rays 近轴光线parent element 母元素parent mass peak 原始峰parent peak 原始峰parhelium 仲氦parity 宇称parity conservation law 宇称守恒律parity violation 宇称不守恒parsec 秒差距partial dislocation 分位错partial equilibrium 部分平衡partial polarization 部分偏振partial pressure 分压partial wave 分波partial wave analysis 分波分析partial wave expansion 分波展开partially conserved axial vector current 轴矢量分守恒partially polarized light 部分偏振光particle 粒子particle acceleration 粒子加速particle accelerator 粒子加速器particle antiparticle conjugation 正反粒子共轭particle aspect of matter 物质的粒子观点particle beam 粒子束particle booster 注入加速器particle collisions 粒子碰撞particle concentration 粒子浓度particle counter 粒子计数器particle hole interaction 粒子空穴相互酌particle hole theory 粒子空穴理论particle hole transformation 粒子空穴变换particle particle correlation 粒子粒子相关particle separation 粒子分离particle separator 粒子分离器particle track detector 粒子径迹探测器particle transfer reaction 粒子转移反应partition function 统计和parton model 部分子模型pascal 帕pascal's principle 帕斯卡原理paschen back effect 帕邢巴克效应paschen runge mounting 帕邢朗格装置paschen series 帕邢系passive electric circuit 无源电路passive network 无源网络passive state 被动状态passivity 被动状态path 路径path difference 程差path integral 路径积分path of vision 视线path tracking 跟踪飞行轨道pattern 图形pattern recognition 图样识别patterson function 帕特森函数patterson method 帕特森方法pauli approximation 泡利近似pauli exclusion principle 泡利不相容原理pauli matrix 泡利矩阵pauli paramagnetism 泡利顺磁性pauli principle 泡利不相容原理pauli spinor 泡利旋量pauli villars regularization 泡利维拉斯正规化pavo 孔雀座peak 峰peak energy 峰值能量峰peak power 峰值功率peak voltage 峰压pearl necklace model 珍珠颈挂式模型peculiar galaxy 特殊星系peculiar minor planet 特殊小行星pegasus 飞马座peierls potential 佩尔斯势peierls transition 佩尔斯跃迁pellet compression 靶丸压缩pellet implosion 靶丸爆聚pellets 靶丸peltier effect 珀耳帖效应pencil 束pencil beam survey 深巡天pencil of light 光束pendular oscillation 摆振动pendulum 摆pendulum clock 摆钟penetrability 贯穿性penetrating power 贯穿本领penetrating shower 贯穿簇射penetration depth 穿透深度penetration depth of london 伦敦穿透深度penetrometer 透度计penning discharge 彭宁放电penning effect 彭宁效应penning gage 彭宁真空计penning ion source 彭宁离子源penning ionization 彭宁电离penrose diagramm 彭罗斯图形penrose lattice 彭罗斯点阵penrose tile 彭罗斯点阵pentagonal prism 五角棱镜pentane lamp 戊烷灯pentode 五极管pentration 贵穿penumbra 半影percent 百分率percolating network 渗透网络percolation 渗滤percussion 冲击perfect conductivity 理想导电性perfect conductor 理想导体perfect cosmological principle 完全宇宙原理perfect crystal 理想晶体perfect diamagnetism 理想抗磁性perfect elasto plastic body 完全弹塑性体perfect fluid 完全铃perfect gas 理想气体perfect liquid 理想液体perfect polarization 全极化perfect solution 理想溶液perfectly black body 绝对黑体perfectly elastic body 完全弹性体perfectly elastic collision 完全弹性碰撞perfectly inelastic collision 完全非弹性碰撞period 周期period luminosity relation 周期光度关系period of oscillation 振荡周期period of revolution 公转周期periodic comet 周期彗星periodic error 周期误差periodic law 周期律periodic motion 周期运动periodic orbit 周期轨道periodic potential 周期势periodic system 周期系periodic table 周期表periodic zone 周期带peripheral collision 边缘碰撞peripheral reaction 圆周反应peripheral vision 周边视觉periscope 潜望镜permalloy 坡莫合金permanent magnet 永磁铁permeability 磁导率permeameter 磁导计permeance 磁导permissible dose 容许剂量permissible error 容许误差permissible stress 容许应力permissible tolerance 容许剂量permitted line 容许谱线permittivity 介电常数permutation 排列permutation group 置换群permutation operator 置换算符perovskite structure 钙钛矿型结构perpendicular band 正交带perpendicular susceptibility 垂直磁化率perpetual mobile 永恒机关perpetual motion 永恒运动perpetuum mobile 永动机perpetuum mobile of the first kind 第一类永动机perpetuum mobile of the second kind 第二类永动机perseus 英仙座persistence of vision 视觉暂留persistent current 持久电流persistent line 暂留谱线personal computer 个人计算机personal error 人为误差personal monitor 个人剂量计personal monitoring 个人监测perturbation 微扰perturbation energy 微扰能perturbation method 摄动法perturbation theory 微扰理论perturbed motion 受摄运动perveance 电子管导电系数peta 拍它petra 正负电子串列存储环型加速器petra pfund series 芬德系phantom 人体模型phase 相位phase advance capacitor 相位超前电容器phase angle 相位角phase average 相平均phase boundary 相界phase coherent state 相位相干态phase conjugate interferometry 相位共轭干涉法phase contrast 相衬phase contrast method 相衬法phase contrast microscope 相衬显微镜phase diagram 平衡图phase difference 相位差phase discriminator 相位鉴别器鉴相器phase displacement 相移phase distortion 相位畸变phase equilibrium 相平衡phase grating 相位衍射光栅phase hologram 相位全息图phase locked loop 锁相环路phase locking 锁相phase locking technique 锁相法phase margin 相位容限phase matching 相位平衡phase meter 功率因数计phase mode 相位模phase modulation 掂phase orbit 相轨道phase oscillation 相位振动phase retrieval 相位复原phase rule 相律phase sensitive detection 相敏检波phase separation 相分离phase shift 相移phase shift oscillator 相移振荡器phase shifter 移相器phase space 相宇phase space average 相平均phase stability 相位稳定性phase transformation 相变phase transition 相变phase transition of the first kind 第一类相变phase transition of the second kind 第二类相变phase transition of vacuum 真空相变phase velocity 相速度phase voltage 相电压phase volume 相体积phason 起伏量子phasotron 稳相加速器phenomenon 现象phoenix 凤凰座phon 方phonometer 声响度计phonon 声子phonon drag 声子曳引phonon echo 声子回波phonon excitation 声子激发phosphor 磷光体phosphorescence 磷光phot 辐透photo acoustic spectroscopy 光声光谱学photo magnetoelectric effect 光磁电效应photoacoustics 光声学photoactivation 光激活photobiology 光生物学photocathode 光电阴极photocell 光电池photoceram 光敏玻璃陶瓷photochemical reaction 光化反应photochemical system 光化学系统photochemistry 光化学photochromic glass 光变色玻璃photocolorimeter 光电比色计photoconduction 光电导photoconductive cell 光电导管photoconductive effect 内光电效应photoconductivity 光电导性photocurrent 光电流photodensitometer 光密度计photodensitometry 光密度分析法photodetachment 光致脱离photodetector 光探测器photodiode 光电二极管photoeffect 光电效应photoelastic effect 光弹性效应photoelastic holography 光弹性全息照相photoelasticimeter 光致弹性测量计photoelasticity 光弹性photoelectret 光永电体photoelectric absorption 光电吸收photoelectric cell 光电池photoelectric current 光电流photoelectric effect 光电效应photoelectric emission 光电发射photoelectric microphotometer 光电测微光度计photoelectric photometer 光电光度计photoelectric photometry 光电测光photoelectric pyrometer 光电高温计photoelectric threshold 光电阈photoelectric tube 光电管photoelectricity 光电photoelectromagnetic effect 光电磁效应photoelectron 光电子photoelectron spectroscopy 光电子谱学photoemission 光电发射photoexcitation 光激发photofission 光核裂变photogalvanic effect 光生伏打效应photographic apparatus 照相机photographic camera 照相机photographic density 照相密度photographic emulsion 照相乳胶photographic film 软片photographic lens 照相物镜photographic magnitude 照相星等photographic material 照相材料photographic photometry 照相测光学photographic plate 照相底板photographic telescope 天体照相机photography 照相术photogun 光电子枪photoionization 光致电离photoirradiation 光致辐照photoluminescence 光致发光photolysis 光解酌photomagnetic effect 光磁效应photometer 光度计photometric cube 光度计立方体photometric distance 测光距离photometric elements 测光要素photometric quantity 光度量photometric standard 光度学标准photometric unit 光度单位photometric wedge 测光楔photometrical paradox 奥伯斯佯谬photometry 光度学photomicrograph 显微镜照片photomicroscopic 显微照相机photomultiplier 光电倍增管photomultiplier tube 光电倍增管photon 光子photon counting method 光子计数法photon coupled pair 光导发光元件photon echo 光子回波photon gas 光子气体photon packet 光子束photonegative effect 负光电效应photoneutron 光中子photonuclear fission 光核裂变photonuclear reaction 光核反应photophoresis 光致迁动photopic vision 亮视觉photoplate 照相底板photoradiometer 光辐射计photorecorder 自动记录照相机photoresist 光致抗蚀剂photosemiconductor 光半导体photosensitive resin 光敏尸photosensitivity 光灵敏度photosensitization 光敏化photosphere 光球photostatistics 光子统计学photosynthesis 光合酌phototelegraphy 传真photothermal displacement 光照位移phototransistor 光电晶体管photovisual magnitude 仿视星等photovoltaic effect 光生伏打效应physical chaos 物理混沌physical chemistry 物理化学physical constant 物理常数physical double star 物理双星physical libration 物理天平动physical mathematics 物理数学physical oceanography 海洋物理学physical optics 物理光学physical pendulum 复摆physical photometer 物理光度计physical photometry 物理光度学physical property 物理性质physical quantity 物理量physical roentgen equivalent 物理伦琴当量physical variable 物理变星physicist 物理学家physico chemical 物理化学的physics 物理学physics of heat 热物理学physics of metals 金属物理学physiological acoustics 生理声学pi bond 键pi electron 电子pi electron approximation 电子近似pi meson 介子pi orbital 轨道pick up reaction 拾取反应pico 微微picofarad 微微法picosecond 微微秒picosecond laser 微微秒激光器picosecond light pulse 微微秒光脉冲picosecond spectroscopy 微微秒光谱学pictor 绘架座pid action 比例积分微分酌pierce type crystal oscillator 皮尔斯石英振荡器pierce type electron gun 皮尔斯电子枪piezo ceramic element 压电陶瓷元件piezo semiconductor transducer 压电半导体换能器piezoceramics 压电陶瓷piezochromism 受压变色piezoelectric 压电piezoelectric actuator 压电传动装置piezoelectric axis 压电轴piezoelectric constant 压电常数piezoelectric crystal 压电晶体piezoelectric effect 压电效应piezoelectric element 压电元件piezoelectric loudspeaker 压电扬声器piezoelectric modulus 压电模量piezoelectric oscillator 压电振荡器piezoelectric polaron 压电极化子piezoelectric transducer 压电转换器piezoelectric vibration 压电振动piezoelectricity 压电piezometer 液体压力计piezoresistor 压电电阻器piezotropy 压性pile 反应堆pile oscillator 反应堆振荡器pile up effect 脉冲堆积效应pilot lamp 指示灯pinch effect 箍缩效应pinching 自压缩pinhole camera 针孔照相机pinning 锁住pinning center 锁住中心pinning force 锁住力pinning potential 锁住势pion 介子pion beam 介子束pion condensation 介子凝聚pionic atom 介原子pionization 介子化过程pipe 导管pipe line 导管pippard equation 皮帕德方程pirani gage 皮拉尼压力计pisces 双鱼座piscis austrinus 南鱼座pitot tube 皮托管planar transistor 平面晶体管planck mass 普朗克质量planck time 普朗克时间planck's constant 普朗克常数planck's function 普朗克函数planck's fundamental length 普朗克基本长度planck's law of radiation 普朗克辐射定律plane concave lens 平凹透镜plane convex lens 平凸透镜plane fault 面缺陷plane grating 平面光栅plane mirror 平面镜plane of incidence 入射面plane of polarization 偏光面plane of projection 射影平面plane of symmetry 对称面plane polarization 平面偏振plane polarized light 平面偏振光plane polarized wave 平面偏振波plane wave 平面波planet 行星planetarium 天象仪planetary aberration 行星光行差planetary cosmogony 行星演化学planetary geology 行星地质学planetary nebula 行星状星云planetary system 行星系planetesimal theory 星子论planetesimals 星子planetoid 小行星planimeter 测面仪plano concave lens 平凹透镜plano convex lens 平凸透镜plano cylindrical lens 平圆柱透镜plano spherical lens 平面球面透镜plasma 等离子体plasma accelerator 等离子体加速器plasma balance 等离子体平衡plasma cluster 等离子粒团plasma confinement 等离子体禁闭plasma containment 等离子体禁闭plasma diagnostics 等离子体诊断学plasma dispersion function 等离子体弥散函数plasma echo 等离子体回波plasma engine 等离子体发动机plasma focus 等离子体聚焦点plasma frequency 等离子体频率plasma gun 等离子体枪plasma heating 等离子体加热plasma instability 等离子体不稳定性plasma membrane 原生质膜plasma oscillation 等离子体振荡plasma physics 等离子体物理学plasma potential 等离子体势plasma source 等离子体源plasma wave 等离子体波plasmapause 等离子体层顶plasmasphere 等离子层plasmoid 等离子粒团plasmon 等离振子plasmon excitation 等离振子激发plastic anisotropy 塑性蛤异性plastic deformation 塑性变形plastic flow 塑性怜plastic material 塑胶plastic potential 塑性势plastic wave 塑性波plastic yield 塑性屈服plasticity 塑性plastics 塑胶plate 正极plate battery 阳极电池组plate circuit 板极电路plate current 板极电流plate detection 板极检波plate resistance 板极电阻plate tectonics 板块构造plate voltage 板极电压plateau 坪platinum 铂platinum group elements 铂族元素platinum resistance thermometer 铂电阻温度计pleochroic halo 多向色晕pleochroism 多色性pleochromatism 多色性plk method plk 法plot 标绘plotter 标绘器plug 插头plural scattering 多重散射plus 加plus sign 加号pluto 冥王星plutonium 钚plutonium reactor 钚堆plutonium regeneration 钚再生pluviometer 雨量器pneumatic laser 气动激光器pockels cell 波克尔斯盒pocket dosimeter 袖珍剂量计pocket of air 气囊point at infinity 无穷远点point charge 点电荷point contact rectifier 点接触整流point contact transistor 点接触晶体管point defect 点缺陷point discharge 尖端放电point group 点群point lattice 点晶格point of action 酌点point of application 酌点point of contact 接触点point source of light 点光源poise 泊poiseuille flow 泊萧叶怜poiseuille's law 泊萧叶定律poisson bracket 泊松括号poisson equation 泊松方程poisson process 泊松过程poisson's ratio 泊松比polar aurora 极光polar binding 极性键polar bond 极性键polar cap 极冠polar cap absorption 极冠吸收polar crystal 极性晶体polar gas 极性气体polar light 极光polar liquid 极性液体polar molecule 极性分子polar motion 极运动polar sequence 北极星序polar telescope 天极仪polar triangle 极三角形polar vector 极矢量polar wandering 极运动polar year 极年polarimeter 偏振计polarimetry 测偏振术polaris 北极星polarisation angle 布儒斯特偏振角polariscope 偏振光镜polariton 电磁耦合振子polarity 极性polarizability 极化率polarizability ellipsoid 极化率椭球polarization 极化polarization charge 极化电荷polarization current 极化电流polarization curve 极化曲线polarization factor 极化因数polarization filter 偏振滤光镜polarization force 极化力polarization interferometer 偏振干涉仪polarization microscope 偏光显微镜polarization of neutron 中子的极化polarization orbital 极化轨道polarization potential 极化势polarization spectroscopy 偏振光光谱学polarized beam 极化束polarized ion source 极化离子源polarized light 偏振光polarized neutron diffraction technique 极化中子衍射法polarized nucleus 极化核polarized raman scattering 偏振喇曼散射polarized relay 极化继电器polarized target 极化靶polarizer 起偏器偏振器polarizing filter 偏振滤光镜polarizing microscope 偏光显微镜polarizing prism 偏振棱镜polarograph 极谱仪polarography 极谱学polaroid 偏光片polaron 极化子pole 极pole of ecliptic 黄极pole piece 极片pole shoe 极片pole strength 磁极强度polestar 北极星polhode 心迹线polishing 抛光poloidal magnetic field 极向磁场polonium 钋polyatomic molecule 多原子分子polycondensation 缩聚酌polycrystal 多晶polycrystalline material 多晶物质polydisperse system 多色散系polygon of forces 力多边形polygonization 多边形化polymer 聚合物polymer complex 聚合络合物polymer crystal 聚合晶体polymer effect 聚合效应polymerization 聚合polymerization of protein 蛋白质聚合polymolecularity 多分子性polymorphism 多形性polyphase 多相polyphase current 多相电流polytrope 多变性polytropic change 多方状态变化polytropic index 多方指标polytropic process 多变过程pomeranchuk effect 坡密朗丘克效应pomeranchuk theorem 坡密兰丘克定理pomeron 坡密子pool type reactor 池式堆population 全域population inversion 粒子数反转pore 小黑子porosity 多孔性porous flow 多孔流position 位置position resolution 位置分辨率position sensitive detector 对位置灵敏的探测器position vector 位置矢量positive 正片positive charge 正电菏positive column 阳极区positive crystal 正晶体positive electricity 正电positive electrode 阳极positive electron 正电子positive element 正元素positive eyepiece 正目镜positive feedback 正反馈positive hole 空子positive ion 阳离子positive lens 正透镜positive magnetostriction 正磁致伸缩positive meniscus 凹凸透镜positive meson 正介子positive rays 阳射线positon 正电子positron 正电子positron annihilation 正电子湮没positron beam 正电子束positron channeling 正电子沟道positron electron annihilation 偶湮没positron electron tandem ring accelerator 正负电子串列存储环型加速器petra positron emission 正电子发射positron factory 正电子工厂positron spectroscopy 正电子谱学positronium 电子偶素post newtonian approximation 后牛顿近似post nova 燃后新星post post newtonian approximation 后后牛顿近似potassium 钾potassium dihydrogenphosphate 磷酸二氢钾potential 势potential barrier 势垒potential difference 势差potential divider 分压器potential energy 势能potential energy curve 势能曲线potential field 势场potential flow 势流potential function 势函数potential instability 对粱稳定性potential motion 势运动potential scattering 势散射potential well 势阱potentiometer 电位计potts model 波特模型pound 磅powder camera 粉末照相机powder diffraction method 粉末法powder pattern 粉末干涉象powder photography 粉末照相术power 功率power amplification 功率放大power demonstration reactor 动力示范堆power density 功率密度power dissipation 耗散功率power factor 功率因数power factor meter 功率因数计power gain 功率增益power of a lens 透镜的焦强power reactor 动力堆power tube 功率管poynting robertson effect 坡印廷罗伯逊效应poynting's vector 坡印廷矢量practical system of units 实用单位制prandtl number 普朗特数praseodymium 镨pre vacuum 初真空pre vacuum pump 预备真空泵preacceleration 预加速preaccelerator 前加速器preamplifier 前置放大器precession 旋进precession camera 旋进照相机precession of orbit 轨道旋进precessional constant 岁差常数precious metal 贵金属precipitation 沉淀precision 精密度precision measurement 精密测量predict earthquake with catfish 用鲶鱼预报地震prediction 预报prediction of solar activity 太阳活动预告predissociation 预离解preferential recombination 优选复合preionization 预电离preliminary vacuum 初真空pressure 压力pressure broadening 压力增宽pressure coefficient 压力系数pressure dispersion 压力弥散pressure drag 压力阻pressure drop 压降pressure gage 压力表pressure head 压头pressure height equation 气压测高公式pressure of light 光压pressure of water vapor 水汽压pressure sensitive diode 压力敏感二极管pressure sensitive transistor 压力敏感晶体管pressure tensor 压强张量pressurized air 压缩空气pressurized water reactor 压水堆primakoff effect 普里马科夫效应primary battery 原电池primary beam 初级束流原射线束primary cell 原电池primary circuit 原电路primary colors 原色primary cosmic radiation 原宇宙辐射primary cosmic rays 原宇宙射线primary electron 原电子primary energy 一次能量primary ionization 一次电离primary rainbow 昼primary recrystallization 一次再结晶primary standard 原标准primary star 智primary target 初始靶primary thermometer 初始温度计primary voltage 初级电压prime meridian 零子午线prime vertical 卯酉圈primeval galaxy 原始星系primitive black hole 原始黑洞primitive lattice 初基点阵primordial solar nebula 太阳系星云principal axes of stress 应力轴principal axis 轴principal axis of inertia 惯性轴principal index for extraordinary ray 非常光线舟射率principal moment of inertia 知动惯量principal plane 纸面principal point 帚principal quantum number 挚子数principal ray 肘线principal refractive indices 舟射率principal series 诌系principal stress 枝力principle 原理principle of constancy of light velocity 光速不变原理principle of corresponding states 对应态原理principle of detailed balancing 细致平衡原理principle of entropy compensation 熵补偿原理。

核临界和辐射防护术语中英文对照

有限线碰撞阻止本领
Resfricted liner collision stopping power 辐射化学产额 Radiation chemical yield 气体中每形成一个离子对所消耗的平均 Mean energy expended in a gas per ion 能量 pair formed 相对生物效应[系数] Relative biological effectiveness RBE 雷姆 rem 拉德 rad 伦琴 Roentgen 希[沃特] Sievert 戈[瑞] grey 靶恩 barn 贝可 becquerel 居里 curie 辐射防护 Radiation protection 放射防护 Rediological protection 辐射防护评价 Assessment of radiation protection 危害 detriment 危险 Risk 危险度 Risk factor 危险指数 Index of harm 有效剂量当量 Effective dose equivalent 集体剂量当里昂 Collective dose equivalent [每]人[平]均剂量当量 Per caput dose equivalent 剂量当量负担 Dose equivalent commitment 待积剂量当量 Committed dose equivalent 遗传有效剂量 Genetically significant dose 群体剂量 Population dose 受到危险的织组 Tissues at risk 可合理做到的尽可能低的原则 As low as reasonably achievable principle 代价利益分析 Cost benefit analysis 正当性判断 Justification 辐射防护最优化 Optimization of radiation protection 实践 Practice 小剂量照射 Low dose of exposure 辐射工作 Radiation work 职业性照射 Occupational exposure

博世汽车SPC

4th Edition, 07.20053rd Edition dated 06.19942nd Edition dated 05.19901st Edition dated 09.19872005 Robert Bosch GmbHTable of ContentsIntroduction (5)1. Terms for Statistical Process Control (6)2. Planning .........................................................................................................................................................8 2.1 Selection of Product Characteristics .................................................................................................8 2.1.1 Test Variable ........................................................................................................................8 2.1.2 Controllability ......................................................................................................................9 2.2 Measuring Equipment .......................................................................................................................9 2.3 Machinery .........................................................................................................................................9 2.4 Types of Characteristics and Quality Control Charts ......................................................................10 2.5 Random Sample Size ......................................................................................................................11 2.6 Defining the Interval for Taking Random Samples (11)3. Determining Statistical Process Parameters ................................................................................................12 3.1 Trial Run .........................................................................................................................................12 3.2 Disturbances ....................................................................................................................................12 3.3 General Comments on Statistical Calculation Methods ..................................................................12 3.4 Process Average ..............................................................................................................................13 3.5 Process Variation . (14)4. Calculation of Control Limits ......................................................................................................................15 4.1 Process-Related Control Limits ......................................................................................................15 4.1.1 Natural Control Limits for Stable Processes ......................................................................16 4.1.1.1 Control Limits for Location Control Charts .........................................................16 4.1.1.2 Control Limits for Variation Control Charts ........................................................18 4.1.2 Calculating Control Limits for Processes with Systematic Changes in the Average .........19 4.2 Acceptance Control Chart (Tolerance-Related Control Limits) .....................................................20 4.3 Selection of the Control Chart .........................................................................................................21 4.4 Characteristics of the Different Types of Control Charts . (22)5. Preparation and Use of Control Charts ........................................................................................................23 5.1 Reaction Plan (Action Catalog) .......................................................................................................23 5.2 Preparation of the Control Chart .....................................................................................................23 5.3 Use of the Control Chart .................................................................................................................23 5.4 Evaluation and Control Criteria ......................................................................................................24 5.5 Which Comparisons Can be Made? (25)6. Quality Control, Documentation .................................................................................................................26 6.1 Evaluation .......................................................................................................................................26 6.2 Documentation .. (26)7. SPC with Discrete Characteristics ...............................................................................................................27 7.1 General ............................................................................................................................................27 7.2 Defect Tally Chart for 100% Testing . (27)8. Tables (28)9. Example of an Event Code for Mechanically Processed Parts ....................................................................29 9.1 Causes .............................................................................................................................................29 9.2 Action ..............................................................................................................................................29 9.3 Handling of the Parts/Goods ...........................................................................................................30 9.4 Action Catalog .. (30)10. Example of an x -s Control Chart (32)11. Literature (33)12. Symbols (34)Index (35)IntroductionStatistical Process Control (SPC) is a procedure for open or closed loop control of manufacturing processes, based on statistical methods.Random samples of parts are taken from the manufacturing process according to process-specific sampling rules. Their characteristics are measured and entered in control charts. This can be done with computer support. Statistical indicators are calculated from the measurements and used to assess the current status of the process. If necessary, the process is corrected with suitable actions.Statistical principles must be observed when taking random samples.The control chart method was developed by Walter Andrew Shewhart (1891-1967) in the 1920´s and described in detail in his book “Economic Control of Quality of Manufactured Product”, published in 1931.There are many publications and self-study programs on SPC. The procedures described in various publications sometimes differ significant-ly from RB procedures.SPC is used at RB in a common manner in all divisions. The procedure is defined in QSP0402 [1] in agreement with all business divisions and can be presented to customers as the Bosch approach.Current questions on use of SPC and related topics are discussed in the SPC work group. Results that are helpful for daily work and of general interest can be summarized and published as QA Information sheets. SPC is an application of inductive statistics. Not all parts have been measured, as would be the case for 100% testing. A small set of data, the random sample measurements, is used to estimate parameters of the entire population.In order to correctly interpret results, we have to know which mathematical model to use, where its limits are and to what extent it can be used for practical reasons, even if it differs from the real situation.We differentiate between discrete (countable) and continuous (measurable) characteristics. Control charts can be used for both types of characteristics.Statistical process control is based on the concept that many inputs can influence a process.The “5 M´s” – man, machine, material, milieu, method – are the primary groups of inputs. Each “M” can be subdivided, e.g. milieu in temperature, humidity, vibration, contamination, lighting, ....Despite careful process control, uncontrolled, random effects of several inputs cause deviation of actual characteristic values from their targets (usually the middle of the tolerance range).The random effects of several inputs ideally result in a normal distribution for the characteristic.Many situations can be well described with a normal distribution for SPC.A normal distribution is characterized with two parameters, the mean µ and the standard deviation σ.The graph of the density function of a normal distribution is the typical bell curve, with inflection points at σµ− and σµ+.In SPC, the parameters µ and σ of the population are estimated based on random sample measurements and these estimates are used to assess the current status of the process.1. Terms for Statistical Process ControlProcessA process is a series of activities and/or procedures that transform raw materials or pre-processed parts/components into an output product.The definition from the standard [3] is: “Set of interrelated or interacting activities which trans-forms inputs into outputs.”This booklet only refers to manufacturing or assembly processes.Stable processA stable process (process in a state of statistical control) is only subject to random influences (causes). Especially the location and variation of the process characteristic are stable over time (refer to [4])Capable processA process is capable when it is able to completely fulfill the specified requirements. Refer to [11] for determining capability indices. Shewhart quality control chartQuality control chart for monitoring a parameter of the probability distribution of a characteristic, in order to determine whether the parameter varies from a specified value.SPCSPC is a standard method for visualizing and controlling (open or closed loop) processes, based on measurements of random samples.The goal of SPC is to ensure that the planned process output is achieved and that corresponding customer requirements are fulfilled.SPC is always linked to (manual or software supported) use of a quality control chart (QCC). QCC´s are filled out with the goal of achieving, maintaining and improving stable and capable processes. This is done by recording process or product data, drawing conclusions from this data and reacting to undesirable data with appropriate actions.The following definitions are the same as or at least equivalent to those in [6].Limiting valueLower or upper limiting valueLower limiting valueLowest permissible value of a characteristic (lower specification limit LSL)Upper limiting valueHighest permissible value of a characteristic (upper specification limit USL)ToleranceUpper limiting value minus lower limiting value:LSLUSLT−=Tolerance rangeRange of permissible characteristic values between the lower and upper limiting valuesCenter point C of the tolerance rangeThe average of the lower and upper limiting values:2LSLUSL C +=Note: For characteristics with one-sided limits (only USL is specified), such as roughness (Rz), form and position (e.g. roundness, perpen-dicularity), it is not appropriate to assume 0=LSL and thus to set 2/USLC= (also refer to the first comment in Section 4.1.1.1).PopulationThe total of all units taken into considerationRandom sampleOne or more units taken from the population or from a sub-population (part of a population)Random sample size nThe number of units taken for the random sample Mean (arithmetic)The sum of theix measurements divided by the number of measurements n:∑=⋅=niixnx11Median of a sampleFor an odd number of samples put in order from the lowest to highest value, the value of the sample number (n+1)/2. For an even number of samples put in order from the lowest to highest value, normally the average of the two samples numbered n/2 and (n/2)+1. (also refer to [13])Example: For a sample of 5 parts put in order from the lowest to the highest value, the median is the middle value of the 5 values.Variance of a sampleThe sum of the squared deviations of the measurements from their arithmetic mean, divided by the number of samples minus 1:()∑=−⋅−=niixxns12211Standard deviation of a sampleThe square root of the variance:2ss=RangeThe largest individual value minus the smallest individual value:minmaxxxR−=2. PlanningPlanning according to the current edition of QSP 0402 “SPC”, which defines responsibilities. SPC control of a characteristic is one possibility for quality assurance during manufacturing and test engineering.2.1 Selection of Product CharacteristicsSpecification of SPC characteristics and their processes should be done as early as possible (e.g. by the simultaneous engineering team). They can also, for example, be an output of the FMEA.This should take• Function,• Reliability,• Safety,•Consequential costs of defects,•The degree of difficulty of the process,• Customer requests, and•Customer connection interfaces, etc.into account.The 7 W-questions can be helpful in specifying SPC characteristics (refer to “data collection” in “Elementary Quality Assurance Tools” [8]): Example of a simple procedure for inspection planning:Why do I need to know what, when, where and how exactly?How large is the risk if I don’t know this? Note: It may be necessary to add new SPC characteristics to a process already in operation. On the other hand, there can be reasons (e.g. change of a manufacturing method or intro-duction of 100% testing) for replacing existing SPC control with other actions.SPC characteristics can be product or process characteristics.Why?Which or what? Which number or how many?Where? Who?When?With what or how exactly?2.1.1 Test VariableDefinition of the “SPC characteristic”, direct or indirect test variable. Note: If a characteristic cannot be measured directly, then a substitute characteristic must be found that has a known relationship to it.2.1.2 ControllabilityThe process must be able to be influenced (controlled) with respect to the test variable. Normally manufacturing equipment can be directly controlled in a manner that changes the test variable in the desired way (small control loop). According to Section 1, “control” in the broadest sense can also be a change of tooling, machine repair or a quality meeting with a supplier to discuss quality assurance activities (large control loop).2.2 Measuring EquipmentDefinition and procurement or check of the measuring equipment for the test variable.Pay attention to:• Capability of measuring and test processes, • Objectiveness,• Display system (digital),• Handling. The suitability of a measurement process for the tested characteristic must be proven with a capability study per [12].In special cases, a measurement process with known uncertainty can be used (pay attention to [10] and [12]).Note: The units and reference value must correspond to the variables selected for the measurement process.2.3 MachineryBefore new or modified machinery is used, a machine capability study must be performed (refer to QSP0402 [1] and [11]). This also applies after major repairs.Short-term studies (e.g. machine capability studies) register and evaluate characteristics of products that were manufactured in one continuous production run. Long-term studies use product measurements from a longer period of time, representative of mass production. Note: The general definition of SPC (Section 1) does not presume capable machines. However, if the machines are not capable, then additional actions are necessary to ensure that the quality requirements for manufactured products are fulfilled.2.4 Types of Characteristics and Control Charts This booklet only deals with continuous anddiscrete characteristics. Refer to [6] for these andother types of characteristics.In measurement technology, physical variables are defined as continuous characteristics. Counted characteristics are special discrete characteristics. The value of the characteristic is called a “counted value”. For example, the number of “bad” parts (defective parts) resulting from testing with a limit gage is a counted value. The value of the characteristic (e.g. the number 17, if 17 defective parts were found) is called a “counted value”.SPC is performed with manually filled out form sheets (quality control charts) or on a computer.A control chart consists of a chart-like grid for entering numerical data from measured samples and a diagram to visualize the statistical indices for the process location and variation calculated from the data.If a characteristic can be measured, then a control chart for continuous characteristics must be used. Normally the sx− chart with sample size 5=n is used.2.5 Random Sample SizeThe appropriate random sample size is a compromise between process performance, desired accuracy of the selected control chart (type I and type II errors, operation characteristic) and the need for an acceptable amount of testing. Normally 5=n is selected. Smaller random samples should only be selected if absolutely necessary.2.6 Defining the Interval for Taking Random SamplesWhen a control chart triggers action, i.e. when the control limits are exceeded, the root cause must be determined as described in Section 5.4, reaction to the disturbance initiated with suitable actions (refer to the action catalog) and a decision made on what to do with the parts produced since the last random sample was taken. In order to limit the financial “damage” caused by potentially necessary sorting or rework, the random sample interval – the time between taking two random samples – should not be too long.The sampling interval must be individually determined for each process and must be modified if the process performance has permanently changed.It is not possible to derive or justify the sampling interval from the percentage of defects. A defect level well below 1% cannot be detected on a practical basis with random samples. A 100% test would be necessary, but this is not the goal of SPC. SPC is used to detect process changes.The following text lists a few examples of SPC criteria to be followed.1. After setup, elimination of disturbances orafter tooling changes or readjustment, measure continuously (100% or with randomsamples) until the process is correctly centered (the average of several measure-ments/medians!). The last measurements canbe used as the first random sample for furtherprocess monitoring (and entered in the control chart). 2. Random sample intervals for ongoingprocess control can be defined in the following manner, selecting the shortest interval appropriate for the process.Definition corresponding to the expected average frequency of disturbances (as determined in the trial run or as is knownfrom previous process experience).Approximately 10 random samples within this time period.Definition depending on specified preventivetooling changes or readjustment intervals.Approximately 3 random samples within thistime period.Specification of tooling changes or readjust-ment depending on SPC random samples.Approximately 5 random samples within theaverage tooling life or readjustment interval.But at least once for the production quantitythat can still be contained (e.g. delivery lot,transfer to the next process, defined lots forconnected production lines)!3. Take a final random sample at the end of aseries, before switching to a different producttype, in order to confirm process capabilityuntil the end of the series.Note: The test interval is defined based on quantities (or time periods) in a manner that detects process changes before defects are produced. More frequent testing is necessary for unstable processes.3. Determining Statistical Process Parameters3.1 Trial RunDefinition of control limits requires knowledge or estimation of process parameters. This is determined with a trial run with sampling size and interval as specified in Sections 2.5 and 2.6. For an adequate number of parts for initial calculations, take a representative number of unsorted parts, at least 25=m samples (with n = 5, for example), yielding no fewer than 125 measured values. It is important to assess the graphs of the measured values themselves, the means and the standard deviations. Their curves can often deliver information on process performance characteristics (e.g. trends, cyclical variations).3.2 DisturbancesIf non-random influences (disturbances) occur frequently during the trial run, then the process is not stable (not in control). The causes of the disturbances must be determined and elimi-nated before process control is implemented (repeat the trial run).3.3 General Comments on Statistical Calculation MethodsComplicated mathematical procedures are no longer a problem due to currently available statistics software, and use of these programs is of course allowed and widespread (also refer to QSP0402 [1]).The following procedures were originally developed for use with pocket calculators. They are typically included in statistics programs.Note: Currently available software programs allow use of methods for preparing, using and evaluation control charts that are better adapted to process-specific circumstances (e.g. process models) than is possible with manual calculation methods. However, this unavoidably requires better knowledge of statistical methods and use of statistics software. Personnel and training requirements must take this into account.Each business division and each plant should have a comprehensively trained SPC specialist as a contact person.Parameter µ is estimated by:Example (Section 10): samplesof number valuesx the of total mxx mj j===∑=1ˆµ3622562862662.......x ˆ=+++==µor:samplesof number mediansthe of total mxx m j j===∑=1~~ˆµ46225626363....x ~ˆ=+++==µIf µˆ significantly deviates from the center point C for a characteristic with two-sided limits, then this deviation should be corrected by adjusting the machine.Parameter σ is estimated by:Example (Section 10):a) ∑=⋅=m j j s m 121ˆσ41125552450550222.......ˆ=+++=σsamplesof number variancesthe of total =σˆNote: s =σˆ is calculated directly from 25 individual measurements taken from sequential random samples (pocket calculator).or b) na s=σˆ, where27125552450550.......s =+++=samplesof number deviationsdard tan s the of total ms s mj j==∑=1351940271...a s ˆn ===σnn a3 0.89 5 0.94 See Section 8, Table 1 7 0.96 for additional valuesor c) ndR =σˆ, with96225611....R =+++= samplesof number rangesthe of total mR R mj j==∑=1271332962...d R ˆn ===σn n d3 1.69 5 2.33 See Section 8, Table 1 7 2.70 for additional values Note: The use of table values n a and n d pre-supposes a normal distribution!Some of these calculation methods were originally developed to enable manual calculation using a pocket calculator. Formula a) is normally used in currently available statistics software.4. Calculation of Control Limits4.1 Process-Related Control LimitsThe control limits (lower control limit LCL andupper control limit UCL) are set such that 99% of all the values lie within the control limits in the case of a process which is only affected by random influences (random causes).If the control limits are exceeded, it must there-fore be assumed that systematic, non-random influences (non-random causes) are affecting the process.These effects must be corrected or eliminated by taking suitable action (e.g. adjustment).Relation between the variance (standard deviation x σ) of the single values (original values, individuals) and the variance (standard deviation x σ) of the mean values: nxx σσ=.4.1.1 Natural Control Limits for Stable Processes4.1.1.1 Control Limits for Location Control Charts (Shewhart Charts)For two-sided tolerances, the limits for controlling the mean must always be based on the center point C. Note: C is replaced by the process mean x =µˆ for processes where the center point C cannot be achieved or for characteristics with one-sided limits.* Do not use for moving calculation of indices!Note: Use of the median-R chart is onlyappropriate when charts are manually filled out, without computer support.n*A E C n c'E EE E3 1.68 1.02 1.16 2.93 1.73 5 1.230.59 1.20 3.09 1.337 1.020.44 1.21 3.19 1.18Estimated values µˆ and σˆ are calculated per Sections 3.4 and 3.5.Refer to Section 8 Table 2 for additional values.Comments on the average chart: For characteristics with one-sided limits (or in general for skewed distributions) and small n , the random sample averages are not necessarily normally distributed. It could be appropriate to use a Pearson chart in this case. This chart has the advantage compared to the Shewhart chart that the control limits are somewhat wider apart. However, it has the disadvantage that calculation of the control limits is more complicated, in actual practice only possible on the computer.Control charts with moving averagesThe x chart with a moving average is a special case of the x chart. For this chart, only single random samples are taken.n sample measurements are formally grouped as a random sample and the average of these n measurements is calculated as the mean.For each new measurement from a single random sample that is added to the group, the first measurement of the last group is deleted, yielding a new group of size n , for which the new average is calculated.Of course, moving averages calculated in this manner are not mutually independent. That is why this chart has a delayed reaction to sudden process changes. The control limits correspond to those for “normal” average charts:σˆn .C LCL ⋅−=582 σˆn.C UCL ⋅+=582Calculate σˆ according to Section 3.5 a)Control limits for )3(1=n :σˆ.C LCL ⋅−=51 σˆ.C UCL ⋅+=51Example for )3(1=n :3 74 741.x = 3 7 4 9 762.x = 3 7 4 9 2 053.x = 3 7 4 9 2 8 364.x =This approach for moving sample measurements can also be applied to the variation, so that an s x − chart with a moving average and moving standard deviation can be used.After intervention in the process or process changes, previously obtained measurements may no longer be used to calculate moving indices.4.1.1.2 Control Limits for Variation Control ChartsThe control limits to monitor the variation (depending on n ) relate to σˆ and s and like-wise R (= “Central line”).s charta) generally applicable formula(also for the moving s x − chart)Example (Section 10):σˆB UCL 'Eob⋅= 62351931...UCL =⋅=σˆB LCL 'Eun ⋅= 30351230...LCL =⋅=b) for standard s x − chartNote: Formula a) must be used in the case ofmoving s calculation. Calculation of σˆ per Section 3.5 a).s B UCL *Eob ⋅= 62271052...UCL =⋅=s B LCL *Eun ⋅=30271240...LCL =⋅=R chartR D UCL Eob ⋅=2696212...UCL =⋅=R D LCL Eun ⋅=70962240...LCL =⋅=Tablen 'Eun B 'Eob B *Eun B *Eob B Eun D Eob D3 5 70.07 0.23 0.34 2.30 1.93 1.76 0.08 0.24 0.35 2.60 2.05 1.88 0.08 0.24 0.34 2.61 2.10 1.91See Section 8, Table 2 for further values4.1.2 Calculating Control Limits for Processes with Systematic Changes in the AverageIf changes of the mean need to be considered as a process-specific feature (trend, lot steps, etc.) and it is not economical to prevent such changes of the mean, then it is necessary to extend the “natural control limits”. The procedure for calculating an average chart with extended control limits is shown below.The overall variation consists of both the “inner” variation (refer to Section 3.5) of the random samples and of the “outer” variation between the random samples.Calculation procedure Control limits for the mean。

Dalitz Plot Analysis of D0--K0bar K+ K-

a r X i v :h e p -e x /0507026v 2 13 S e p 2005B A B A R -PUB-05/023SLAC-PUB-11333Dalitz Plot Analysis of D 0→J.W.Berryhill,C.Campagnari,A.Cunha,B.Dahmes,T.M.Hong,M.A.Mazur,J.D.Richman,and W.Verkerke University of California at Santa Barbara,Santa Barbara,California93106,USAT.W.Beck,A.M.Eisner,C.J.Flacco,C.A.Heusch,J.Kroseberg,W.S.Lockman,G.Nesom, T.Schalk,B.A.Schumm,A.Seiden,P.Spradlin,D.C.Williams,and M.G.Wilson University of California at Santa Cruz,Institute for Particle Physics,Santa Cruz,California95064,USAJ.Albert,E.Chen,G.P.Dubois-Felsmann,A.Dvoretskii,D.G.Hitlin,I.Narsky,T.Piatenko,F.C.Porter,A.Ryd,and A.SamuelCalifornia Institute of Technology,Pasadena,California91125,USAR.Andreassen,S.Jayatilleke,G.Mancinelli,B.T.Meadows,and M.D.SokoloﬀUniversity of Cincinnati,Cincinnati,Ohio45221,USAF.Blanc,P.Bloom,S.Chen,W.T.Ford,U.Nauenberg,A.Olivas,P.Rankin,W.O.Ruddick,J.G.Smith,K.A.Ulmer,S.R.Wagner,and J.ZhangUniversity of Colorado,Boulder,Colorado80309,USAA.Chen,E.A.Eckhart,A.Soﬀer,W.H.Toki,R.J.Wilson,and Q.ZengColorado State University,Fort Collins,Colorado80523,USAD.Altenburg,E.Feltresi,A.Hauke,and B.SpaanUniversit¨a t Dortmund,Institut fur Physik,D-44221Dortmund,GermanyT.Brandt,J.Brose,M.Dickopp,V.Klose,cker,R.Nogowski,S.Otto,A.Petzold,G.Schott,J.Schubert,K.R.Schubert,R.Schwierz,and J.E.SundermannTechnische Universit¨a t Dresden,Institut f¨u r Kern-und Teilchenphysik,D-01062Dresden,GermanyD.Bernard,G.R.Bonneaud,P.Grenier,S.Schrenk,Ch.Thiebaux,G.Vasileiadis,and M.VerderiEcole Polytechnique,LLR,F-91128Palaiseau,FranceD.J.Bard,P.J.Clark,W.Gradl,F.Muheim,S.Playfer,and Y.XieUniversity of Edinburgh,Edinburgh EH93JZ,United KingdomM.Andreotti,V.Azzolini,D.Bettoni,C.Bozzi,R.Calabrese,G.Cibinetto,E.Luppi,M.Negrini,and L.Piemontese Universit`a di Ferrara,Dipartimento di Fisica and INFN,I-44100Ferrara,ItalyF.Anulli,R.Baldini-Ferroli,A.Calcaterra,R.de Sangro,G.Finocchiaro,P.Patteri,I.M.Peruzzi,∗M.Piccolo,and A.ZalloLaboratori Nazionali di Frascati dell’INFN,I-00044Frascati,ItalyA.Buzzo,R.Capra,R.Contri,M.Lo Vetere,M.Macri,M.R.Monge,S.Passaggio,C.Patrignani,E.Robutti,A.Santroni,and S.TosiUniversit`a di Genova,Dipartimento di Fisica and INFN,I-16146Genova,ItalyS.Bailey,G.Brandenburg,K.S.Chaisanguanthum,M.Morii,E.Won,and J.WuHarvard University,Cambridge,Massachusetts02138,USAR.S.Dubitzky,ngenegger,J.Marks,S.Schenk,and U.UwerUniversit¨a t Heidelberg,Physikalisches Institut,Philosophenweg12,D-69120Heidelberg,GermanyW.Bhimji,D.A.Bowerman,P.D.Dauncey,U.Egede,R.L.Flack,J.R.Gaillard,G.W.Morton,J.A.Nash,M.B.Nikolich,G.P.Taylor,and W.P.VazquezImperial College London,London,SW72AZ,United KingdomM.J.Charles,W.F.Mader,U.Mallik,and A.K.MohapatraUniversity of Iowa,Iowa City,Iowa52242,USAJ.Cochran,H.B.Crawley,V.Eyges,W.T.Meyer,S.Prell,E.I.Rosenberg,A.E.Rubin,and J.YiIowa State University,Ames,Iowa50011-3160,USAN.Arnaud,M.Davier,X.Giroux,G.Grosdidier,A.H¨o cker,F.Le Diberder,V.Lepeltier,A.M.Lutz,A.Oyanguren, T.C.Petersen,M.Pierini,S.Plaszczynski,S.Rodier,P.Roudeau,M.H.Schune,A.Stocchi,and G.WormserLaboratoire de l’Acc´e l´e rateur Lin´e aire,F-91898Orsay,FranceC.H.Cheng,nge,M.C.Simani,and D.M.WrightLawrence Livermore National Laboratory,Livermore,California94550,USAA.J.Bevan,C.A.Chavez,J.P.Coleman,I.J.Forster,J.R.Fry,E.Gabathuler,R.Gamet,K.A.George,D.E.Hutchcroft,R.J.Parry,D.J.Payne,K.C.Schoﬁeld,and C.TouramanisUniversity of Liverpool,Liverpool L6972E,United KingdomC.M.Cormack,F.Di Lodovico,and R.SaccoQueen Mary,University of London,E14NS,United KingdomC.L.Brown,G.Cowan,H.U.Flaecher,M.G.Green,D.A.Hopkins,P.S.Jackson,T.R.McMahon,S.Ricciardi,and F.SalvatoreUniversity of London,Royal Holloway and Bedford New College,Egham,Surrey TW200EX,United KingdomD.Brown and C.L.DavisUniversity of Louisville,Louisville,Kentucky40292,USAJ.Allison,N.R.Barlow,R.J.Barlow,M.C.Hodgkinson,ﬀerty,M.T.Naisbit,and J.C.WilliamsUniversity of Manchester,Manchester M139PL,United KingdomC.Chen,A.Farbin,W.D.Hulsbergen,A.Jawahery,D.Kovalskyi,e,V.Lillard,D.A.Roberts,and G.SimiUniversity of Maryland,College Park,Maryland20742,USAG.Blaylock,C.Dallapiccola,S.S.Hertzbach,R.Koﬂer,V.B.Koptchev,X.Li,T.B.Moore,S.Saremi,H.Staengle,and S.WillocqUniversity of Massachusetts,Amherst,Massachusetts01003,USAR.Cowan,K.Koeneke,G.Sciolla,S.J.Sekula,M.Spitznagel,F.Taylor,and R.K.Yamamoto Massachusetts Institute of Technology,Laboratory for Nuclear Science,Cambridge,Massachusetts02139,USAH.Kim,P.M.Patel,and S.H.RobertsonMcGill University,Montr´e al,Quebec,Canada H3A2T8zzaro,V.Lombardo,and F.PalomboUniversit`a di Milano,Dipartimento di Fisica and INFN,I-20133Milano,ItalyJ.M.Bauer,L.Cremaldi,V.Eschenburg,R.Godang,R.Kroeger,J.Reidy,D.A.Sanders,D.J.Summers,and H.W.ZhaoUniversity of Mississippi,University,Mississippi38677,USAS.Brunet,D.Cˆo t´e,P.Taras,and B.ViaudUniversit´e de Montr´e al,Laboratoire Ren´e J.A.L´e vesque,Montr´e al,Quebec,Canada H3C3J7H.NicholsonMount Holyoke College,South Hadley,Massachusetts01075,USAN.Cavallo,†G.De Nardo,F.Fabozzi,†C.Gatto,L.Lista,D.Monorchio,P.Paolucci,D.Piccolo,and C.Sciacca Universit`a di Napoli Federico II,Dipartimento di Scienze Fisiche and INFN,I-80126,Napoli,ItalyM.Baak,H.Bulten,G.Raven,H.L.Snoek,and L.WildenNIKHEF,National Institute for Nuclear Physics and High Energy Physics,NL-1009DB Amsterdam,The NetherlandsC.P.Jessop and J.M.LoSeccoUniversity of Notre Dame,Notre Dame,Indiana46556,USAT.Allmendinger,G.Benelli,K.K.Gan,K.Honscheid,D.Hufnagel,P.D.Jackson,H.Kagan,R.Kass,T.Pulliam,A.M.Rahimi,R.Ter-Antonyan,and Q.K.WongOhio State University,Columbus,Ohio43210,USAJ.Brau,R.Frey,O.Igonkina,M.Lu,C.T.Potter,N.B.Sinev,D.Strom,J.Strube,and E.TorrenceUniversity of Oregon,Eugene,Oregon97403,USAA.Dorigo,F.Galeazzi,M.Margoni,M.Morandin,M.Posocco,M.Rotondo,F.Simonetto,R.Stroili,and C.VociUniversit`a di Padova,Dipartimento di Fisica and INFN,I-35131Padova,ItalyM.Benayoun,H.Briand,J.Chauveau,P.David,L.Del Buono,Ch.de la Vaissi`e re,O.Hamon,M.J.J.John,Ph.Leruste,J.Malcl`e s,J.Ocariz,L.Roos,and G.Therin Universit´e s Paris VI et VII,Laboratoire de Physique Nucl´e aire et de Hautes Energies,F-75252Paris,FranceP.K.Behera,L.Gladney,Q.H.Guo,and J.PanettaUniversity of Pennsylvania,Philadelphia,Pennsylvania19104,USAM.Biasini,R.Covarelli,S.Pacetti,and M.PioppiUniversit`a di Perugia,Dipartimento di Fisica and INFN,I-06100Perugia,ItalyC.Angelini,G.Batignani,S.Bettarini,F.Bucci,G.Calderini,M.Carpinelli,R.Cenci,F.Forti,M.A.Giorgi,A.Lusiani,G.Marchiori,M.Morganti,N.Neri,E.Paoloni,M.Rama,G.Rizzo,and J.WalshUniversit`a di Pisa,Dipartimento di Fisica,Scuola Normale Superiore and INFN,I-56127Pisa,ItalyM.Haire,D.Judd,and D.E.WagonerPrairie View A&M University,Prairie View,Texas77446,USAJ.Biesiada,N.Danielson,P.Elmer,u,C.Lu,J.Olsen,A.J.S.Smith,and A.V.TelnovPrinceton University,Princeton,New Jersey08544,USAF.Bellini,G.Cavoto,A.D’Orazio,E.Di Marco,R.Faccini,F.Ferrarotto,F.Ferroni,M.Gaspero,L.Li Gioi,M.A.Mazzoni,S.Morganti,G.Piredda,F.Polci,F.Safai Tehrani,and C.Voena Universit`a di Roma La Sapienza,Dipartimento di Fisica and INFN,I-00185Roma,ItalyH.Schr¨o der,G.Wagner,and R.WaldiUniversit¨a t Rostock,D-18051Rostock,GermanyT.Adye,N.De Groot,B.Franek,G.P.Gopal,E.O.Olaiya,and F.F.WilsonRutherford Appleton Laboratory,Chilton,Didcot,Oxon,OX110QX,United Kingdom R.Aleksan,S.Emery,A.Gaidot,S.F.Ganzhur,P.-F.Giraud,G.Graziani,G.Hamel de Monchenault, W.Kozanecki,M.Legendre,G.W.London,B.Mayer,G.Vasseur,Ch.Y`e che,and M.ZitoDSM/Dapnia,CEA/Saclay,F-91191Gif-sur-Yvette,FranceM.V.Purohit,A.W.Weidemann,J.R.Wilson,and F.X.YumicevaUniversity of South Carolina,Columbia,South Carolina29208,USAT.Abe,M.T.Allen,D.Aston,R.Bartoldus,N.Berger,A.M.Boyarski,O.L.Buchmueller,R.Claus, M.R.Convery,M.Cristinziani,J.C.Dingfelder,D.Dong,J.Dorfan,D.Dujmic,W.Dunwoodie,S.Fan, R.C.Field,T.Glanzman,S.J.Gowdy,T.Hadig,V.Halyo,C.Hast,T.Hryn’ova,W.R.Innes,M.H.Kelsey, P.Kim,M.L.Kocian,D.W.G.S.Leith,J.Libby,S.Luitz,V.Luth,H.L.Lynch,H.Marsiske,R.Messner,D.R.Muller,C.P.O’Grady,V.E.Ozcan,A.Perazzo,M.Perl,B.N.Ratcliﬀ,A.Roodman,A.A.Salnikov, R.H.Schindler,J.Schwiening,A.Snyder,J.Stelzer,D.Su,M.K.Sullivan,K.Suzuki,S.Swain,J.M.Thompson, J.Va’vra,M.Weaver,W.J.Wisniewski,M.Wittgen,D.H.Wright,A.K.Yarritu,K.Yi,and C.C.YoungStanford Linear Accelerator Center,Stanford,California94309,USAP.R.Burchat,A.J.Edwards,S.A.Majewski,B.A.Petersen,and C.RoatStanford University,Stanford,California94305-4060,USAM.Ahmed,S.Ahmed,M.S.Alam,J.A.Ernst,M.A.Saeed,F.R.Wappler,and S.B.ZainState University of New York,Albany,New York12222,USAW.Bugg,M.Krishnamurthy,and S.M.SpanierUniversity of Tennessee,Knoxville,Tennessee37996,USAR.Eckmann,J.L.Ritchie,A.Satpathy,and R.F.SchwittersUniversity of Texas at Austin,Austin,Texas78712,USAJ.M.Izen,I.Kitayama,X.C.Lou,and S.YeUniversity of Texas at Dallas,Richardson,Texas75083,USAF.Bianchi,M.Bona,F.Gallo,and D.GambaUniversit`a di Torino,Dipartimento di Fisica Sperimentale and INFN,I-10125Torino,ItalyM.Bomben,L.Bosisio,C.Cartaro,F.Cossutti,G.Della Ricca,S.Dittongo,S.Grancagnolo,nceri,and L.Vitale Universit`a di Trieste,Dipartimento di Fisica and INFN,I-34127Trieste,ItalyF.Martinez-VidalIFIC,Universitat de Valencia-CSIC,E-46071Valencia,SpainR.S.Panvini‡Vanderbilt University,Nashville,Tennessee37235,USASw.Banerjee,B.Bhuyan,C.M.Brown,D.Fortin,K.Hamano,R.Kowalewski,J.M.Roney,and R.J.Sobie University of Victoria,Victoria,British Columbia,Canada V8W3P6J.J.Back,P.F.Harrison,tham,and G.B.MohantyDepartment of Physics,University of Warwick,Coventry CV47AL,United KingdomH.R.Band,X.Chen,B.Cheng,S.Dasu,M.Datta,A.M.Eichenbaum,K.T.Flood,M.Graham,J.J.Hollar,J.R.Johnson,P.E.Kutter,H.Li,R.Liu,B.Mellado,A.Mihalyi, Y.Pan,R.Prepost,P.Tan,J.H.von Wimmersperg-Toeller,S.L.Wu,and Z.YuUniversity of Wisconsin,Madison,Wisconsin53706,USAH.NealYale University,New Haven,Connecticut06511,USAA Dalitz plot analysis of approximately12500D0events reconstructed in the hadronic decayD0→K0K+K−)=(15.8±0.1(stat.)±0.5(syst.))×10−2.K0π+π−)Estimates of fractions and phases for resonant and non-resonant contributions to the Dalitz plot arealso presented.The a0(980)→¯KK projection has been extracted with little background.A searchfor CP asymmetries on the Dalitz plot has been performed.PACS numbers:13.25.Hw,12.15.Hh,11.30.ErItaly6I.INTRODUCTIONThe Dalitz plot analysis is the most complete methodof studying the dynamics of three-body charm decays.These decays are expected to proceed through interme-diate quasi-two-body modes[1]and experimentally thisis the observed pattern.Dalitz plot analyses can pro-vide new information on the resonances that contributeto observed three-bodyﬁnal states.In addition,since the intermediate quasi-two-bodymodes are dominated by light quark meson resonances,new information on light meson spectroscopy can be ob-tained.Also,old puzzles related to the parameters andthe internal structure of several light mesons can receivenew experimental input.Puzzles still remain in light meson spectroscopy.Thereare new claims for the existence of broad states close tothreshold such asκ(800)andσ(500)[2].The new evi-dence has reopened discussion of the composition of theground state J P C=0++nonet,and of the possibilitythat states such as the a0(980)or f0(980)may be4-quark states due to their proximity to the¯KK thresh-old[3].This hypothesis can only be tested through an ac-curate measurement of branching fractions and couplingsto diﬀerentﬁnal states.In addition,comparison betweenthe production of these states in decays of diﬀerentlyﬂa-vored charmed mesons D0(c¯u),D+(c¯d)and D+s(c¯s)canyield new information on their possible quark composi-tion.Another beneﬁt of studying charm decays is that,in some cases,partial wave analyses are able to isolatethe scalar contribution almost background free.This paper focuses on the study of the three-body D0 meson decayD0→K0is detected via the decay K0S→π+π−.All references in this paper to an explicit decay mode,unless otherwise speciﬁed,imply the use of the charge conjugate decay also.This paper is organized as follows.Section II brieﬂy describes the B A B A R detector,while Section III gives de-tails on the event reconstruction.Section IV is devoted to the evaluation of the eﬃciency and the measurement of the branching fraction is reported in Section V.Sec-tion VII deals with a partial wave analysis of the K+K−system,while sections VI,VIII,IX and X describe the Dalitz plot analysis.K0K+K−)K0π+π−).Therefore the selection of both the data samples corre-sponding toD0→K0K+K−(2)is described.The twoﬁnal states are referred to collec-tively as K0h+h−.The decay D∗+→D0π+is used to distinguish between D0andK0π+π−,D∗−→7 K0(for the latter,ignoring the small contribution fromdoubly-Cabibbo-suppressed decay of the D0).A D0→K0S h+h−candidate is reconstructed froma K0S→π+π−candidate plus two additional chargedtracks,each with at least12hits in the DCH.The slowpion is required to have momentum less than0.6GeV/cand to have at least6hits in the SVT.In addition,allthe tracks are required to have transverse momentump T>100MeV/c and,except for the K0S decay pions,to point back to the nominal collision axis within1.5cmtransverse to this axis and within±3cm of the nominal interaction point along this axis.A K0S candidate is reconstructed by means of a ver-texﬁt to a pair of oppositely-charged tracks with the K0 mass constraint.The reconstructed K0S candidate is then ﬁt to a common vertex with all remaining combinations of pairs of oppositely-charged tracks to form a D0candi-date vertex.K0S candidates are further required to have aﬂight distance greater than0.4cm with respect to the candidate D0vertex.The D0candidate is then combined with each slow pion candidate,andﬁt to a common D∗vertex,which is constrained to be located in the interac-tion region.In all cases theﬁt probability is required to be greater than0.1%.To reduce combinatorial background,a D0candidate is required to have a center of mass momentum greater than2.2GeV/c.Kaon identiﬁcation is performed by combining dE/dx information from the tracking detectors with associated Cherenkov angle and photon information from the DIRC. The resulting eﬃciency is above95%for kaons with less than3GeV/c momentum that reach the DIRC.Each D0sample is characterized by the distributions of two variables,the invariant mass of the candidate D0, and the diﬀerence in invariant mass of the D∗+and D0 candidates∆m=m(K0h+h−).The distributions of∆m for those candidates for which m(K0π+π−andK0π+π−(statistical errors only). TheK0π+π−andK0h+h−mass distributions using a linear background and a Gaussian function for the signal gives the following mass and width(statistical errors only)for the decay D0→K0K+K−:FIG.1:a)and c)The∆m distributions for D0→K0h+h−invariant massis within two standard deviations of the D0mass value.Thearrows indicate the region of∆m used to select the D0can-didates.b)and d)K0h+h−) used to produce the∆m distributions.m=1864.74±0.03MeV/c2;σ=3.37±0.03MeV/c2. The mass resolution for reaction(2)is much better thanthat for reaction(1)because of the much smaller Q-value involved(380MeV/c2compared to1088MeV/c2).The≈1MeV/c2shift between the two mass measurements is within the expected systematic error and is due to thediﬀerent kinematics of the two D0decay modes.IV.EFFICIENCYThe selection eﬃciency for each of the D0decay modesis determined from a sample of Monte Carlo events in which each decay mode was generated according to phase space(i.e.such that the Dalitz plot is uniformly popu-lated).These events were passed through afull detector simulation based on the GEANT4toolkit[5]and sub-jected to the same reconstruction and event selection pro-cedure as were the data.The distribution of the selected events in each Dalitz plot is then used to determine the relevant reconstruction eﬃciency.Typical Monte Carlo samples used to compute these eﬃciencies consist of2×105generated events.Each Dalitz plot is divided into small cells and the eﬃciency distributionﬁt to a third-FIG.2:Eﬃciency on the Dalitz plot for (a)D 0→K 0K +K −.order polynomial in two dimensions.Cells with fewer than 100generated events were ignored in the ﬁt.The resulting χ2per degree of freedom (χ2/NDF )is typically 1.1using≈500cells.The ﬁtted eﬃciencies are shown in ing the weighting procedure described in the next section the weighted eﬃciencies values (17.94±0.25)%for K 0K +K −are obtained.The above errors include the uncertainties on the weighting procedure.V.BRANCHING FRACTIONSSince the two K 0h +h −decay channels have similar topologies,the ratio of branching fractions,calculated relative to theǫ1(x,y )ǫ0(x,y ),where N i (x,y )represents the number of events measured for channel i ,and ǫi (x,y )is the corresponding eﬃciency in a given Dalitz plot cell (x,y ).To obtain the yields and measure the relative branch-ing fractions,eachK 0π+π−:N =92935±305D 0→K 0K +K −)K 0π+π−)=(15.8±0.1(stat.)±0.5(syst.))×10−2to be compared with the PDG value of:(17.2±1.4)×10−2[6].The best previous measurement of this branch-ing fraction comes from the CLEO experiment (136events for reaction (2)),which obtains the value BR =(17.0±2.2)×10−2[7].The branching ratio measurements have been validated using a fully inclusive e +e −→c ¯c Monte Carlo simulationincorporating all known D 0decay modes.The Monte Carlo events were subjected to the same reconstruction,event selection and analysis procedures as for the data.The results were found to be consistent,within statistical uncertainty,with the branching fraction values used in the Monte Carlo generation.FIG.3:Dalitz plot of D 0→K 0K +K −Selecting events within ±2σof the ﬁtted D 0mass value,a signal fraction of 97.3%is obtained for the 12540events selected.The Dalitzplot for these D 0→K 0K +axis can also be seen in thevicinity of the φ(1020)signal,which is most probably the result of interference between S and P -wave amplitude contributions to the K +K −system.The f 0(980)and a 0(980)S -wave resonances are,in fact,just below the K +K −threshold,and might be expected to contribute in the vicinity of φ(1020).An accumulation of events due to a charged a 0(980)+can be observed on the lower right edge of the Dalitz plot.This contribution,how-ever,does not overlap with the φ(1020)region and this allows the K +K −scalar and vector components to be separated using a partial wave analysis in the low mass K +K −region.VII.PARTIAL W A VE ANALYSISIt is assumed that near threshold the production of the K +K −system can be described in terms of the diagram shown in Fig.4.The helicity angle,θK ,is then deﬁned asFIG.4:The kinematics describing the production of the K +K −system in the threshold region.the angle between the K +for D 0(or K −forK 0)rest frame.The K +K −mass distribution has been modiﬁed by weighting each D 0candidate by the sphericalharmonic Y 0L (cos θK )(L=0-4)divided by its (Dalitz-plot-dependent)ﬁtted eﬃciency.The resulting distributions Y 0Lare shown in Fig.5and are proportional to the K +K −mass-dependent harmonic moments.It is found that all the Y 0Lmoments are small or consistent with zero,except for Y 00 ,Y 01 and Y 02 .In order to interpret these distributions a simple partial wave analysis has been performed,involving only S -and P -wave amplitudes.This results in the following set of equations [8]:√4π Y 01=2|S ||P |cos φSP(3)√√m 2r −m 2AB −i ΓAB m r(4)FIG.5:The unnormalized spherical harmonic moments Y 0Las functions of K +K −invariant mass.The histograms represent the result of the full Dalitz plot analysis.where for aspinJ=1particleFr is the Blatt-Weisskopf damping factor [9]F r =q r)2J +1(m rK 0K +mass spectra obtained from theMonte Carlo generation of D 0decays toK 0K +mass distribution is entirely due to a 0(980)+(Fig.7(c)).FIG.6: Y02 spherical harmonic moment as a function of theK+K−eﬀective mass.The line is the result from theﬁt witha relativistic spin-1Breit Wigner.•The angleφSP(Fig.7(d))is obtainedﬁtting the S,P waves and cosφSP with c aBW a+cφBWφe iα.Here BW aand BWφare the Breit-Wigner describ-ing the a0(980)andφ(1020)resonances.The a0(980)scalar resonance has a mass very close tothe¯KK threshold and decays mostly toηπ.It has beendescribed by a coupled channel Breit Wigner of the form:BW ch(a0)(m)=g¯KKg2¯KK=1.03±0.14.This corresponds to a value of g¯KK=329±27(MeV)1/2.Since in the current analysis only the¯KK projectionsare available,it is not possible to measure m0and gηπ.Therefore,these two quantities have beenﬁxed to theCrystal Barrel measurements.The parameter g¯KK,onthe other hand,has been left free in theﬁt.The resultis(statistical error only):g¯KK=464±29(MeV)1/2.Figure7(e)shows the residual a0(980)phase,obtainedbyﬁrst computingφSP in the range(0,π)and then sub-tracting the known phase motion due to theφ(1020)resonance.Theﬁt gives a value of a relative phaseα=2.12±0.04and has aχ2/NDF=167/92.Theﬁt isof rather poor quality,indicating an undetermined sourceof systematic uncertainty comparable with the statisticaluncertainty.However the issue related to the determina-tion of g¯KK will be rediscussed in the complete Dalitzplot analysis described in section VIII.The entire procedure has been tested with Monte Carlosimulations with diﬀerent input values of the a0(980)pa-rameters.The partial wave analysis performed on thesesimulated data yielded the input value of g¯KK,withinthe errors.In thisﬁt the possible presence of an f0(980)contri-bution has not been considered.This assumption canbe tested by comparing the K+K−andK0K+.Therefore an ex-cess in the K+K−mass spectrum with respect toK0K+mass distri-butions,normalised to the same area between0.992and1.05GeV/c2and corrected for phase space.It is possibleto observe that the two distributions show a good agree-ment,supporting the argument that the f0(980)contri-bution is small.Notice that the enhancedK0K+mass distributions,corrected for phase space,aretabulated as a function of mass in Table I.VIII.DALITZ PLOT ANALYSIS OFD0→K0K+K−in order to usethe distribution of events in the Dalitz plot to determinethe relative amplitudes and phases of intermediate reso-nant and non-resonant states.The likelihood function has been written in the follow-ing way:L=β·G(m)ǫ(m2x,m2y)i,jc i c∗j A i A∗jFIG.7:Results from the K+K−Partial Wave Analysis corrected for phase space.(a)P-wave strength,(b)S-wave strength.(c)m(j,k c j c∗kA j A∗kdm2x dm2y.The fractions f i do not necessarily add up to1because of interference eﬀects among the amplitudes.The errors on the fractions have been evaluated by propagating the full covariance matrix obtained from theﬁt.The phase of each amplitude is measured with respect toFIG.8:Comparison between the phase-space-correctedK+K−andK0K−,has beenalso included in theﬁt.IX.RESULTS FROM THE DALITZ PLOTANALYSIS.The D0→K0f0(980)andK+a0(980)−(DCS),beingconsistentwithzero,onlythefractions have been tabulated.The results from the Dalitz plot analysis can be sum-marised as follows:TABLE I:K+K−andmass(GeV/c2)K+K−0.988644±1050.992474±52575±1540.996417±37484±821.000392±37414±651.004304±35282±481.008299±33331±491.012259±39213±381.016240±62235±381.020178±84189±331.024210±45153±281.028178±30197±321.032157±23129±251.036164±19140±251.040147±20102±211.044135±17117±221.048139±15132±231.052126±13114±221.056101±14119±221.060101±12108±201.064104±1172±171.068120±1263±15K0a0(980)0,D0→K0f0(980)and DCS contributions upper limitshave been bining statistical and system-atic errors in quadrature,the following95%c.l.upperlimits on the fractions have been obtained:BF(D0→K0K−))(DCS)<2.5%.TABLE II:Results from the Dalitz plot analysis of D 0→Final state Amplitude Phase (radians)Fraction (%)K 0a 0(980)01.0.66.4±1.6±7.0K 0φ(1020)0.437±0.006±0.0601.91±0.02±0.1045.9±0.7±0.7K +a 0(980)−0.8±0.3±0.8FIG.9:Dalitz plot projections for D 0→K 0a 0(980)0dominantcontribution.A large uncertainty is included in the upper limit on the presence of f 0(980)in this D 0decay mode due to the poor knowledge of the f 0(980)parameters.A small signal of f 0(980)is indeed present (in thiscase asa shoulder)in the D 0→K 0f 0(980).However,a reli-able estimate of the expected contribution of the f 0(980)in D 0→D 0.Notice that in these two ﬁts good values of χ2/NDF have been obtained.TABLE III:Results from the Dalitz plot Analysis of D0→D0.D0→D0→K0a0(980)066.3±2.0 1.0.643/646K0φ(1020)46.3±0.80.438±0.009 1.93±0.03D0→K−a0(980)+13.2±1.30.456±0.025 3.58±0.07D0→D0→K0f0(1400) 3.6±0.90.421±0.038-2.68±0.14K0π+π−.Thearrow indicates the position of the f0(980).We do not observe any statistically signiﬁcant asym-metries in fractions,amplitudes,or phases between D0andK0K+K−has been performed.The following ratio ofbranching fractions has been obtained:BR=Γ(D0→Γ(D0→K0a0(980)0,D0→D0do not show anystatistically signiﬁcant asymmetries in fractions,ampli-tudes,or phases.XII.ACKNOWLEDGMENTSWe are grateful for the extraordinary contributions ofour PEP-II colleagues in achieving the excellent lumi-nosity and machine conditions that have made this workpossible.The success of this project also relies criti-cally on the expertise and dedication of the computingorganizations that support B A B A R.The collaboratinginstitutions wish to thank SLAC for its support and thekind hospitality extended to them.This work is sup-ported by the US Department of Energy and NationalScience Foundation,the Natural Sciences and Engineer-ing Research Council(Canada),Institute of High EnergyPhysics(China),the Commissariat`a l’Energie Atom-ique and Institut National de Physique Nucl´e aire et dePhysique des Particules(France),the Bundesministeriumf¨u r Bildung und Forschung and Deutsche Forschungsge-meinschaft(Germany),the Istituto Nazionale di FisicaNucleare(Italy),the Foundation for Fundamental Re-search on Matter(The Netherlands),the Research Coun-cil of Norway,the Ministry of Science and Technology ofthe Russian Federation,and the Particle Physics and As-tronomy Research Council(United Kingdom).Individu-als have received support from CONACyT(Mexico),theA.P.Sloan Foundation,the Research Corporation,andthe Alexander von Humboldt Foundation.[1]M.Bauer et al.,Z.Phys.C34,103(1987).[2]E.M.Aitala et al.,Phys.Rev.Lett.89,121201(2002).。

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a r X i v :h e p -p h /9403382v 1 29 M a r 1994CLNS 94/1267CLEO 94-2February 1,2008Measurement of the branching fraction for D +→K −π+π+R.Balest,1K.Cho,1M.Daoudi,1W.T.Ford,1D.R.Johnson,1K.Lingel,1M.Lohner,1P.Rankin,1J.G.Smith,1J.P.Alexander,2C.Bebek,2K.Berkelman,2K.Bloom,2T.E.Browder,2∗D.G.Cassel,2H.A.Cho,2D.M.Coﬀman,2P.S.Drell,2R.Ehrlich,2P.Gaiderev,2M.Garcia-Sciveres,2B.Geiser,2B.Gittelman,2S.W.Gray,2D.L.Hartill,2B.K.Heltsley,2C.D.Jones,2S.L.Jones,2J.Kandaswamy,2N.Katayama,2P.C.Kim,2D.L.Kreinick,2G.S.Ludwig,2J.Masui,2J.Mevissen,2N.B.Mistry,2C.R.Ng,2E.Nordberg,2J.R.Patterson,2D.Peterson,2D.Riley,2S.Salman,2M.Sapper,2F.W¨u rthwein,2P.Avery,3A.Freyberger,3J.Rodriguez,3R.Stephens,3S.Yang,3J.Yelton,3D.Cinabro,4S.Henderson,4T.Liu,4M.Saulnier,4R.Wilson,4H.Yamamoto,4T.Bergfeld,5B.I.Eisenstein,5G.Gollin,5B.Ong,5M.Palmer,5M.Selen,5J.J.Thaler,5A.J.Sadoﬀ,6R.Ammar,7S.Ball,7P.Baringer,7A.Bean,7D.Besson,7D.Coppage,7N.Copty,7R.Davis,7N.Hancock,7M.Kelly,7N.Kwak,m,7Y.Kubota,ttery,8J.K.Nelson,8S.Patton,8D.Perticone,8R.Poling,8V.Savinov,8S.Schrenk,8R.Wang,8M.S.Alam,9I.J.Kim,9B.Nemati,9J.J.O’Neill,9H.Severini,9C.R.Sun,9M.M.Zoeller,9G.Crawford,10C.M.Daubenmier,10R.Fulton,10D.Fujino,10K.K.Gan,10K.Honscheid,10H.Kagan,10R.Kass,10J.Lee,10R.Malchow,10Y.Skovpen,10†M.Sung,10C.White,10F.Butler,11X.Fu,11G.Kalbﬂeisch,11W.R.Ross,11P.Skubic,11J.Snow,11P.L.Wang,11M.Wood,11D.N.Brown,12J.Fast ,12R.L.McIlwain,12T.Miao,12ler,12M.Modesitt,12D.Payne,12E.I.Shibata,12I.P.J.Shipsey,12P.N.Wang,12M.Battle,13J.Ernst,13Y.Kwon,13S.Roberts,13E.H.Thorndike,13C.H.Wang,13J.Dominick,mbrecht,14S.Sanghera,14V.Shelkov,14T.Skwarnicki,14R.Stroynowski,14I.Volobouev,14G.Wei,14P.Zadorozhny,14M.Artuso,15M.Goldberg,15D.He,15N.Horwitz,15R.Kennett,15R.Mountain,15G.C.Moneti,15F.Muheim,15Y.Mukhin,15S.Playfer,15Y.Rozen,15S.Stone,15M.Thulasidas,15G.Vasseur,15G.Zhu,15J.Bartelt,16S.E.Csorna,16Z.Egyed,16V.Jain,16K.Kinoshita,17K.W.Edwards,18M.Ogg,18D.I.Britton,19E.R.F.Hyatt,19D.B.MacFarlane,19P.M.Patel,19D.S.Akerib,20B.Barish,20M.Chadha,20S.Chan,20D.F.Cowen,20G.Eigen,ler,20C.O’Grady,20J.Urheim,20A.J.Weinstein,20D.Acosta,21M.Athanas,21G.Masek,21H.P.Paar,21J.Gronberg,22R.Kutschke,22S.Menary,22R.J.Morrison,22S.Nakanishi,22H.N.Nelson,22T.K.Nelson,22C.Qiao,22J.D.Richman,22A.Ryd,22H.Tajima,22D.Sperka,22M.S.Witherell,22and M.Procario 23(CLEO Collaboration)1University of Colorado,Boulder,Colorado80309-03902Cornell University,Ithaca,New York148533University of Florida,Gainesville,Florida326114Harvard University,Cambridge,Massachusetts021385University of Illinois,Champaign-Urbana,Illinois,618016Ithaca College,Ithaca,New York148507University of Kansas,Lawrence,Kansas660458University of Minnesota,Minneapolis,Minnesota554559State University of New York at Albany,Albany,New York1222210Ohio State University,Columbus,Ohio,4321011University of Oklahoma,Norman,Oklahoma7301912Purdue University,West Lafayette,Indiana4790713University of Rochester,Rochester,New York1462714Southern Methodist University,Dallas,Texas7527515Syracuse University,Syracuse,New York1324416Vanderbilt University,Nashville,Tennessee3723517Virginia Polytechnic Institute and State University,Blacksburg,Virginia,2406118Carleton University,Ottawa,Ontario K1S5B6and the Institute of Particle Physics,Canada 19McGill University,Montr´e al,Qu´e bec H3A2T8and the Institute of Particle Physics,Canada 20California Institute of Technology,Pasadena,California9112521University of California,San Diego,La Jolla,California9209322University of California,Santa Barbara,California9310623Carnegie-Mellon University,Pittsburgh,Pennsylvania15213(February1,2008)AbstractUsing the CLEO-II detector at CESR we have measured the ratio of branchingfractions,B(D+→K−π+π+)/B(D0→K−π+)=2.35±0.16±0.16.Ourrecent measurement of B(D0→K−π+)then gives B(D+→K−π+π+)=(9.3±0.6±0.8)%.PAC numbers:13.20.Fc,13.25.Ft,14.40.LbTypeset using REVT E XThe decay D+→K−π+π+is the most commonly used mode for normalizing D+ yields,since it has a relatively large branching fraction and is one of the simplest to re-construct.Many current charm and bottom meson decay results are limited by the precision of B(D+→K−π+π+).Previous measurements of this decay mode were performed by the Mark III[1]and ACCMOR[2]collaborations.Mark III used the relative number of singly detected D±mesons to the number of reconstructed D+D−events to determine the branch-ing fraction.The ACCMOR collaboration measured the ratio of D+→K−π+π+relative to the total number of3-prong decays,and used topological branching ratios determined by other experiments to obtain a branching fraction.However,ACCMOR could not eas-ily distinguish D+,D+s andΛ+c decay vertices,and had to rely on estimates of the relative production ratios of these particles.In this analysis,we use the exclusive yields,N Kπand N Kππ,of the(D∗+→D0π+,D0→K−π+)and the(D∗+→D+π0,D+→K−π+π+)de-cay sequences,respectively,to measure the ratio,B(D+→K−π+π+)/B(D0→K−π+), and apply our measurement of the branching fraction for B(D0→K−π+)[3]to obtain B(D+→K−π+π+).The data used in this analysis consist of1.79fb−1of e+e−collisions recorded with the CLEO-II detector operating at the Cornell Electron Storage Ring(CESR).The CLEO-II detector has been described in detail elsewhere[4].Data were recorded at theΥ(4S) resonance and in the continuum both below and above(the e+e−center of mass energies ranged from10.52to10.70GeV).We obtain clean samples of D∗mesons by requiring theπ0and theπ+emitted in their decays to fulﬁll strict selection criteria.To reconstructπ0’s,we start with neutral showers which satisfy isolation cuts and cannot be matched to any charged track in the event.These photons candidates must have|cosθγ|≤0.71,(θγis the polar angle measured relative to the beam axis)to ensure that they lie in that portion of the electromagentic calorimeter which has the best eﬃciency and resolution,and the least systematic uncertainty.In addition,photon energies have to be greater than30MeV.We then kinematically constrainγγcombinations with masses between125and145MeV/c2to the knownπ0mass to improve the momentum resolution.To reduceγγcombinatoric background,π0candidates are required to have momenta greater than200MeV/c.In addition,the kinematically constrainedπ0candidates must have|cosθπ0|≤0.70.Charged pions are selected if they have momentum greater than200MeV/c,and|cosθπ±|≤0.70.The polar angle cuts onπ+’s andπ0’s ensure that D∗+mesons reconstructed with either charged or neutral pions have the same geometric acceptance.The ratio N Kππ/N Kπof the measured yields can be expressed in terms of branching ratios and eﬃciencies as,N Kππ(1)N D∗+B(D∗+→D0π+)B KπǫKπwhere B Kππand B Kπare the relevant D+and D0branching fractions,respectively.The total number of D∗+’s produced in the data sample is N D∗+(which cancels in the ratio);ǫKππand ǫKπare the eﬃciencies for reconstructing D+→K−π+π+and D0→K−π+,respectively, with their respective D∗+ing isospin invariance,the CLEO-II measurements of the D∗+−D+and D∗+−D0mass diﬀerences[5],and the fact that these decays are p-wave,we estimate the ratio[6]B(D∗+→π+D0)B(D+→K−π+π+)REFERENCES[1]Mark III Collaboration,J.Adler et al.,Phys.Rev.Lett.60,89(1988)[2]ACCMOR Collaboration,S.Barlag et al.,Z.Phys.C55,383(1992);S.Barlag et al.,Z.Phys.C48,29(1990).[3]CLEO Collaboration,D.Akerib et al.,Phys.Rev.Lett.71,3070(1993).[4]CLEO Collaboration,Y.Kubota et al.,Nucl.Intr.and Meth.A320,66(1992).[5]CLEO Collaboration,D.Bortoletto et al.,Phys.Rev.Lett.69,2046(1992).[6]CLEO Collaboration,F.Butler et al.,Phys.Rev.Lett.69,2041(1992).[7]The average momentum for slow pions emitted in D∗decays which pass the selectioncriteria is approximately260MeV/c,whereas the average momenta of the D decay daughters is approximately1.3GeV/c for D+and1.7GeV/c for D0.The eﬃciency for reconstructing kaons and pions from D decays is known to an accuracy of±2%[3].[8]Particle Data Group,K.Hikasa et al.,Phys.Rev.45,1(1992).[9]The scale factor is such that the number of events in the sideband region is the same asthe number of events in the background under the mass diﬀerence signal.We investigated diﬀerent mass diﬀerence sidebands to estimate the systematic error associated with this technique.The yields quoted in the text are obtained from the sideband where the D∗+−D mass diﬀerence is in the range146.6-155.6MeV/c2for D∗+−D+,and151.4 -160.4MeV/c2for D∗+−D0.[10]The eﬀect ofﬁnal state decay radiation on D0→K−π+and D+→K−π+π+is toreduce their reconstruction eﬃciencies by approximately1%.Therefore,the ratio of the two eﬃciencies,ǫKπandǫKππis very insensitive to the eﬀects of decay radiation.We used the program PHOTOS to estimate these eﬀects-E.Barberio,B.van Eijk and Z.Was,mun.66115(1991).FIGURESFIG.1.Mass distribution for D+→K−π+π+candidates tagged via D∗+→D+π0decays;the histogram represent events in the mass diﬀerence signal region,triangles with error bars represent events in the(scaled)mass diﬀerence sideband region.The solid line is theﬁt to the data.FIG.2.Mass distribution for D0→K−π+tagged via D∗+→D0π+decays;the histogram represent events in the mass diﬀerence signal region,triangles represent events in the(scaled)mass diﬀerence sideband region.The solid line is theﬁt to the data.This figure "fig1-1.png" is available in "png" format from: /ps/hep-ph/9403382v1This figure "fig1-2.png" is available in "png" format from: /ps/hep-ph/9403382v1。