Measurement of the Pseudoscalar Decay Constant fDs Using Charm-Tagged Events in e+e- Collis
Study of B - rho pi decays at Belle
a r X i v :h e p -e x /0207007v 1 1 J u l 2002BELLEBelle Prerpint 2002-18KEK Preprint 2002-59Study of B →ρπdecays at BelleBelle Collaboration A.Gordon u ,Y.Chao z ,K.Abe h ,K.Abe aq ,N.Abe at ,R.Abe ac ,T.Abe ar ,Byoung Sup Ahn o ,H.Aihara as ,M.Akatsu v ,Y.Asano ay ,T.Aso aw ,V.Aulchenko b ,T.Aushev ℓ,A.M.Bakich an ,Y.Ban ag ,A.Bay r ,I.Bedny b ,P.K.Behera az ,jak m ,A.Bondar b ,A.Bozek aa ,M.Braˇc ko t ,m ,T.E.Browder g ,B.C.K.Casey g ,M.-C.Chang z ,P.Chang z ,B.G.Cheon am ,R.Chistov ℓ,Y.Choi am ,Y.K.Choi am ,M.Danilov ℓ,L.Y.Dong j ,J.Dragic u ,A.Drutskoy ℓ,S.Eidelman b ,V.Eiges ℓ,Y.Enari v ,C.W.Everton u ,F.Fang g ,H.Fujii h ,C.Fukunaga au ,N.Gabyshev h ,A.Garmash b ,h ,T.Gershon h ,B.Golob s ,m ,R.Guo x ,J.Haba h ,T.Hara ae ,Y.Harada ac ,N.C.Hastings u ,H.Hayashii w ,M.Hazumi h ,E.M.Heenan u ,I.Higuchi ar ,T.Higuchi as ,L.Hinz r ,T.Hokuue v ,Y.Hoshi aq ,S.R.Hou z ,W.-S.Hou z ,S.-C.Hsu z ,H.-C.Huang z ,T.Igaki v ,Y.Igarashi h ,T.Iijima v ,K.Inami v ,A.Ishikawa v ,H.Ishino at ,R.Itoh h ,H.Iwasaki h ,Y.Iwasaki h ,H.K.Jang a ℓ,J.H.Kang bc ,J.S.Kang o ,N.Katayama h ,Y.Kawakami v ,N.Kawamura a ,T.Kawasaki ac ,H.Kichimi h ,D.W.Kim am ,Heejong Kim bc ,H.J.Kim bc ,H.O.Kim am ,Hyunwoo Kim o ,S.K.Kim a ℓ,T.H.Kim bc ,K.Kinoshita e ,S.Korpar t ,m ,P.Krokovny b ,R.Kulasiri e ,S.Kumar af ,A.Kuzmin b ,Y.-J.Kwon bc ,nge f ,ai ,G.Leder k ,S.H.Lee a ℓ,J.Li ak ,A.Limosani u ,D.Liventsevℓ,R.-S.Lu z,J.MacNaughton k,G.Majumder ao, F.Mandl k,D.Marlow ah,S.Matsumoto d,T.Matsumoto au,W.Mitaroffk,K.Miyabayashi w,Y.Miyabayashi v,H.Miyake ae,H.Miyata ac,G.R.Moloney u,T.Mori d,T.Nagamine ar,Y.Nagasaka i,T.Nakadaira as,E.Nakano ad, M.Nakao h,J.W.Nam am,Z.Natkaniec aa,K.Neichi aq, S.Nishida p,O.Nitoh av,S.Noguchi w,T.Nozaki h,S.Ogawa ap, T.Ohshima v,T.Okabe v,S.Okuno n,S.L.Olsen g,Y.Onuki ac, W.Ostrowicz aa,H.Ozaki h,P.Pakhlovℓ,H.Palka aa,C.W.Park o,H.Park q,L.S.Peak an,J.-P.Perroud r, M.Peters g,L.E.Piilonen ba,J.L.Rodriguez g,F.J.Ronga r, N.Root b,M.Rozanska aa,K.Rybicki aa,H.Sagawa h,S.Saitoh h,Y.Sakai h,M.Satapathy az,A.Satpathy h,e,O.Schneider r,S.Schrenk e,C.Schwanda h,k,S.Semenovℓ,K.Senyo v,R.Seuster g,M.E.Sevior u,H.Shibuya ap,V.Sidorov b,J.B.Singh af,S.Staniˇc ay,1,M.Stariˇc m,A.Sugi v, A.Sugiyama v,K.Sumisawa h,T.Sumiyoshi au,K.Suzuki h,S.Suzuki bb,S.Y.Suzuki h,T.Takahashi ad,F.Takasaki h, K.Tamai h,N.Tamura ac,J.Tanaka as,M.Tanaka h,G.N.Taylor u,Y.Teramoto ad,S.Tokuda v,S.N.Tovey u,T.Tsuboyama h,T.Tsukamoto h,S.Uehara h,K.Ueno z, Y.Unno c,S.Uno h,hiroda h,G.Varner g,K.E.Varvell an,C.C.Wang z,C.H.Wang y,J.G.Wang ba,M.-Z.Wang z,Y.Watanabe at,E.Won o,B.D.Yabsley ba,Y.Yamada h, A.Yamaguchi ar,Y.Yamashita ab,M.Yamauchi h,H.Yanai ac,P.Yeh z,Y.Yuan j,Y.Yusa ar,J.Zhang ay,Z.P.Zhang ak,Y.Zheng g,and D.ˇZontar aya Aomori University,Aomori,Japanb Budker Institute of Nuclear Physics,Novosibirsk,Russiac Chiba University,Chiba,Japand Chuo University,Tokyo,Japane University of Cincinnati,Cincinnati,OH,USAf University of Frankfurt,Frankfurt,Germanyg University of Hawaii,Honolulu,HI,USAh High Energy Accelerator Research Organization(KEK),Tsukuba,Japani Hiroshima Institute of Technology,Hiroshima,Japanj Institute of High Energy Physics,Chinese Academy of Sciences,Beijing,PRChinak Institute of High Energy Physics,Vienna,Austria ℓInstitute for Theoretical and Experimental Physics,Moscow,Russiam J.Stefan Institute,Ljubljana,Slovenian Kanagawa University,Yokohama,Japano Korea University,Seoul,South Koreap Kyoto University,Kyoto,Japanq Kyungpook National University,Taegu,South Korear Institut de Physique des Hautes´Energies,Universit´e de Lausanne,Lausanne,Switzerlands University of Ljubljana,Ljubljana,Sloveniat University of Maribor,Maribor,Sloveniau University of Melbourne,Victoria,Australiav Nagoya University,Nagoya,Japanw Nara Women’s University,Nara,Japanx National Kaohsiung Normal University,Kaohsiung,Taiwany National Lien-Ho Institute of Technology,Miao Li,Taiwanz National Taiwan University,Taipei,Taiwanaa H.Niewodniczanski Institute of Nuclear Physics,Krakow,Polandab Nihon Dental College,Niigata,Japanac Niigata University,Niigata,Japanad Osaka City University,Osaka,Japanae Osaka University,Osaka,Japanaf Panjab University,Chandigarh,Indiaag Peking University,Beijing,PR Chinaah Princeton University,Princeton,NJ,USAai RIKEN BNL Research Center,Brookhaven,NY,USAaj Saga University,Saga,Japanak University of Science and Technology of China,Hefei,PR ChinaaℓSeoul National University,Seoul,South Koreaam Sungkyunkwan University,Suwon,South Koreaan University of Sydney,Sydney,NSW,Australiaao Tata Institute of Fundamental Research,Bombay,Indiaap Toho University,Funabashi,Japanaq Tohoku Gakuin University,Tagajo,Japanar Tohoku University,Sendai,Japanas University of Tokyo,Tokyo,Japanat Tokyo Institute of Technology,Tokyo,Japanau Tokyo Metropolitan University,Tokyo,Japanav Tokyo University of Agriculture and Technology,Tokyo,Japanaw Toyama National College of Maritime Technology,Toyama,Japanay University of Tsukuba,Tsukuba,Japanaz Utkal University,Bhubaneswer,Indiaba Virginia Polytechnic Institute and State University,Blacksburg,VA,USAbb Yokkaichi University,Yokkaichi,Japanbc Yonsei University,Seoul,South KoreaB events collected with the Belle detector at KEKB.Thebranching fractions B(B+→ρ0π+)=(8.0+2.3+0.7−2.0−0.7)×10−6and B(B0→ρ±π∓)=(20.8+6.0+2.8−6.3−3.1)×10−6are obtained.In addition,a90%confidence level upper limitof B(B0→ρ0π0)<5.3×10−6is reported.Key words:ρπ,branching fractionPACS:13.25.hw,14.40.Nd1on leave from Nova Gorica Polytechnic,Nova Gorica,Sloveniamodes are examined.Here and throughout the text,inclusion of charge con-jugate modes is implied and for the neutral decay,B0→ρ±π∓,the notation implies a sum over both the modes.The data sample used in this analysis was taken by the Belle detector[9]at KEKB[10],an asymmetric storage ring that collides8GeV electrons against3.5GeV positrons.This produces Υ(4S)mesons that decay into B0B pairs.The Belle detector is a general purpose spectrometer based on a1.5T su-perconducting solenoid magnet.Charged particle tracking is achieved with a three-layer double-sided silicon vertex detector(SVD)surrounded by a central drift chamber(CDC)that consists of50layers segmented into6axial and5 stereo super-layers.The CDC covers the polar angle range between17◦and 150◦in the laboratory frame,which corresponds to92%of the full centre of mass(CM)frame solid angle.Together with the SVD,a transverse momen-tum resolution of(σp t/p t)2=(0.0019p t)2+(0.0030)2is achieved,where p t is in GeV/c.Charged hadron identification is provided by a combination of three devices: a system of1188aerogelˇCerenkov counters(ACC)covering the momentum range1–3.5GeV/c,a time-of-flight scintillation counter system(TOF)for track momenta below1.5GeV/c,and dE/dx information from the CDC for particles with very low or high rmation from these three devices is combined to give the likelihood of a particle being a kaon,L K,or pion, Lπ.Kaon-pion separation is then accomplished based on the likelihood ratio Lπ/(Lπ+L K).Particles with a likelihood ratio greater than0.6are identified as pions.The pion identification efficiencies are measured using a high momentum D∗+data sample,where D∗+→D0π+and D0→K−π+.With this pion selection criterion,the typical efficiency for identifying pions in the momentum region0.5GeV/c<p<4GeV/c is(88.5±0.1)%.By comparing the D∗+data sample with a Monte Carlo(MC)sample,the systematic error in the particle identification(PID)is estimated to be1.4%for the mode with three charged tracks and0.9%for the modes with two.Surrounding the charged PID devices is an electromagnetic calorimeter(ECL) consisting of8736CsI(Tl)crystals with a typical cross-section of5.5×5.5cm2 at the front surface and16.2X0in depth.The ECL provides a photon energy resolution of(σE/E)2=0.0132+(0.0007/E)2+(0.008/E1/4)2,where E is in GeV.Electron identification is achieved by using a combination of dE/dx measure-ments in the CDC,the response of the ACC and the position and shape of the electromagnetic shower from the ECL.Further information is obtained from the ratio of the total energy registered in the calorimeter to the particle momentum,E/p lab.Charged tracks are required to come from the interaction point and have transverse momenta above100MeV/c.Tracks consistent with being an elec-tron are rejected and the remaining tracks must satisfy the pion identification requirement.The performance of the charged track reconstruction is studied using high momentumη→γγandη→π+π−π0decays.Based on the relative yields between data and MC,we assign a systematic error of2%to the single track reconstruction efficiency.Neutral pion candidates are detected with the ECL via their decayπ0→γγ. Theπ0mass resolution,which is asymmetric and varies slowly with theπ0 energy,averages toσ=4.9MeV/c2.The neutral pion candidates are selected fromγγpairs by requiring that their invariant mass to be within3σof the nominalπ0mass.To reduce combinatorial background,a selection criteria is applied to the pho-ton energies and theπ0momenta.Photons in the barrel region are required to have energies over50MeV,while a100MeV requirement is made for photons in the end-cap region.Theπ0candidates are required to have a momentum greater than200MeV/c in the laboratory frame.Forπ0s from BE2beam−p2B and the energy difference∆E=E B−E beam.Here, p B and E B are the momentum and energy of a B candidate in the CM frame and E beam is the CM beam energy.An incorrect mass hypothesis for a pion or kaon produces a shift of about46MeV in∆E,providing extra discrimination between these particles.The width of the M bc distributions is primarily due to the beam energy spread and is well modelled with a Gaussian of width 3.3MeV/c2for the modes with a neutral pion and2.7MeV/c2for the mode without.The∆E distribution is found to be asymmetric with a small tail on the lower side for the modes with aπ0.This is due toγinteractions withmaterial in front of the calorimeter and shower leakage out of the calorimeter. The∆E distribution can be well modelled with a Gaussian when no neutral particles are present.Events with5.2GeV/c2<M bc<5.3GeV/c2and|∆E|< 0.3GeV are selected for thefinal analysis.The dominant background comes from continuum e+e−→qB events and jet-like qi,j|p i||p j|P l(cosθij)i,k|p i||p k|,r l=),where L s and L qqD0π+ decays.By comparing the yields in data and MC after the likelihood ratiorequirement,the systematic errors are determined to be4%for the modes with aπ0and6%for the mode without.Thefinal variable used for continuum suppression is theρhelicity angle,θh, defined as the angle between the direction of the decay pion from theρin the ρrest frame and theρin the B rest frame.The requirement of|cosθh|>0.3 is made independently of the likelihood ratio as it is effective in suppressing the background from B decays as well as the qB events is used[14].The largest component of this background is found to come from decays of the type B→Dπ;when the D meson decays via D→π+π−,events can directly reach the signal region while the decay D→K−π+can reach the signal region with the kaon misidentified as a pion.Decays with J/ψandψ(2S) mesons can also populate the signal region if both the daughter leptons are misidentified as pions.These events are excluded by making requirements on the invariant mass of the intermediate particles:|M(π+π−)−M D0|>0.14 GeV/c2,|M(π+π0)−M D+|>0.05GeV/c2,|M(π+π−)−M J/ψ|>0.07GeV/c2 and|M(π+π−)−Mψ(2S)|>0.05GeV/c2.The widest cut is made around the D0mass to account for the mass shift due to misidentifying the kaons in D0 decays as pions.Fig.1shows the∆E and M bc distributions for the three modes analysed after all the selection criteria have been applied.The∆E and M bc plots are shown for events that lie within3σof the nominal M bc and∆E values,respectively. The signal yields are obtained by performing maximum likelihoodfits,each using a single signal function and one or more background functions.The signal functions are obtained from the MC and adjusted based on comparisons of B+→B0are assumed to be equal.The M bc distribution for all modes isfitted with a single Gaussian and an ARGUS background function[15].The normalization of the ARGUS function is left tofloat and shape of the function isfixed from the∆E sideband:−0.25 GeV<∆E<−0.08GeV and5.2GeV/c2<M bc<5.3GeV/c2.For the mode with only charged pions in thefinal state,the∆E distribution isfitted with a single Gaussian for the signal and a linear function withfixed shape for the continuum background.The normalization of the linear function is left to float and the slope isfixed from the M bc sideband,5.2GeV/c2<M bc<5.26GeV/c2,|∆E|<0.3GeV.There are also other rare B decays that are expected to contaminate the∆E distribution.For the mode without aπ0,these modes are of the type B0→h+h−(where h denotes aπor K),B→ρρ(including all combinations of charged and neutralρmesons,where the polarizations of theρmesons are assumed to be longitudinal)and B→Kππ(including the decays B+→ρ0K+,B+→K∗0π+,B+→K∗0(1430)0π+,B+→f0(980)K+ and B+→f0(1370)K+)[16].These background modes are accounted for by using smoothed histograms whose shapes have been determined by combining MC distributions.The three B→ρρmodes are combined into one histogram. The normalization of this component is allowed tofloat in thefit due to the uncertainty in the branching fractions of the B→ρρmodes.Likewise,the B→hh and all the B→Kππmodes are combined to form one hh and one Kππcomponent.The normalizations of these components arefixed to their expected yields,which are calculated using efficiencies determined by MC and branching fractions measured by previous Belle analyses[16,17].The∆Efits for the modes with aπ0in thefinal state have the signal compo-nent modelled by a Crystal Ball function[18]to account for the asymmetry in the∆E distribution.As for the B+→ρ0π+mode,the continuum background is modelled by a linear function withfixed slope.Unlike the B+→ρ0π+mode, a component is included for the background from the b→c transition.The pa-rameterization for rare B decays includes one component for the B→Kππ0 modes(B0→ρ+K−and B0→K∗+π−)[19]and one for all the B→ρρmodes.The normalization of the B→ρρcomponent is left tofloat while the other components from B decays arefixed to their expected yields.Table1summarizes the results of the∆Efits,showing the number of events, signal yields,reconstruction efficiencies,statistical significance and branching fractions or upper limits for eachfit.The statistical significance is defined assystematic error in thefitted signal yield is estimated by independently varying eachfixed parameter in thefit by1σ.Thefinal results are B(B+→ρ0π+)=(8.0+2.3+0.7−2.0−0.7)×10−6and B(B0→ρ±π∓)=(20.8+6.0+2.8−6.3−3.1)×10−6where thefirst error is statistical and the second is systematic.For theρ0π0mode,one standard deviation of the systematic error is added to the statistical limit to obtain a conservative upper limit at90%confidence of5.3×10−6.The possibility of a nonresonant B→πππbackground is also examined.To check for this type of background,the M bc and∆E yields are determined for differentππinvariant mass bins.Byfitting the M bc distribution inππinvariant mass bins with B→ρπand B→πππMC distributions,the nonresonant contribution is found to be below4%.To account for this possible background, errors3.7%and3.2%are added in quadrature to the systematic errors of the ρ+π−andρ0π+modes,respectively.Theππinvariant mass distributions are shown in Fig.2.Two plots are shown for theρ+π−andρ0π+modes,one with events from the M bc sideband superimposed over the events from the signal region(upper)and one with events from signal MC superimposed over events from the signal region with the sideband subtracted(lower).Fig.3 shows the distribution of the helicity variable,cosθh,for the two modes with all selection criteria applied except the helicity condition.Events fromρπdecays are expected to follow a cos2θdistribution while nonresonant and other background decays have an approximately uniform distribution.The helicity plots are obtained byfitting the M bc distribution in eight helicity bins ranging from−1to1.The M bc yield is then plotted against the helicity bin for each mode and the expected MC signal distributions are superimposed.Both the ππmass spectrum and the helicity distributions provide evidence that the signal events are consistent with being fromρπdecays.The results obtained here can be used to calculate the ratio of branching frac-tions R=B(B0→ρ±π∓)/B(B+→ρ0π+),which gives R=2.6±1.0±0.4, where thefirst error is statistical and second is systematic.This is consistent with values obtained by CLEO[20]and BaBar[21,22]as shown in Table2. Theoretical calculations done at tree level assuming the factorization approx-imation for the hadronic matrix elements give R∼6[3].Calculations that include penguin contributions,off-shell B∗excited states or additionalππres-onances[4–8]might yield better agreement with the the measured value of R.In conclusion,statistically significant signals have been observed in the B→ρπmodes using a31.9×106BWe wish to thank the KEKB accelerator group for the excellent operation of the KEKB accelerator.We acknowledge support from the Ministry of Ed-ucation,Culture,Sports,Science,and Technology of Japan and the Japan Society for the Promotion of Science;the Australian Research Council and the Australian Department of Industry,Science and Resources;the National Science Foundation of China under contract No.10175071;the Department of Science and Technology of India;the BK21program of the Ministry of Education of Korea and the CHEP SRC program of the Korea Science and Engineering Foundation;the Polish State Committee for Scientific Research under contract No.2P03B17017;the Ministry of Science and Technology of the Russian Federation;the Ministry of Education,Science and Sport of the Republic of Slovenia;the National Science Council and the Ministry of Education of Taiwan;and the U.S.Department of Energy.References[1] A.E.Snyder and H.R.Quinn,Phys.Rev.D48,2139(1993).[2]I.Bediaga,R.E.Blanco,C.G¨o bel,and R.M´e ndez-Galain,Phys.Rev.Lett.81,4067(1998).[3]M.Bauer,B.Stech,and M.Wirbel,Z.Phys.C34,103(1987).[4] A.Deandrea et al.,Phys.Rev.D62,036001(2000).[5]Y.H.Chen,H.Y.Cheng,B.Tseng and K.C.Yang,Phys.Rev.D60,094014(1999).[6] C.D.Lu and M.Z.Yang,Eur.Phys.J C23,275(2002).[7]J.Tandean and S.Gardner,SLAC-PUB-9199;hep-ph/0204147.[8]S.Gardner and Ulf-G.Meißner,Phys.Rev.D65,094004(2002).[9]Belle Collaboration,A.Abashian et al.,Nucl.Instr.and Meth.A479,117(2002).[10]E.Kikutani ed.,KEK Preprint2001-157(2001),to appear in Nucl.Instr.andMeth.A.[11]G.C.Fox and S.Wolfram,Phys.Rev.Lett.41,1581(1978).[12]This modification of the Fox-Wolfram moments wasfirst proposed in a seriesof lectures on continuum suppression at KEK by Dr.R.Enomoto in May and June of1999.For a more detailed description see Belle Collaboration,K.Abe et al.,Phys.Lett.B511,151(2001).[13]CLEO Collaboration,D.M.Asner et al.,Phys.Rev.D53,1039(1996).[14]These MC events are generated with the CLEO group’s QQ program,see/public/CLEO/soft/QQ.The detector response is simulated using GEANT,R.Brun et al.,GEANT 3.21,CERN Report DD/EE/84-1,1984.[15]The ARGUS Collaboration,H.Albrecht et al.,Phys.Lett.B241,278(1990).[16]Belle Collaboration,A.Garmash et al.,Phys.Rev.D65,092005(2002).[17]Belle Collaboration,K.Abe et al.,Phys.Rev.Lett.87,101801(2001).[18]J.E.Gaiser et al.,Phys.Rev.D34,711(1986).[19]Belle Collaboration,K.Abe et al.,BELLE-CONF-0115,submitted as acontribution paper to the2001International Europhysics Conference on High Energy Physics(EPS-HEP2001).[20]CLEO Collaboration,C.P.Jessop et al.,Phys.Rev.Lett.85,2881(2000).[21]Babar Collaboration,B.Aubert et al.,submitted as a contribution paper tothe20th International Symposium on Lepton and Photon Interactions at High Energy(LP01);hep-ex/0107058.[22]BaBar Collaboration,B.Aubert et al.,submitted as a contribution paper tothe XXXth International Conference on High Energy Physics(ICHEP2000);hep-ex/0008058.Table1∆Efit results.Shown for each mode are the number of events in thefit,the signal yield,the reconstruction efficiency,the branching fraction(B)or90%confidence level upper limit(UL)and the statistical significance of thefit.Thefirst error in the branching fraction is statistical,the second is systematic.ρ0π+15424.3+6.9−6.29.68.0+2.3+0.7−2.0−0.74.4σρ+π−30144.6+12.8−13.46.820.8+6.0+2.8−6.3−3.13.7σρ0π0116−4.4±8.58.5<5.3-Experiment B(B0→ρ±π∓)×10−6B(B+→ρ0π+)×10−6RE v e n t s /16 M e VE v e n t s /3 M e V /c2(b) ρ0π+Signal backgrd02.557.51012.51517.52022.55.25.225 5.25 5.2755.3E v e n t s /18 M e VE v e n t s /2 M e V /c2(d) ρ+π-Signal backgrd051015202530355.25.225 5.25 5.2755.3∆E(GeV)E v e n t s /18 M e V(e) ρ0π024681012-0.2-0.10.10.2(GeV/c 2)E v e n t s /2 M e V /c2M bc (f) ρ0πSignal backgrd02468101214165.25.225 5.25 5.2755.3Fig.1.The ∆E (left)and M bc (right)fits to the three B →ρπmodes:ρ0π+,ρ+π−and ρ0π0.The histograms show the data,the solid lines show the total fit and the dashed lines show the continuum component.In (a)the contribution from the B →ρρand B →hh modes is shown by the cross hatched component.In (c)the cross hatched component shows the contribution from the b →c transition and B →ρρmodes.102030405060+0(GeV/c 2)E v e n t s /0.1 G e V /c2M(π+π0)(GeV/c 2)E v e n t s /0.1 G e V /c2(GeV/c 2)E v e n t s /0.1 G e V /c2+-(GeV/c 2)E v e n t s /0.1 G e V /c2M(π+ π-)510152025Fig.2.The M (ππ)distributions for B 0→ρ±π∓(left)and B +→ρ0π+(right)events in the signal region.Plots (a)and (b)show sideband events superimposed;plots (c)and (d)show the sideband subtracted plots with signal MC superimposed.-1-0.500.51M b c y i e l d (E v e n t s )cos θh-1-0.500.51M b c y i e l d (E v e n t s )cos θhFig.3.The ρmeson helicity distributions for B 0→ρ±π∓(a)and B +→ρ0π+(b).Signal MC distributions are shown superimposed.。
Masses and decay constants of B_q mesons in the QCD string approach
a rXiv:h ep-ph/61193v116Oct26Masses and decay constants of B q mesons in the QCD string approach A.M.Badalian ∗and Yu.A.Simonov †Institute of Theoretical and Experimental Physics,Moscow,Russia B.L.G.Bakker ‡Vrije Universiteit,Amsterdam,The Netherlands February 2,2008Abstract The relativistic string Hamiltonian is used to calculate the masses and decay constants of B q mesons:they appear to be expressed through onlythree fundamental values:the string tension σ,αs ,and the quark pole masses.The values f B =186MeV,f B s =222MeV are calculated while f B c depends on the c -quark pole mass used,namely f B c =440(424)MeV for m c =1.40(1.35)GeV.For the 1P states we predict the spin-averaged masses:¯M (B J )=5730MeV and ¯M (B sJ )=5830MeV which are in good agreement with the recent data of the D0and CDF Collaborations,at the same time owningto the string correction being by ∼50MeV smaller than in other calculations.1IntroductionThe decay constants of pseudoscalar (P)mesons f P can be directly mea-sured in P →µνdecays [1]and therefore they can be used as an importantcriterium to compare different theoretical approaches and estimate their ac-curacy.Although during the last decade f P were calculated many times:in potential models[2,3,4],the QCD sum rule method[5],and in lattice QCD [6,7],here we again address the properties of the B,B s,B c mesons for several reasons.First,we use here the relativistic string Hamiltonian(RSH)[8],which is derived from the QCD Lagrangian with the use of thefield correlator method (FCM)[9]and successfully applied to light mesons and heavy quarkonia [10,11].Here we show that the meson Green’s function and decay constants can also be derived with the use of FCM.Second,the remarkable feature of the RSH H R and also the correlator of the currents G(x)is that they are fully determined by a minimal number of fundamental parameters:the string tensionσ,ΛMS=250(5)MeV;(1) and the pole masses taken arem u(d)=0;m s=170(10)MeV;m c=1.40GeV;m b=4.84GeV.(2) Third,recently new data on the masses of B c and the P-wave mesons: B1,B2,and B s2have been reported by the D0and CDF Collaborations [12,13],which give additional information on the B q-meson spectra.Here we calculate the spin-averaged masses of the P-wave states B and B s.We would like to emphasize here that in our relativistic calculations no constituent masses are used.In the meson mass formula an overall(fitting) constant,characteristic for potential models,is absent and the whole scheme appears to be rigid.Nevertheless,we take into account an important nonperturbative(NP) self-energy contribution to the quark mass,∆SE(q)(see below eq.(18)).For the heavy b quark∆SE(b)=0and for the c quark∆SE(c)≃−20MeV[10], which is also small.For any kind of mesons we use a universal static potential with pure scalarconfining term,V0(r)=σr−4r,(3)2where the couplingαB(r)possesses the asymptotic freedom property and saturates at large distances withαcrit(n f=4)=0.52[14].The coupling can be expressed throughαB(q)in momentum space,αB(r)=2qαB(q),(4)whereαB(q)=4πβ20ln t BΛ2B.Here the QCD constantΛB,is expressed as[15]ΛB(n f)=Λ2β0· 319n f (6)and M B(σ,ΛB)=(1.00±0.05)GeV is the so called background mass[14]. For heavy-light mesons withΛ2+m2i+p2In (8)m 1(m 2)is the pole (current)mass of a quark (antiquark).The variable ωi is defined from extremum condition,which is taken either from(1)The exact condition:∂H 0p 2+m 2i .(10)ThenH 0ϕn = p 2+m 22+V 0(r ) ϕn =M n ϕn(11)reduces to the Salpeter equation,which just defines ωi (n )=∂˜ωi =0(the so-called einbein approxima-tion).As shown in [9]the difference between ωi and ˜ωi is <∼5%.For the RSH (7)the spin-averaged massM (nL )=ω12+m 212ωb +E n (µ)−2σηf p 2+m 2i nL ;µ=ω1ωbπωf ;(14)with ηf =0.9for a u (d )quark,ηf ∼=0.7for an s quark,ηf =0.4for a c quark,and ηb =0.Therefore,for a b quark ∆SE (b )=0.The mass formula(12)does not contain any overall constant C .Note that the presence of C violates linear behavior of Regge trajectories.The calculated masses of the low-lying states of B ,B s ,and B c mesons are given in Table 2,as well as their values taken from [2,3,6,7].It is of interest to notice that in our calculations the masses of the P -wave states appear to be by 30-70MeV lower than in [2]due to taking into account a string correction [11].4Table1:Masses of the low-lying B q mesons in the QCD String Approach B5280(5)a5279.0(5)5310252753B1(1P)¯M=5730a5721(8)D05734(5)CDFB s5369a5369.6(24)5390253623B s2¯M=58305839(3)D058802B∗c6330(5)a633826321(20)63Current CorrelatorThe FCM can be also used to define the correlator GΓ(x)of the currents jΓ(x),jΓ(x)=¯ψ1(x)Γψ2(x),(15) for S,P,V,and A channels(here the operatorΓ=t a⊗(1,γ5,γµ,iγµγ5)).The correlator,GΓ(x)≡ jΓ(x)jΓ(0) vac,(16) with the use of spectral decomposition of the currents jΓand the definition, vac|¯ψ1γ0γ5ψ2|P n(k=0) =f P n M n,(A,P)vac|¯ψ1γµψ2|V n(k,ε) =f V n M nεµ,(V)(17) can be presented as[3]GΓ(x)d x= n M n0|YΓe−H0T|0ω1ω2N c YΓ=p2 .(20)3Then from Eqs.(18)and(19)one obtains the following analytical expression for the decay constants(for a given state labelled n):f P(V)n 2=2N c M n|ϕn(0)|2.(21)This very transparent formula contains only well defined factors:ω1andωb, the meson mass M n,andϕn the eigenvector ofˆH0.Then in the P channelf P n 2=6(m1m2+ω1ω2− p2 )Table2:Pseudoscalar constants of B q mesons(in MeV)f B189216(34)186(5)f B s218249(42)222(2)f B swhere the w.f.at the origin,ϕn(0),is a relativistic one.In the nonrelativistic limitωi→m i,ϕn(0)→ϕNR n(0)and one comes to the standard expression:f P n(0) 2→12•In our analytic approach with minimal input of fundamental parame-ters(σ,αs,m i)the calculated decay constants are f B=186MeV,f B s=222MeV,f B s/f B=1.19.•For B c the decay constant is very sensitive to m c(pole):f B c=440MeV(m c=1.40GeV)and f B c=425MeV(m c=1.35GeV)References[1]D.Silverman and H.Yao,Phys.Rev.D38,214(1988).[2]S.Godfrey and N.Isgur,Phys.Rev.D32,189(1985);S.Godfrey,Phys.Rev.D70,054017(2004).[3]D.Ebert,R.N.Faustov,and V.O.Galkin,hep-ph/0602110;Mod.Phys.Lett.A17,803(2002),and references therein.[4]G.Cvetic,C.S.Kim,G.L.Wang,and W.K.Namgung,Phys.Lett.B596,84(2004).[5]M.Jamin,nge,Phys.Rev.D65,056005(2002)and referencestherein.[6]A.Ali Khan et al.,Phys.Rev.D70,114501(2004),ibid.64,054504(2004);C.T.H.Davies et al.,Phys.Rev.Lett.92,022001(2004).[7]A.S.Kronfeld,hep-lat/0607011and references therein;I.F.Allison etal.,Phys Rev.Lett.94172001(2005);A.Gray et al.,Phys.Rev.Lett.95,212001(2005).[8]A.Yu.Dubin,A.B.Kaidalov,and Yu.A.Simonov,Phys.Lett.B323,41(1994);Phys.Atom Nucl.56,1745(1993);E.L.Gubankova and A.Yu.Dubin,Phys.Lett.B334,180(1994).[9]H.G.Dosch and Yu.A.Simonov,Phys.Lett.B205,339(1988);Yu.A.Simonov,Z.Phys.C53,419(1992);Yu.S.Kalashnikova,A.V.Nefediev,and Yu.A.Simonov,Phys.Rev.D64,014037(2001);Yu.A.Simonov,Phys.Atom.Nucl.67,553(2004).[10]A.M.Badalian,A.I.Veselov,and B.L.G.Bakker,Phys.Rev.D70,016007(2004);Phys.Atom.Nucl.67,1367(2004).8[11]A.M.Badalian and B.L.G.Bakker,Phys.Rev.D66,034025(2002);A.M.Badalian,B.L.G.Bakker,and Yu.A.Simonov,Phys.Rev.D66,034025(2002).[12]P.Catastini(for the D0and CDF Collab.),hep-ex/0605051;M.D.Cor-coran,hep-ex/0506061.[13]D.Acosta et al.(CDF Collab.),Phys.Rev.Lett.96,202001(2006);hep-ex/0508022.[14]A.M.Badalian and D.S.Kuzmenko,Phys.Rev.D65,016004(2002);A.M.Badalian and Yu.A.Simonov,Phys.Atom.Nucl.60,636(1997).[15]M.Peter,Phys.Rev.Lett.76,602(1997);Y.Schr¨o der,Phys.Lett.B447,321(1999).[16]Yu.A.Simonov,Phys.Lett.B515,137(2001).[17]Particle Data Group,S.Eidelman,et al.,Phys.Lett.B592,1(2004).[18]A.M.Badalian and Yu.A.Simonov(in preparation).9。
Screening mass responses to the chemical potential at finite temperature
−5 0.00
0.01 ma
0.02
0.03
(4) .
ˆ 2 /dµ Figure 1. d2 M ˆ2 S for the pseudoscalar meson versus ma at T < Tc (β = 5.26, triangles) and T > Tc (β = 5.34, circles). Extrapolation to ma = 0 is also shown.
−
Lx 2
10
L2 + x 4 Lx x ˆ− 2 .
5
0
−Lx
ˆ tanh M
In this work, we consider the flavor non-singlet mesons in QCD with two flavors. The hadron correlator is then given by H (n)H (0)† = = G Tr P (ˆ µu )n0 ΓP (ˆ µd )0n Γ
3. Numerical Simulations and Results The simulations have been performed at finite temperature T /Tc ∈∼ [0.9, 1.1] on a 16 × 82 × 4 lattice with standard Wilson gauge action and with two dynamical flavors of staggered quarks. We use the R-algorithm, with quark masses ma = 0.0125, 0.017 and 0.025. We also use a cornertype wall source after Coulomb gauge fixing in each (y, z, t)-hyperplane. The first derivative of the pseudoscalar meson correlator with respect to the isoscalar chemical potential is identically zero. For the isovector chemical potential, our simulation values for the first derivative are very small in both phases. 3.1. Response of the pseudoscalar meson to the isoscalar chemical potential In the low temperature phase, the dependence of the mass on µ ˆ S is small. This behavior is to be expected, since, below the critical temperature and in the vicinity of zero µ ˆS , the pseudoscalar meson is still a Goldstone boson. In fact, the chiral extrapolation of the isoscalar response is
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|]
f
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The called “Longstanding puzzle” in Charm decay!
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(3770)
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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
The decay $rho^{0}to pi^{+}+pi^{-}+gamma$ and the coupling constant g$_{rhosigmagamma}$
a rXiv:n ucl-t h /441v28Ma y2The decay ρ0→π++π−+γand the coupling constant g ρσγA.Gokalp ∗and O.Yilmaz †Physics Department,Middle East Technical University,06531Ankara,Turkey(February 8,2008)Abstract The experimental branching ratio for the radiative decay ρ0→π++π−+γis used to estimate the coupling constant g ρσγfor a set of values of σ-meson parameters M σand Γσ.Our results are quite different than the values of this constant used in the literature.PACS numbers:12.20.Ds,13.40.HqTypeset using REVT E XThe radiative decay processρ0→π++π−+γhas been studied employing different approaches[1,5].There are two mechanisms that can contribute to this radiative decay: thefirst one is the internal bremsstrahlung where one of the charged pions from the decay ρ0→π++π−emits a photon,and the second one is the structural radiation which is caused by the internal transformation of theρ-meson quark structure.Since the bremsstrahlung is well described by quantum electrodynamics,different methods have been used to estimate the contribution of the structural radiation.Singer[1]calculated the amplitude for this decay by considering only the bremsstrahlung mechanism since the decayρ0→π++π−is the main decay mode ofρ0-meson.He also used the universality of the coupling of theρ-meson to pions and nucleons to determine the coupling constant gρππfrom the knowledge of the coupling constant gρter,Renard [3]studied this decay among other vector meson decays into2π+γfinal states in a gauge invariant way with current algebra,hard-pion and Ward-identities techniques.He,moreover, established the correspondence between these current algebra results and the structure of the amplitude calculated in the single particle approximation for the intermediate states.In corresponding Feynman diagrams the structural radiation proceeds through the intermediate states asρ0→S+γwhere the meson S subsequently decays into aπ+π−pair.He concluded that the leading term is the pion bremsstrahlung and that the largest contribution to the structural radiation amplitude results from the scalarσ-meson intermediate state.He used the rough estimate gρσγ≃1for the coupling constant gρσγwhich was obtained with the spin independence assumption in the quark model.The coupling constant gρππwas determined using the then available experimental decay rate ofρ-meson and also current algebra results as3.2≤gρππ≤4.9.On the other hand,the coupling constant gσππwas deduced from the assumed decay rateΓ≃100MeV for theσ-meson as gσππ=3.4with Mσ=400MeV. Furthermore,he observed that theσ-contribution modifies the shape of the photon spectrum for high momenta differently depending on the mass of theσ-meson.We like to note, however,that the nature of theσ-meson as a¯q q state in the naive quark model and therefore the estimation of the coupling constant gρσγin the quark model have been a subject ofcontroversy.Indeed,Jaffe[6,7]lately argued within the framework of lattice QCD calculation of pseudoscalar meson scattering amplitudes that the light scalar mesons are¯q2q2states rather than¯q q states.Recently,on the other hand,the coupling constant gρσγhas become an important input for the studies ofρ0-meson photoproduction on nucleons.The presently available data[8] on the photoproduction ofρ0-meson on proton targets near threshold can be described at low momentum transfers by a simple one-meson exchange model[9].Friman and Soyeur [9]showed that in this picture theρ0-meson photoproduction cross section on protons is given mainly byσ-exchange.They calculated theγσρ-vertex assuming Vector Dominance of the electromagnetic current,and their result when derived using an effective Lagrangian for theγσρ-vertex gives the value gρσγ≃2.71for this coupling ter,Titov et al.[10]in their study of the structure of theφ-meson photoproduction amplitude based on one-meson exchange and Pomeron-exchange mechanisms used the coupling constant gφσγwhich they calculated from the above value of gρσγinvoking unitary symmetry arguments as gφσγ≃0.047.They concluded that the data at low energies near threshold can accommodate either the second Pomeron or the scalar mesons exchange,and the differences between these competing mechanisms have profound effects on the cross sections and the polarization observables.It,therefore,appears of much interest to study the coupling constant gρσγthat plays an important role in scalar meson exchange mechanism from a different perspective other than Vector Meson Dominance as well.For this purpose we calculate the branching ratio for the radiative decayρ0→π++π−+γ,and using the experimental value0.0099±0.0016for this branching ratio[11],we estimate the coupling constant gρσγ.Our calculation is based on the Feynman diagrams shown in Fig.1.Thefirst two terms in thisfigure are not gauge invariant and they are supplemented by the direct term shown in Fig.1(c)to establish gauge invariance.Guided by Renard’s[3]current algebra results,we assume that the structural radiation amplitude is dominated byσ-meson intermediate state which is depicted in Fig. 1(d).We describe theρσγ-vertex by the effective LagrangianL int.ρσγ=e4πMρMρ)2 3/2.(3)The experimental value of the widthΓ=151MeV[11]then yields the value g2ρππ2gσππMσ π· πσ.(4) The decay width of theσ-meson that follows from this effective Lagrangian is given asΓσ≡Γ(σ→ππ)=g2σππ8 1−(2Mπ2iΓσ,whereΓσisgiven by Eq.(5).Since the experimental candidate forσ-meson f0(400-1200)has a width (600-1000)MeV[11],we obtain a set of values for the coupling constant gρσγby considering the ranges Mσ=400-1200MeV,Γσ=600-1000MeV for the parameters of theσ-meson.In terms of the invariant amplitude M(Eγ,E1),the differential decay probability for an unpolarizedρ0-meson at rest is given bydΓ(2π)31Γ= Eγ,max.Eγ,min.dEγ E1,max.E1,min.dE1dΓ[−2E2γMρ+3EγM2ρ−M3ρ2(2EγMρ−M2ρ)±Eγfunction ofβin Fig.5.This ratio is defined byΓβRβ=,Γtot.= Eγ,max.50dEγdΓdEγ≃constant.(10)ΓσM3σFurthermore,the values of the coupling constant gρσγresulting from our estimation are in general quite different than the values of this constant usually adopted for the one-meson exchange mechanism calculations existing in the literature.For example,Titov et al.[10] uses the value gρσγ=2.71which they obtain from Friman and Soyeur’s[9]analysis ofρ-meson photoproduction using Vector Meson Dominance.It is interesting to note that in their study of pion dynamics in Quantum Hadrodynamics II,which is a renormalizable model constructed using local gauge invariance based on SU(2)group,that has the sameLagrangian densities for the vertices we use,Serot and Walecka[14]come to the conclusion that in order to be consistent with the experimental result that s-waveπN-scattering length is anomalously small,in their tree-level calculation they have to choose gσππ=12.Since they use Mσ=520MeV this impliesΓσ≃1700MeV.If we use these values in our analysis,we then obtain gρσγ=11.91.Soyeur[12],on the other hand,uses quite arbitrarly the values Mσ=500 MeV,Γσ=250MeV,which in our calculation results in the coupling constant gρσγ=6.08.We like to note,however,that these values forσ-meson parameters are not consistent with the experimental data onσ-meson[11].Our analysis and estimation of the coupling constant gρσγusing the experimental value of the branching ratio of the radiative decayρ0→π++π−+γgive quite different values for this coupling constant than used in the literature.Furthermore,since we obtain this coupling constant as a function ofσ-meson parameters,it will be of interest to study the dependence of the observables of the reactions,such as for example the photoproduction of vector mesons on nucleonsγ+N→N+V where V is the neutral vector meson, analyzed using one-meson exchange mechanism on these parameters.AcknowledgmentsWe thank Prof.Dr.M.P.Rekalo for suggesting this problem to us and for his guidance during the course of our work.We also wish to thank Prof.Dr.T.M.Aliev for helpful discussions.REFERENCES[1]P.Singer,Phys.Rev.130(1963)2441;161(1967)1694.[2]V.N.Baier and V.A.Khoze,Sov.Phys.JETP21(1965)1145.[3]S.M.Renard,Nuovo Cim.62A(1969)475.[4]K.Huber and H.Neufeld,Phys.Lett.B357(1995)221.[5]E.Marko,S.Hirenzaki,E.Oset and H.Toki,Phys.Lett.B470(1999)20.[6]R.L.Jaffe,hep-ph/0001123.[7]M.Alford and R.L.Jaffe,hep-lat/0001023.[8]Aachen-Berlin-Bonn-Hamburg-Heidelberg-Munchen Collaboration,Phys.Rev.175(1968)1669.[9]B.Friman and M.Soyeur,Nucl.Phys.A600(1996)477.[10]A.I.Titov,T.-S.H.Lee,H.Toki and O.Streltrova,Phys.Rev.C60(1999)035205.[11]Review of Particle Physics,Eur.Phys.J.C3(1998)1.[12]M.Soyeur,nucl-th/0003047.[13]S.I.Dolinsky,et al,Phys.Rep.202(1991)99.[14]B.D.Serot and J.D.Walecka,in Advances in Nuclear Physics,edited by J.W.Negeleand E.Vogt,Vol.16(1986).TABLESTABLE I.The calculated coupling constant gρσγfor differentσ-meson parametersΓσ(MeV)gρσγ500 6.97-6.00±1.58 8008.45±1.77600 6.16-6.68±1.85 80010.49±2.07800 5.18-9.11±2.64 90015.29±2.84900 4.85-10.65±3.14 90017.78±3.23Figure Captions:Figure1:Diagrams for the decayρ0→π++π−+γFigure2:The photon spectra for the decay width ofρ0→π++π−+γ.The contributions of different terms are indicated.Figure3:The pion energy spectra for the decay width ofρ0→π++π−+γ.The contri-butions of different terms are indicated.Figure4:The decay width ofρ0→π++π−+γas a function of minimum detected photon energy.Figure5:The ratio Rβ=Γβ。
Pi and PiPi Decays of Excited D Mesons
a r X i v :h e p -p h /0112223v 1 17 D e c 2001πand ππDecays of Excited D MesonsT.A.L¨a hde a and D.O.Riska aa HelsinkiInstitute of Physics,University of Helsinki,PL 64Helsinki,Finland(Received:February 1,2008)The πand ππdecay widths of the excited charm mesons are calculated using a Hamiltonian model within the framework of the covariant Blankenbecler-Sugar equation.The pion-light constituent quark coupling is described by the chiral pseudovector Lagrangian.1IntroductionThe pionic decay widths of the excited charm mesons (D mesons)are interesting observables,since they depend straightforwardly on the coupling of pions to light constituent quarks.The D mesons consist of one light (u,d )quark and a heavy charm (c )antiquark,of which it is only the light constituent quark that couples to pions.The coupling of light constituent quarks to pions may be described by the chiral model [1],which includes the pseudovector Lagrangian and,for ππdecay,also a Weinberg-Tomozawa term.In order to predict the decay widths of the excited D meson states,a model for the radial wavefunctions is needed.Here the interaction between the quarks is modeled as the sum of a screened one-gluon exchange (OGE)and a scalar linear confining interaction.The wavefunctions are obtained as solutions of the covariant Blankenbecler-Sugar equation [2].These are then used together with the chiral Lagrangian to obtain predictions for the π[3]and ππ[4]decays of the excited D mesons.1800200022002400260028003000320034001S 03S 1 1P 1 3P 0 3P 1 3P 2 1D 2 3D 1 3D 2 3D 3Empirical and calculated D meson spectra (State energies in MeV)DD *D ** ?D 1D 2*Experimental CalculatedFigure 1:Empirical and calculated spec-tra of the D meson from ref.[3].The D ∗is an S -wave spin-triplet state which lies almost exactly at threshold for decay to Dπ.The decay widths for πdecay of the D ∗are predicted here along with those of the four L =1states,which can de-cay to both D ∗πand Dπ.These states can also decay to D ∗ππand Dππ.Note that empirical data is only available for the spin triplet states with L =1and total angular momentum J =1and J =2.2Single pion decayThe chiralLagrangian describingthecoupling between pions and light constituent quarks may be written as [3]L =ig q A2f π4EE ′1−P 2−k 2/42f π2m ¯q +E +E ′4EE ′(E +m ¯q )(E ′+m ¯q )ωπ σq ·p ′+ p g qA =0.8729keV 64keV 41keV4f 2π¯ψq γµ τ· φπ×∂µ φπψq .(4)Together,the Lagrangians(1,4)give rise to amplitudes forππdecay,which are usually expressed in the form T=δab T++12fπ 24m q,(5)A−=0,(6) B+=− g q A s−m2q−12fπ2 2+4m2q 1u−m2q +1πwidth Total15.718.813.614.927.727.813.221.8。
磁共振中一些常用简化附缩写用语
( Homonuclear chemical shift ) COrrelation SpectroscopY
CP
Cross Polarization
CPD
Composite-Pulse Decoupling
CP/MAS
Cross Polarization/Magic Angle Spinning
BBDR
Broad Band Double Resonance
BIRD
Bilinear Rotation Decoupling
BOLD
Blood Oxygenation Level Dependent
BR-24
Burum & Rhim (pulse sequence)
CAMELSPIN
Cross-relaxation Appropriate for Minimolecules Emulated by Locked SPNs
GRASS
Gradient-Recalled Acquisition in the Steady State
GRASP
Gradient-Accelerated Spectroscopy
GROPE
Generalized compensation for Resonance Offset and Pulse length errors
MQ(C)
Multiple-Quantum ( Coherence )
MQF
Multiple-Quantum Filter
MQMAS
Multiple-Quantum Magic-Angle Spinning
MQS
Multi Quantum Spectroscopy
Parity-even and Parity-odd Mesons in Covariant Light-front Approach
–
–
fsu¯ (160)
22 (210) −186
11
–
–
fcu¯ (200)
86 (220) −127
45
130
−36
fcs¯ (230)
71 (230) −121
38
122
−38
fbu¯ (180) 112 (180) −123
68
140
−15
From Table 1 we see that the decay constants of light scalar resonances are sup-
for form factors in B → D, D∗, D∗∗ (D∗∗ denoting generic p-wave charmed mesons) transitions agree with those in the ISGW2 model.4 Relativistic effects are mild in
B → D transition, but they could be more prominent in heavy-to-light transitions,
especially at maximum recoil (q2 = 0). For example, we obtain V0Ba1 ay constants and form factors
Consider the decay constants for mesons with the quark content q1q¯2 in the 2S+1LJ = 1S0, 3P0, 3S1, 3P1, 1P1 configurations. In the SU(N)-flavor limit (m1 = m2) the decay constants fS(3P0) and f1P1 should vanish.6 In the heavy quark limit (m1 → ∞), it is more convenient to use the LjJ = P23/2, P13/2, P11/2 and P01/2 basis as the heavy quark spin sQ and the total angular momentum of the light
CP Asymmetries in Higgs decays to ZZ at the LHC
a r X i v :0708.3612v 1 [h e p -p h ] 27 A u g 2007CP Asymmetries in Higgs decays to ZZ at the LHCRohini M.Godbole 1,David ler 2,M.Margarete M¨u hlleitner 3,41Centre for High Energy Physics,Indian Institute of Science,Bangalore,560012,India.2Dept.of Physics and Astronomy,University of Glasgow,Glasgow G128QQ,U.K.3Theory Division,Physics Department,CERN,CH-1211Geneva 23,Switzerland.4Laboratoire d’Annecy-Le-Vieux de Physique Th´e orique,LAPTH,France.Abstract.We examine the effect of a general HZZ coupling through a study of the Higgs decay to leptons via Z bosons at the LHC.We discuss various methods for placing limits on additional couplings,including measurement of the partial width,threshold scans,and asymmetries constructed from angular observables.We find that only the asymmetries provide a definitive test of additional couplings.We further estimate the significances they provide.1.IntroductionThe verification of the Higgs mechanism as the cause of electroweak symmetry breaking and the discovery of the Higgs boson is the next big goal of particle physics.However,it is not enough to simply find a new resonance in the Higgs search channels at the next generation of colliders.One must ensure that this resonance is indeed the Higgs boson by measuring its properties:its CP and spin,to demonstrate its predicted scalar nature;its couplings to known particles,to verify that these couplings are proportional to the particle’s mass;and the Higgs self couplings,in order to reconstruct the Higgs potential itself.This will be a challenging programme and will not be fully realised at the Large Hadron Collider (LHC)(e.g.the quartic Higgs self coupling will be out of reach).However,such an analysis will be crucial in our investigation of electroweak symmetry breaking in scenarios where the suspected Higgs boson is all we find at the LHC,as well as scenarios where new physics is discovered.In the former case,testing for deviations from the Standard Model (SM)may provide clues to resolving some of the SM’s long standing problems;in the latter case,the Higgs boson properties will provide essential information on the nature of the new physics.It is interesting to note that the Higgs boson’s CP (and spin)is intimately related to its couplings to other SM particles,since its scalar or pseudoscalar nature allow or forbid certain tensor structures in the Higgs boson couplings.In this report,we investigate the tensor structure of the HZZ vertex in order to shed some light on the Higgs boson’s CP.We write down the most general tensor vertex for this coupling and investigate how the additional terms influence the decay H →ZZ (∗)→4leptons at the LHC.For a more detailed description of this analysis,see Ref.[1].The most general vertex for a spinless particle coupling to a pair of Z bosons,with four-momenta q 1and q 2,is given by,V µνHZZ=igm Zm 2Z+c ǫµναβp αk βwhere p=q1+q2and k=q1−q2,θW denotes the weak-mixing angle andǫµναβis the totally antisymmetric tensor withǫ0123=1.The CP conserving tree-level Standard Model coupling is recovered for a=1and b=c=0.Terms containing a and b are associated with the coupling of a CP-even Higgs,while that containing c is associated with that of a CP-odd Higgs boson.The simulanteous appearance of a non-zero a(and/or b)together with a non-zero c would lead to CP violation.In general these parameters can be momentum-dependent form factors that may be generated from loops containing new heavy particles or equivalently from the integration over heavy degrees of freedom giving rise to higher dimensional operators.The form factors b and c may,in general,be complex, but since an overall phase will not affect the observables studied here,we are free to adopt the convention that a is real.2.The total widthOne method of investigating the tensor structure of the HZZ coupling is to examine the threshold behaviour of the decay H→ZZ∗[2].Notice that the additional terms in the vertexwidth on the virtuality of the most virtual Z boson.width from the SM prediction.Alternatively,one could examine the magnitude of the total decay width for H→ZZ∗→4leptons to see if it differs from the SM.For the vertex of Equation1,the dependence on the coefficients a,b and c is given by,∂2ΓHm4H +|b|2m4H4+|c|28q21q22m2Zβ2 m4H ,(2)whereβis the usual Lorentz boost factor for the Z-bosons.(Notice that the only term with a linearβdependence(from the phase space)is proportional to a2,illustrating the principle described above for the threshold scan.)If additional terms are present one expects them toincrease or decrease the width according to this equation.We used the ATLAS study of Ref.[3,4] (including cuts and efficiencies)to estimate the number of signal and background events for the SM and CP-violating scenarios(scaling the signal according to Equation2).In Figure2we plot the number of standard deviations from the SM that the CP-violating scenario would imply,for a150GeV Higgs boson and an integrated luminosity of300fb−1(we set b=0for simplicity). The white area represents scenarios where the significance of the deviation is less than3σ,the light blue/grey region represents a3−5σdeviation,while the dark blue/grey region represents a greater than5σdeviation.This measurement would allow one to rule out much of the a−|c| parameter space,but does not allow one to definitively rule out(or place significant limits on) the CP-odd coupling|c|.A SM-like rate is perfectly consistent with a large value of|c|and a small value of a.3.Asymmetries as a probe of CP violationTo definitively ascertain whether or not extra tensor structures are present in the HZZ vertex one is better served by measuring asymmetries which vanish when such terms are absent.Such an asymmetry can be constructed from an observable,O,based on the angles of thefinal state leptons,Γ(O>0)−Γ(O<0)A=。
磁共振中一些常用的简化及缩写用语
Pseudoscalar Decay Constants $ f_{D} $ and $ f_{D_s} $ in Lattice QCD with Exact Chiral Sym
National Taiwan University, Taipei 106, Taiwan
Abstract
We determine the masses and decay constants of pseudoscalar mesons D, Ds, and K in quenched lattice QCD with exact chiral symmetry. For 100 gauge configurations generated with single-plaquette action at β = 6.1 on the 203 × 40 lattice, we compute point-to-point quark propagators for 30 quark masses in the range 0.03 ≤ mqa ≤ 0.80, and measure the time-correlation functions of pseudoscalar and vector mesons. The inverse lattice spacing a−1 is determined with the experimental input of fπ, while the strange quark bare mass msa = 0.08, and the charm quark bare mass mca = 0.80 are fixed such that the masses of the corresponding vector mesons are in good agreement with φ(1020) and J/ψ(3097) respectively. Our results of pseudoscalar-meson decay constants are fK = 152(6)(10) MeV, fD = 235(8)(14) MeV, and fDs = 266(10)(18) MeV.
CURRENTS AND THEIR COUPLINGS IN THE WEAK SECTOR OF THE STANDARD MODEL
(4)
which is effective four-fermion interaction with the Fermi constant given √the familiar 2 2 h ℓ by GF / 2 = g /(8mW ). Here Jµ and Jµ are known as the hadron and lepton currents, where
(2)
1 where t3L (i) is the weak isospin of fermion i ( + 1 2 for ui and νi ; − 2 for di and ℓi ) and qi is the charge of ψi in units of e. The three terms in the interaction Lagrangian of Eq. 1 represent the chargedcurrent weak interaction, the electromagnetic interaction and the neutral-current weak interaction respectively. Note that the Lorentz structure involves only vectors and axial vectors; there is no compelling experimental evidence for scalars, pseudoscalars or tensor constructions. The minimal Standard Model as described by Eq. 1 successfully3 explains W and Z decays, neutrino-hadron scattering, neutrino-electron scattering and parity-violating electron-hadron neutral-current experiments, providing that radiative corrections to order α, the fine-structure constant, are applied. In this chapter we will focus our discussion on the charged-current weak interaction in semi-leptonic decays involving quarks and leptons from the first family. As an example, consider the decay d → ue− ν e , for which the T -matrix is2
示差扫描量热计示值误差测量不确定度评定
化学分析计量CHEMICAL ANAL Y SIS AND METERAGE第30卷,第5期2021年5月V ol. 30,No. 5May 202185doi :10.3969/j.issn.1008–6145.2021.05.019示差扫描量热计示值误差测量不确定度评定戴宝峰(河北省计量监督检测研究院,石家庄 050200)摘要 采用示差扫描量热(DSC)法测定热分析标准物质的熔化温度和熔化热,对示值误差的测量不确定度进行评定。
建立示值误差的测量模型,分析不确定度来源,计算各不确定度分量,最终合成标准不确定度和扩展不确定度。
铟、锌的温度示值误差的扩展不确定度分别为0.34、0.62 ℃(k =2),热量示值误差的相对扩展不确定度均为1.2%(k =2)。
测量重复性引入的不确定度对测量结果影响最大。
关键词 示差扫描量热法;示值误差;不确定度中图分类号:O657.9 文献标识码:A 文章编号:1008–6145(2021)05–0085–04Evaluation of uncertainty in the measurement of indication error of differential scanning calorimeterDai Baofeng(Institute of Metrology of Hebei Province, Shijiazhuang 050200, China )Abstract The melting temperature and heat of reference materials for thermal analysis were determined by differential scanning calorimetry(DSC), and the measurement uncertainty of indication error was evaluated. The measurement model of indication error was established, the source of uncertainty was analyzed, each uncertainty component was calculated, and fi nally the standard uncertainty and expanded uncertainty were synthesized. The expanded uncertainty of indium and zinc temperature indication error was 0.34,0.62 ℃(k =2), respectively, and the relative expanded uncertainty of heat indication error was 1.2%(k =2). The uncertainty introduced by measurement repeatability has the greatest in fluence on the determination results.Keywords differential scanning calorimetry; indication error; uncertainty示差扫描量热(DSC)法是在程序控制温度下,测量输入到试样和参比物的功率差与温度差关系的一种技术[1]。
计量经济学中英文词汇对照
Controlled experiments Conventional depth Convolution Corrected factor Corrected mean Correction coefficient Correctness Correlation coefficient Correlation index Correspondence Counting Counts Covaห้องสมุดไป่ตู้iance Covariant Cox Regression Criteria for fitting Criteria of least squares Critical ratio Critical region Critical value
Asymmetric distribution Asymptotic bias Asymptotic efficiency Asymptotic variance Attributable risk Attribute data Attribution Autocorrelation Autocorrelation of residuals Average Average confidence interval length Average growth rate BBB Bar chart Bar graph Base period Bayes' theorem Bell-shaped curve Bernoulli distribution Best-trim estimator Bias Binary logistic regression Binomial distribution Bisquare Bivariate Correlate Bivariate normal distribution Bivariate normal population Biweight interval Biweight M-estimator Block BMDP(Biomedical computer programs) Boxplots Breakdown bound CCC Canonical correlation Caption Case-control study Categorical variable Catenary Cauchy distribution Cause-and-effect relationship Cell Censoring
测绘类词汇中英文对照(1)
测绘类词汇中英文对照(1)阿贝比长原理Abbe comparator principle阿达马变换Hadamard transformation安平精度setting accuracy岸台,*固定台base station暗礁reef靶道工程测量target road engineering survey半导体激光器semiconductor laser半日潮港semidiurnal tidal harbor半色调halftone饱和度saturation北极星任意时角法method by hour angle of Polaris贝塞尔大地主题解算公式Bessel formula for solution of geodetic problem 贝塞尔椭球Bessel ellipsoid贝叶斯分类Bayesian classification被动式遥感passive remote sensing本初子午线prime meridian比较地图学comparative cartography比较地图学comparative cartography比例尺scale比例量表ratio scaling比例误差proportional error比值变换ratio transformation比值增强ratio enhancement闭合差closing error闭合差closure闭合差closing error闭合差closure闭合导线closed traverse闭合导线closed traverse闭合水准路线closed leveling line闭合水准路线closed leveling line边长中误差mean square error of side length边交会法linear intersection边角测量triangulateration边角交会法linear-angular intersection边角网triangulateration network边缘检测edge detection边缘增强edge enhancement编绘compilation编绘compilation编绘原图compiled original编绘原图compiled original变比例投影varioscale projection变换光束测图affine plotting变线仪variomat变形观测控制网control network for deformation observation 变形观测控制网control network for deformation observation 变形椭圆indicatrix ellipse标称精度nominal accuracy标称精度nominal accuracy标尺rod标尺staff标高差改正correction for skew normals标高差改正correction for skew normals标界测量survey for marking of boundary标志灯,*回光灯signal lamp标准差standard deviation标准配置点Gruber point标准纬线standard parallel冰后回弹post glacial rebound波茨坦重力系统Potsdam gravimetric system波带板zone plate波浪补偿compensation of undulation波浪补偿compensation of undulation波浪补偿heave compensation波浪补偿器,*涌浪滤波器heave compensator波罗-科普原理Porro-Koppe principle波谱测定仪spectrometer波谱集群spectrum cluster波谱特征空间spectrum feature space波谱特征曲线spectrum character curve波谱响应曲线spectrum response curve波束角beam angle波束角wave beam angle泊位Berth补偿器compensator补偿器compensator补偿器补偿误差compensating error of compensator补偿器补偿误差compensating error of compensator布格改正Bouguer correction布格异常Bouguer anomaly布隆斯公式Bruns formula布耶哈马问题Bjerhammar problem采剥工程断面图striping and mining engineering profile采剥工程综合平面图synthetic plan of striping and mining采场测量stope survey采掘工程平面图mining engineering plan采区测量survey in mining panel采区联系测量connection survey in mining panel 采区联系测量connection survey in mining panel 采样sampling采样间隔sampling interval彩色编码color coding彩色编码color coding彩色变换color transformation彩色变换color transformation彩色复制color reproduction彩色复制color reproduction彩色感光器材color sensitive material彩色感光器材color sensitive material彩色红外片,*假彩色片false color film彩色红外片,*假彩色片color infrared film彩色红外片,*假彩色片color infrared film彩色片color film彩色片color film彩色摄影color photography彩色摄影color photography彩色校样color proof彩色校样color proof彩色样图color manuscript彩色样图color manuscript彩色增强color enhancement彩色增强color enhancement彩色坐标系color coordinate system彩色坐标系color coordinate system参考数据reference data参考椭球reference ellipsoid参考效应reference effect参数平差,*间接平差parameter adjustment侧方交会side intersection侧扫声呐side scan sonar侧视雷达side-locking radar测标[measuring] mark测杆measuring bar测高仪Altimeter测绘标准standards of surveying and mapping测绘联合会International Union of Surveying and Mapping 测绘学geomatics测绘学SM测绘学surveying and mapping测绘仪器instrument of surveying and mapping测角中误差mean square error of angle observation测距定位系统,*圆-圆定位系统range positioning system 测距雷达range-only radar测距盲区range hole测距仪rangefinder测量标志survey mark测量船survey vessel测量规范specifications of surveys测量控制网surveying control network测量平差adjustment of observation测量平差survey adjustment测量学surveying测流current surveying测流current surveying测深改正correction of depth测深改正correction of depth测深杆sounding pole测深精度total accuracy of sounding测深仪读数精度reading accuracy of sounder测深仪发射参数,*测深仪零线transmiting line of sounder 测深仪回波信号echo signal of sounder测深仪记录纸recording paper of sounder测速标marks for measuring velocity测图卫星mapping satellite测微密度计microdensitometer测微目镜micrometer eyepiece测微器micrometer测线survey line测站station测站归心station centring层间改正plate correction觇牌target长度标准检定场standard field of length厂址测量surveying for site selection超导重力仪superconductor gravimeter超焦点距离hyperfocal distance超近摄影测量macrophotogrammetry潮汐表tidal tables潮汐波tidal wave潮汐调和常数tidal harmonic constants潮汐调和分析tidal harmonic analysis潮汐非调和常数tidal nonharmonic constants潮汐非调和分析tidal nonharmonic analysis潮汐摄动tidal perturbation潮汐因子tidal factor潮汐预报tidal prediction潮信表tidal information panel沉船wreck沉降观测settlement observation成像光谱仪imaging spectrometer成像雷达imaging radar城市测量urban survey城市地形测量urban topographic survey城市地形图topographic map of urban area城市基础地理信息系统UGIS城市基础地理信息系统urban geographical information system 城市控制测量urban control survey城市制图urban mapping乘常数multiplication constant尺度参数scale parameter抽象符号abstract symbol触觉地图tactual map船台,*移动台mobile station垂核面vertical epipolar plane垂核线vertical epipolar line垂球plumb bob垂线偏差改正correction for deflection of the vertical垂线偏差改正correction for deflection of the vertical垂直角vertical angle垂直折光误差vertical refraction error垂直折光系数vertical refraction coefficient垂准仪,*铅垂仪plumb aligner纯重力异常pure gravity anomaly磁变年差annual change of magnetic variation磁测深magnetic sounding磁测深线magnetic sounder磁方位角magnetic azimuth磁力扫海测量magnetic sweeping磁力异常区magnetic anomaly area磁偏角magnetic variation磁倾角magnetic dip磁像限角magnetic bearing磁子午线magnetic meridian粗差gross error粗差检测gross error detection粗码C/A Code粗码Coare/Acquision Code粗码C/A Code粗码Coare/Acquision Code打样Proofing大比例尺测图large scale topographical mapping大潮升spring rise大地测量边值问题geodetic boundary value problem 大地测量参考系geodetic reference system大地测量数据库geodetic database大地测量学geodesy大地测量仪器geodetic instrument大地方位角geodetic azimuth大地高ellipsoidal height大地高geodetic height大地基准geodetic datum大地经度geodetic longitude大地水准面geoid大地水准面高geoidal height大地水准面高geoidal undulation大地天顶延迟atmosphere zenith delay大地天文学geodetic astronomy大地网geodetic network大地纬度geodetic latitude大地线geodesic大地原点geodetic origin大地主题反解inverse solution of geodetic problem大地坐标geodetic coordinate大地坐标系geodetic coordinate system大陆架地形测量continental shelf topographic survey大陆架地形测量continental shelf topographic survey大气传输特性characteristics of atmospheric transmission 大气传输特性characteristics of atmospheric transmission 大气窗atmospheric window大气改正,*气象改正atmospheric correction大气透过率atmospheric transmissivity大气噪声atmospheric noise大气阻力摄动atmospheric drag perturbation大像幅摄影机large format camera大像幅摄影机LFC大洋地势图GEBCO大洋地势图general bathymetric chart of the oceans大圆航线图great circle sailing chart带谐系数coefficient of zonal harmonics带谐系数coefficient of zonal harmonics带状平面图zone plan单差相位观测single difference phase observation单点定位point positioning单片坐标量测仪monocomparator单位权unit weight单位权方差,*方差因子variance of unit weight弹道摄影测量ballistic photogrammetry弹道摄影机ballistic camera当地平均海面local mean sea level挡差改正correction of scale difference挡差改正correction of scale difference导标leading beacon导弹定向测量missile orientation survey导弹试验场工程测量engineering survey of missile test site 导航台定位测量navigation station location survey导航台定位测量navigation station location survey导航图navigation chart导航图navigation chart导航线,*叠标线leading line导入高程测量induction height survey导线边traverse leg导线测量traverse survey导线点traverse point导线横向误差lateral error of traverse导线角度闭合差angle closing error of traverse导线结点junction point of traverses导线曲折系数meandering coefficient of traverse导线全长闭合差total length closing error of traverse导线网traverse network导线相对闭合差relative length closing error of traverse 导线折角traverse angle导线纵向误差longitudinal error of traverse岛屿测量island survey岛屿联测island-mainland connection survey岛屿图island chart倒锤[线]观测,倒锤法inverse plummet observation灯[光性]质characteristic of light灯[光性]质characteristic of light灯标light beacon灯船light ship灯船light vessel灯浮标light buoy灯高height of light灯光节奏flashing rhythm of light灯光射程light range灯光遮蔽Eclipse灯光周期light period灯色light color灯塔light house等比线isometric parallel等高距contour interval等高距contour interval等高棱镜contour prism等高棱镜contour prism等高线Contour等高线Contour等高仪astrolabe等积投影equivalent projection等级结构hierarchical organization等角定位格网equiangular positioning grid等角条件,*正形投影conformal projection等角条件,*正形投影conformal projection等精度[曲线]图equiaccuracy chart等距量表interval scaling等距投影equidistant projection等距圆弧格网equilong circle arc grid等量纬度isometric latitude等偏摄影parallel-averted photography等倾摄影equally tilted photography等权代替法method of equalweight substitution 等值灰度尺equal value gray scale等值区域图,*分区量值地图choroplethic map 等值区域图,*分区量值地图choroplethic map 等值线地图isoline map等值线法isoline method低潮线low water line底板测点floor station底点纬度latitude of pedal底色去除under color removal底色增益under color addition底质bottom characteristics底质quality of the bottom底质采样bottom characteristics sampling底质调查bottom characteristics exploration底质分布图bottom sediment chart地产界测量property boundary survey地磁经纬仪magnetism theodolite地磁仪magnetometer地底点ground nadir point地固坐标系body-fixed coordinate system 地固坐标系earth-fixed coordinate system 地基系统ground-based system地极坐标系coordinate system of the pole 地极坐标系coordinate system of the pole 地籍cadastre地籍cadastre地籍簿land register地籍册cadastral lists地籍册cadastral lists地籍测量cadastral survey地籍测量cadastral survey地籍调查cadastral inventory地籍调查cadastral inventory地籍更新renewal of the cadastre地籍管理cadastral survey manual地籍管理cadastral survey manual地籍图cadastral map地籍图cadastral map地籍修测cadastral revision地籍修测cadastral revision地籍制图cadastral mapping地籍制图cadastral mapping地界测量land boundary survey地壳均衡isostasy地壳均衡改正isostatic correction地壳形变观测crust deformation measurement地壳形变观测crust deformation measurement地块测量parcel survey地类界图land boundary map地理格网geographic grid地理视距geographical viewing distance地理信息传输geographic information communication 地理信息系统geographic information system地理信息系统GIS地理坐标geographic graticule地理坐标参考系geographical reference system地貌图geomorphological map地貌形态示量图morphometric map地面接收站ground receiving station地面立体测图仪terrestrial stereoplotter地面摄谱仪terrestrial spectrograph地面摄影测量terrestrial photogrammetry地面摄影机terrestrial camera地面实况ground truth地面照度illuminance of ground地名geographical name地名place name地名标准化place-name standardization地名录gazetteer地名数据库place-name database地名索引geographical name index地名通名geographical general name地名学toponomastics地名学toponymy地名转写geographical name transcription地名转写geographical name transliteration地平线摄影机horizon camera地平线像片horizon photograph地倾斜观测ground tilt measurement地球定向参数earth orientation parameter地球定向参数EOP地球同步卫星geo-synchronous satellite地球椭球earth ellipsoid地球位,*大地位geopotential地球位数geopotential number地球位系数potential coefficient of the earth地球形状earth shape地球形状Figure of the earth地球仪globe地球引力摄动terrestrial gravitational perturbation地球重力场模型earth gravity model地球资源卫星earth resources technology satellite地球资源卫星ERTS地球自转参数earth rotation parameter地球自转参数ERP地球自转角速度rotational angular velocity of the earth 地势图hypsometric map地图map地图编绘map compilation地图编辑map editing地图编辑大纲map editorial policy地图表示法cartographic presentation地图表示法cartographic presentation地图传输cartographic communication地图传输cartographic communication地图叠置分析map overlay analysis地图分类cartographic classification地图分类cartographic classification地图分析cartographic analysis地图分析cartographic analysis地图符号库map symbols bank地图符号学cartographic semiology地图符号学cartographic semiology地图负载量map load地图复杂性map complexity地图复制map reproduction地图感受map perception地图更新map revision地图集信息系统Atlas information system地图利用map use地图量算法cartometry地图量算法cartometry地图模型,*制图模型cartographic model地图模型,*制图模型cartographic model地图内容结构cartographic organization地图内容结构cartographic organization地图判读map interpretation地图评价cartographic evaluation地图评价cartographic evaluation地图潜信息cartographic potential information 地图潜信息cartographic potential information地图清晰性map clarity地图色标color chart地图色标color chart地图色标map color standard地图色谱map color atlas地图设计map design地图数据结构map data structure地图数据库cartographic database地图数据库cartographic database地图数字化map digitizing地图投影map projection地图显示map display地图信息cartographic information地图信息cartographic information地图信息系统cartographic information system 地图信息系统CIS地图信息系统cartographic information system 地图信息系统CIS地图选取cartographic selection地图选取cartographic selection地图学cartography地图学cartography地图研究法cartographic methodology地图研究法cartographic methodology地图易读性map legibility地图印刷map printing地图语法cartographic syntactics地图语法cartographic syntactics地图语言cartographic language地图语言cartographic language地图语义cartographic semantics地图语义cartographic semantics地图语用cartographic pragmatics地图语用cartographic pragmatics地图阅读map reading地图整饰map decoration地图制图map making地图制图软件cartographic software地图制图软件cartographic software地图注记map lettering地下管线测量underground pipeline survey地下铁道测量subway survey地下铁道测量underground railway survey地下油库测量underground oil depot survey地心经度geocentric longitude地心纬度geocentric latitude地心引力常数geocentric gravitational constant地心坐标系geocentric coordinate system地形测量topographic survey地形底图base map of topography地形改正topographic correction地形数据库topographic database地形图topographic map地形图更新revision of topographic map地形图图式topographic map symbols地震台精密测量precise survey at seismic station 地质测量geological survey地质点测量geological point survey地质略图geological scheme地质剖面测量geological profile survey地质剖面图geological section map典型图形平差adjustment of typical figures点方式point mode点位中误差mean square error of a point点下对中centering under point点下对中centering under point点状符号point symbol电磁波测距electromagnetic distance measurement电磁波测距仪electromagnetic distance measuring instrument电磁传播[时延]改正correction for radio wave propagation of time signal 电磁传播[时延]改正correction for radio wave propagation of time signal 电荷耦合器件CCD电荷耦合器件charge-coupled device电荷耦合器件CCD电荷耦合器件charge-coupled device电离层折射改正ionospheric refraction correction电子测距仪EDM电子测距仪electronic distance measuring instrument电子出版系统electronic publishing system电子地图集electronic atlas电子分色机color scanner电子分色机color scanner电子海图electronic map电子海图数据库ECDB电子海图数据库electronic chart database电子海图显示和信息系统ECDIS电子海图显示和信息系统electronic chart display and information system电子经纬仪electronic theodolite电子平板仪electronic plane-table电子求积仪electronic planimeter电子水准仪electronic level电子速测仪,*全站仪electronic tachometer 电子显微摄影测量nanophotogrammetry电子显微摄影测量nanophotogrammetry电子相关electronic correlation电子印像机electronic printer调绘Annotation调焦误差error of focusing调频频率modulation frequency调制传递函数modulation transfer function 调制传递函数MTF调制器modulator叠栅条纹图,*莫尔条纹图moirétopography 顶板测点roof station定深扫海sweeping at definite depth定位标记positioning mark定位点间距positioning interval定位检索,*开窗检索retrieval by windows 定位统计图表法positioning diagram method 定线测量Alignment survey定向连接点connection point定向连接点connection point for orientation 定向连接点connection point定向连接点connection point for orientation 定性检索retrieval by header定影Fixing动感autokinetic effect动画引导animated steering动画制图animated mapping动态定位kinematic positioning独立交会高程点elevation point by independent intersection独立模型法空中三角测量independent model aerial triangulation 独立坐标系independent coordinate system度盘circle度盘circle断面仪Profiler对景图front view对流层折射改正tropospheric refraction correction对数尺logarithmic scale对中杆centering rod对中杆centering rod多倍仪multiplex多边形地图polygonal map多边形结构polygon structure多边形平差法Adjustment by method of polygon多波束测探multibeam echosounding多波束测探系统multibeam sounding system多层结构multi layer organization多级纠正multistage rectification多焦点投影polyfocal projection多路径效应multipath effect多媒体地图multimedia map多年平均海面multi-year mean sea level多谱段扫描仪MSS多谱段扫描仪multispectral scanner多谱段摄影multispectral photography多谱段摄影机multispectral camera多谱段遥感multispectral remote sensing多时相分析multi-temporal analysis多时相遥感multi-temporal remote sensing多星等高法equal-altitude method of multi-star 多用途地籍multi-purpose cadastre多余观测redundant observation多圆锥投影polyconic projection厄特沃什效应Eötvös effect二值图像binary image发光二极管LED发光二极管light-emitting diode法方程normal equation法方程normal equation法截面normal section法截面normal section法伊改正Faye correction反差Contrast反差Contrast反差系数contrast coefficient反差系数contrast coefficient反差增强contrast enhancement反差增强contrast enhancement反立体效应pseudostereoscopy反射波谱reflectance spectrum反束光导管摄影机return beam vidicon camera 反像mirror reverse反像wrong-reading反转片reversal film范围法area method方差-协方差传播律variance-covariance propagation law 方差-协方差矩阵variance-covariance matrix方里网kilometer grid方位角中误差mean square error of azimuth方位圈compass rose方位圈compass rose方位投影azimuthal projection方向观测法method by series方向观测法method of direction observation防波堤Breakwater防波堤mole房地产地籍real estates cadastre仿射纠正affine rectification放样测量setting-out survey非地形摄影测量nontopographic photogrammetry非地形摄影测量nontopographic photogrammetry非监督分类unsupervised classification非量测摄影机non-metric camera非量测摄影机non-metric camera菲列罗公式Ferrero's formula分版原图Flaps分瓣投影interrupted projection分层layer分层设色表graduation of tints分层设色法hypsometric layer分潮Constituent分潮Constituent分潮迟角epoch of partial tide分潮振幅amplitude of partial tide分带纠正zonal rectification分带子午线zone dividing meridian分类器classifier分类器classifier分区统计图表法cartodiagram method分区统计图表法chorisogram method分区统计图表法cartodiagram method分区统计图表法chorisogram method分区统计图表法,*等值区域法cartogram method 分区统计图表法,*等值区域法cartogram method 分区统计图法,*等值区域法choroplethic method 分区统计图法,*等值区域法choroplethic method 分色,*分色参考图color separation分色,*分色参考图color separation分析地图analytical map风讯信号杆wind signal pole浮标Buoy浮雕影像地图picto-line map浮子验潮仪float gauge符号化symbolization辐射三角测量radial triangulation辐射线格网radial positioning grid辐射校正radiometric correction辐射遥感器radiation sensor负荷潮load tide负片negative负片negative附参数条件平差condition adjustment with parameters附参数条件平差condition adjustment with parameters附合导线connecting traverse附合导线connecting traverse附合水准路线annexed leveling line附加位additional potential附条件参数平差,*附条件间接平差parameter adjustment with conditions 复测法repetition method复垦测量reclaimation survey复照仪reproduction camera副台slave station概率判决函数Probability decision function概然误差probable error干出礁covers and uncovers rock干出礁covers and uncovers rock干涉雷达INSAR干涉雷达interometry SAR感光sensitization感光材料sensitive material感光测定sensitometry感光度sensitivity感光特性曲线characteristic curve of photographic transmission感光特性曲线characteristic curve of photographic transmission感受效果perceptual effect港界harbor boundary港口port港口工程测量harbor engineering survey港湾测量harbor survey港湾锚地图集harbor/anchorage atlas港湾图harbor chart高差仪statoscope高程height高程导线height traverse高程点elevation point高程基准height datum高程控制测量vertical control survey高程控制点vertical control point高程控制网vertical control network高程系统height system高程异常height anomaly高程中误差mean square error of height高度角altitude angle高度角elevation angle高密度数字磁带HDDT高密度数字磁带high density digital tape高斯-克吕格投影Gauss-Krüger projection高斯平面子午线收敛角Gauss grid convergence高斯平面坐标系Gauss plane coordinate system高斯投影方向改正arc-to-chord correction in Gauss projection 高斯中纬度公式Gauss midlatitude formula格网单元cell格网单元cell跟踪数字化tracing digitizing工厂现状图测量survey of present state at industrial site工程测量engineering survey工程测量学engineering surveying工程经纬仪engineer's theodolite工程控制网engineering control network工程摄影测量engineering photogrammetry 工程水准仪engineer's level工业测量系统industrial measuring system 工业摄影测量industrial photogrammetry 公路工程测量road engineering survey功率谱power spectrum共面方程coplanarity equation共面方程coplanarity equation共线方程collinearity equation共线方程collinearity equation构像方程imaging equation古地图ancient map骨架航线,*构架航线,测控条control strip 骨架航线,*构架航线,测控条control strip 固定平极fixed mean pole固定误差fixed error固定相移fixed phase drift固体潮[solid] Earth tide固体激光器solid-state laser管道测量pipe survey管道综合图synthesis chart of pipelines贯通测量holing through survey贯通测量breakthrough survey惯性测量系统inertial surveying system惯性测量系统ISS惯性坐标系inertial coordinate system惯用点conventional name惯用点conventional name灌区平面布置图irrigation layout plan光电测距导线EDM traverse光电测距仪electro-optical distance measuring instrument光电等高仪photoelectric astrolabe光电遥感器photoelectric sensor光电中星仪photoelectric transit instrument光碟,*光盘CD光碟,*光盘compact disc光碟,*光盘CD光碟,*光盘compact disc光谱感光度,*光谱灵敏度spectral sensitivity光圈,*有效孔径Aperture光圈号数f-number光圈号数stop-number光束法空中三角测量bundle aerial triangulation光栅grating广播星历broadcast ephemeris归化纬度reduced latitude归心改正correction for centering归心改正correction for centering归心元素elements of centring龟纹moire规划地图planning map规矩线register mark国际测绘联合会IUSM国际测量师联合会Fédération Internationale des Géométres国际测量师联合会FIG国际大地测量协会IAG国际大地测量协会International Association of Geodesy国际大地测量与地球物理联合会International Union of Geodesy and Geophysics国际大地测量与地球物理联合会IUGG国际地球参考架international terrestrial reference frame国际地球参考架ITRF国际地球自转服务局IERS国际地球自转服务局International Earth Rotation Service国际海道测量组织IHO国际海道测量组织International Hydrography Organization国际海图international chart国际航天测量与地球学学院ITC国际矿山测量学会International Society of Mine Surveying国际摄影测量与遥感学会International Society for Photogrammetry and Remote S国际摄影测量与遥感学会ISPRS国际天球参考架ICRF国际天球参考架international celestial reference frame国际协议原点CIO国际协议原点Conventional International Origin国际协议原点CIO国际协议原点Conventional International Origin国际原子时IA T国际原子时international atomic time国际制图协会ICA国际制图协会International Cartographic Association国家地图集national atlas国家地图集national atlas国家基础地理信息系统national fundamental geographic information system国家基础地理信息系统national fundamental geographic information system海[洋]图集marine atlas海岸coast海岸coast海岸地形测量coast topographic survey海岸地形测量coast topographic survey海岸图coast chart海岸图coast chart海岸线coast line海岸线coast line海岸性质nature of the coast海岸性质nature of the coast海拔height above sea level海道测量,*水道测量hydrographic survey海道测量学,*水道测量学hydrography海底成像系统seafloor imaging system海底地貌submarine geomorphology海底地貌图submarine geomorphologic chart海底地势图submarine situation chart海底地形测量bathymetric surveying海底地形图bathymetric chart海底地质构造图submarine structural chart海底电缆submarine cable海底管道submarine pipeline海底控制网submarine control network海底倾斜改正seafloor slope correction海底声标acoustic beacon on bottom海底施工测量submarine construction survey海底隧道测量submarine tunnel survey海福德椭球Hayford ellipsoid海军导航卫星系统Navy Navigation Satellite System 海军导航卫星系统NNSS海军导航卫星系统Navy Navigation Satellite System 海军导航卫星系统NNSS海军勤务测量naval service survey海军勤务测量naval service survey海控点hydrographic control point海流计current meter海流计current meter海面地形sea surface topography海区界线sea area bounding line海区资料调查sea area information investigation海区总图general chart of the sea海图Chart海图Chart海图比例尺Chart scale海图比例尺Chart scale海图编号Chart numbering海图编号Chart numbering海图编制Chart compilation海图编制Chart compilation海图标题Chart title海图标题Chart title海图大改正Chart large correction海图大改正Chart large correction海图分幅Chart subdivision海图分幅Chart subdivision海图改正Chart correction海图改正Chart correction海图投影Chart projection海图投影Chart projection海图图廓Chart boarder海图图廓Chart boarder海图图式symbols and abbreviations on chart 海图小改正Chart small correction海图小改正Chart small correction海图制图charting海图制图charting海图注记lettering of chart海洋测绘marine charting海洋测绘数据库marine charting database海洋测量marine survey海洋测量定位marine survey positioning海洋磁力测量marine magnetic survey海洋磁力图marine magnetic chart海洋磁力异常marine magnetic anomaly海洋大地测量marine geodetic survey海洋大地测量学marine geodesy海洋工程测量marine engineering survey海洋划界测量marine demarcation survey海洋环境图marine environmental chart海洋气象图marine meteorological chart海洋生物图marine biological chart海洋水文图marine hydrological chart海洋水准测量marine leveling海洋卫星Seasat海洋质子采样器marine bottom proton sampler 海洋质子磁力仪marine proton magnetometer 海洋重力测量marine gravimetry海洋重力仪marine gravimeter海洋重力异常marine gravity anomaly海洋重力异常图Chart of marine gravity anomaly 海洋重力异常图Chart of marine gravity anomaly 海洋专题测量marine thematic survey海洋资源图marine resource chart航标表list of lights航带法空中三角测量strip aerial triangulation航道channel航道channel航道fairway航道图navigation channel chart航道图navigation channel chart航高flight height航高flying height航海天文历nautical almanac航海天文历nautical almanac航海通告NM航海通告notice to mariners航海通告NM航海通告notice to mariners航海图nautical chart航海图nautical chart航迹track航空摄谱仪aerial spectrograph航空摄影aerial photography航空摄影测量aerial photogrammetry航空摄影测量aerophotogrammetry航空摄影机aerial camera航空图aeronautical chart航空遥感aerial remote sensing航空重力测量airborne gravity measurement航路指南sailing directions航路指南SD航摄计划flight plan of aerial photography航摄领航navigation of aerial photography航摄领航navigation of aerial photography航摄漏洞aerial photographic gap航摄软片aerial film航摄像片,航空像片aerial photograph航摄质量quality of aerophotography航速speed航天飞机space shuttle航天摄影space photography航天摄影测量,*太空摄影测量space photogrammetry 航天遥感space remote sensing航向course航向course航向倾角longitudinal tilt航向倾角pitch航向重叠end overlap航向重叠fore-and-aft overlap航向重叠forward overlap航向重叠longitudinal overlap航行通告notice to navigator航行通告notice to navigator航行图sailing chart航行障碍物navigation obstruction航行障碍物navigation obstruction合成地图synthetic map合成孔径雷达SAR合成孔径雷达synthetic aperture radar合点控制vanishing point control河道整治测量river improvement survey河外致密射电源,*类星体extragalactic compact radio source 核点epipole核面epipolar plane核线epipolar line核线epipolar ray核线相关epipolar correlation盒式分类法box classification method黑白片black-and-white film黑白摄影black-and-white photography恒时钟sidereal clock恒星摄影机stellar camera恒星时sidereal time恒星中天测时法method of time determination by star transit 横断面测量cross-section survey横断面测量cross-section survey横断面图cross-section profile横断面图cross-section profile横轴投影transverse projection红外测距仪infrared EDM instrument红外辐射计infrared radiometer红外片infrared film红外扫描仪infrared scanner红外摄影infrared photography红外图像infrared imagery。
Radiative Penguin decays
4.23 ± 0.40 ± 0 .¼ 22 ± 62 ± 0.22 · 3.83à · 0¼. ¼ ¼ à · ÃË ÃË 3 . 91 ± 0 . 23 ± 0 . 35 4 . 21 ± 0 . 0.31 ´½¿ ¾ ¦ ¼ µ± ´ ½¾ ¦ ¼ ¿ µ± ´¾ ¼ ¦ ¼ ¾35 µ±±´¼ ¦ ¼ ¼ µ± ± 3.76 ± 0 ±.86 ± 0.28 ½½ ± 4.55 ¾± ± 0.70 ± 0.34 ¼± ± 0.20 ± 0¼ ± 3.98 ± ¼0 ±.28 ± 0.16 ¼ ± 4.17 .18
Workshop on the CKM Unitarity Triangle, IPPP Durham, April 2003
CKM 03
Radiative Penguin decays
S.Playfer School of Physics, University of Edinburgh
arXiv:hep-ex/0308004v1 4 Aug 2003
2
5.26
5.28
The measurement of the gamma energy spectrum in the Figure results on B→ γ Ö ÓÖ Ô ÖØ Ð Ö Ø Ø Ö ×ÙÐØ× ÓÖ Ø 2. BELLE Ñ ÓÒ×ØÖ Ò Ñ ××exclusive ×ØÖ ÙØ ÓÒ× ÓÖ ØK ∗ × process b → sγ has recently been used by CLEO to im- Á º ×ÝÑÑ ØÖݺ prove the extraction of the CKM elements Vcb and Vub from inclusive semileptonic b decays [ 2]. Details of these moments analyses can be found in [ 3] B0 → K ∗0 γ/10−5 B+ → K ∗+ γ/10−5 BABAR 20fb−1 I will also discuss the FCNC transition b → d, which we BELLE 60fb−1 expect to find experimental evidence for in the near future. Ê ÓÒ×ØÖÙ Ø ÓÒ Æ Ò Ý −1 Ö Ø ÓÒ Ð ÖÖÓÖ× 9 fb CLEO Measurements of this transition are sensitive to the CKM ÆÙÑ Ö Ó Ñ ×ÓÒ Ô Ö× Average element Vtd . È ÓØÓÒ × Ð Ø ÓÒ Ò ¡ ÙØ
Measurement of fluorescence decay times
专利名称:Measurement of fluorescence decay times发明人:Shiv Sharma申请号:US10381451申请日:20030324公开号:US20040012780A1公开日:20040122专利内容由知识产权出版社提供专利附图:摘要:Laser pulses from laser head pass through objective lens to a focal spot in sample spot If a pulse hits a fluorophore molecule in the focal spot a fluorescence photon is emitted which is collected by lens reflected by dichroic mirror through filter which blocks photons of other wavelengths, to single photon counting photomultiplierunit On detecting a photon, photomultiplier unit generates an output pulse which is coupled, with a short delay, by pulse controller to driver circuit which causes laser head to generate another laser pulse. Thus the interval between the laser pulses is substantially equal to the time between excitation of, and fluorescence emission by, the fluorophore molecule. Computer coupled to photomultiplier unit and driver circuit determines the decay time by measurement of a number of fluorescence events.申请人:SHARMA SHIV更多信息请下载全文后查看。
Anton Paar 产品说明 - 奶油和奶制品质量控制解决方案说明书
The Hand in Hand Solution for Milk and Dairy ProductsRelevant for: Dairy industryDairy products are subject to the strongest quality control regulations throughout production and in the packaged product. Both Anton Paar’s laboratory and process instrumentation are reliablesolutions to fulfill these high demands.1 IntroductionMilk and dairy products are very complex substances that are composed of an expansive diversity of different molecular species. Being the product of mammary glands, milk is the primary food source for neonatal mammals. The milk from cows is the main source of dairy products and will therefore subsequently be looked at in more detail.Many factors affect the composition of raw milk such as the cow‘s breed, age, physical state and seasonal variations in the animal‘s diet [1]. Therefore, only an approximate milk composition of 87 % - 88 % water and 12 % - 13 % total solids can be given. The total solids consist of approx. 4 % fat and 9 % solids-non-fat (SNF) such as proteins, lactose, minerals, vitamins, and many more [2].2 Why density measurement?The determination of physical parameters, such as the density of milk, plays an important role in the dairy industry. The density measurement of raw milk with Anton Paar density meters has been successfully used for quality control for many years [3]. Milk is composed of many different constituents with different densities. The density measurement of milk proves useful as a fast and precise method for the detection of deviations of milk composition, e.g. the addition of water. Density measurement is a simple and robust method which provides a simple analysis parameter which is measured in process as well as in the laboratory.The oscillating U-tube principle, or digital density measurement, is applied in Anton Paar density meters. It replaces older methods, such as hydrometers, pycnometers and lactometers and is recognized by many agencies as the laboratory standard for good density measurement.The advantages of digital density instruments are: •Highest level of accuracy•Ease of operation•Rapid results•Robust, long life.3 The density of milkThe density of raw milk depends on its composition, temperature and previous handling and can usually be found in the range of 1.026 g/cm3- 1.034 g/cm3at 20 °C, although literature data varies.The inclusion of air strongly influences the density of milk and dairy products. Included air is "trapped" in viscous dairy products like yogurt and escapes only very slowly or not at all. The amount of dissolved air in fresh milk is around 6 %, but may be up to 10 % after transport [4]. This entrapped air may influence the density of milk and dairy products and lead to erroneous measurement results and bad repeatabilities. Thus, samples are pretreated before measurement for consistent results.A phenomenon observed in 1883, named after Recknagel, describes the fact that milk density increases slowly after milking by up to 0.001 g/cm3. This increase takes up to two days at 15 °C but completely stops at 5 °C after only six hours. The density increase is attributed to the removal of air and the slow solidification of milk fat [5]. As a consequence, small differences in density may be observed due to the temperature history of the milk or dairy product. For example, different densities may be found for the same sample, dependingon whether it was held at 40 °C or 20 °C before measuring at 20 °C.Table 1: Density of various dairy products as a function of fat and solids-non-fat (SNF) content [6]Table 1 [6] gives an overview of the density results of various dairy products as a function of fat and the solids non-fat (SNF) content, obtained at different temperatures.4 The temperature dependence of milkIt can be seen from Table 1the density of milk decreases with increasing temperature. The higher the fat content of milk, the more the density changes with increasing temperature because the volume of fat changes more with temperature than the volume of water. The temperature coefficient of milk is in the range of 0.003 g/(cm3K), the temperature coefficient of cream is between 0.006 g/(cm3K) and 0.008 g/(cm3K).5 The calculation of total solids in milkAs mentioned before, raw milk contains approx. 12 % to 13 % total solids (TS) that consist of approx. 4 % fat and 9 % solids-non-fat (proteins, lactose, minerals, vitamins, etc.). There is a direct relationship between milk density, fat content and solids-non-fat.The fat content of milk is routinely determined in dairies. In combination with the milk density it can be used for the calculation of total milk solids (TS) according to the Fleischmann formula [7]:TS [%] = 1.2 * f + 266.5 * (SG - 1)/SGTS ....total solids contentf ....fat contentSG ... specific gravity SG15/15. The formula is based on the specific gravity SG at 15 °C [8]. The fat content of milk can be determined in different ways, e.g. according to the Roese Gottlieb reference method or the Babcock or Gerber tests (butyrometric procedure) [9]. Provided that the fat content of milk is known, the measurement results of the DMA™ density meter can be transferred to a PC program, such as Excel, via a LIMS system where the total solids can be calculated automatically.6 Quality control of milkAs milk is a multi-component system it is not possible to determine the concentration of one component by density measurement alone. Yet, the density measurement of milk quickly indicates deviations from the normal milk composition due to the addition of water. The addition of 10 % water to the milk will result in a density decrease of approx. 0.003 g/cm3. Considering the fairly large natural variations in milk composition, the addition of water to milk can only be detected by density measurement if at least 10 % water are added.Skimming, i.e. the removal of fat, causes the milk density to increase. If skimming (causing a density increase) and water addition (causing the density to decrease) are done at the same time, a "normal" milk density can be observed. For this reason density measurement alone does not represent a method for quantitative quality analysis.While Infrared Analysis (IR) is a well-established and widely used method for routine analyses of milk proteins, fat or carbohydrates [10], density measurement remains a very useful control methodfor indicating deviations from the normal milk composition. Especially for quick quality checks of the delivered raw milk, the portable DMA™ 35 and the laboratory density meters DMA™ 501 and DMA™ 1001 are well suited. 7Volume to weight conversion with proper milk density On delivery, the volume of the milk is usually measured using volumetric flow meters. However, account settlement is often based on the weight. Additionally, for declarations of the package quantity by volume, the exact density is determined using an appropriate instrument.For the conversion of volume to weight the density of the milk is required. Mass = Density x VolumeMilk density is influenced by different factors. As the density of milk changes over time as mentioned before, milk density must be measured on the spot to calculate an average density that represents the actual conversion factor. Experimental results obtained in the laboratory under different conditions cannot be compared with on-the-spot measurements. The on-site determination of density as a conversion factor from volume to weight can be carried out with the portable D MA™ 35 and the laboratory density meters DMA™ 501 and DMA™ 1001 as they measure milk density with high accuracyTo achieve the most accurate weight measurement, a combination of density and volumetric flow is used. Mass flow sensors, while very popular, are not the most accurate. The most accurate mass flow sensors claim an accuracy of ±0.0001 g/cm³, however this is for the top of the line sensor which will cost significantly more than a combination of density and volumetric flow meter.Anton Paar process density sensors for milk and dairy applications provide a 4-digit accuracy. They offer, combined with a very compact yet precise volumetric flow sensor, highly accurate mass flow results at a very competitive price. 8 Density measurement during production and in the final package 8.1GeneralPortable density meters have proven to be ideally suited for the initial quality control of delivered raw milk. However, for measurements in the laboratory and for products with higher viscosity values, bench-top density meters are better suited.All subsequently described density meters provide integrated tables or formulas for the conversion ofdensity results to various concentrations and product specific parameters. These can be selected by the user for the measurement of specific samples. In addition to the large number of pre-installed conversion tables, custom specific measuring units can also be programmed. For example, for sweetened products, the relative Brix value can be determined directly. 8.2Laboratory instrumentsAnton Paar laboratory density meters have been used successfully for quality control of dairy products for many years. The relative density of milk, in combination with the fat content, can be used to calculate the total solids [11].Considering the relatively large natural variations of milk density, an uncertainty of measurement of0.001 g/cm 3may be considered sufficient for routine measurements. For these applications, the density meters DMA™ 35 (Figure 1), DMA™ 501 or DMA™ 1001 (Figure 2) represent the ideal solution.Figure 2: DMA™ 501 and DMA™ 1001 Density MetersFor university institutes, national dairy institutes and larger dairies the more accurate density meters such as DMA™ 4100 M, DMA™ 4500 M and DMA™ 5000 M [12] (Figure 3) might be required.8.3 Process milk standardization using densitymeasurementOnline density measurement is routinely used forprocess control in the milk industry. The processdensity sensor L-Dens 7400 (Figure 4) coupled withthe mPDS 5 evaluation unit (Figure 5) is a mostsuitable solution for reliable continuous processmonitoring due to their long and successful history inthe milk industry.Figure 4: Inline installation of the density sensor L-Dens 7400Milk standardization is a process in which a specifiedamount of milk fat is added to skim milk to producethe desired product, i.e. whole milk, reduced fat milk,etc. The densities of the skimmed milk and milk fat areknown. The change in density following addition of themilk fat is monitored and the fat content of thestandardized milk is determined.9 A new milk application from Anton Paar9.1 GeneralA new application program developed by Anton Paarincorporates several standard milk industry formulasinto the DMA™ M digital laboratory density meter andthe process milk fat monitor (mPDS 5).Together with the fat content obtained with the Gerberor Babcock tests, the total solids (TS), solids non-fat(SNF) and corrected lactometer reading (CLR) arecalculated.9.2 Laboratory solutionsIn certain countries, milk farmers are paid based onthe milk’s fat and solid-non-fat content. Sometimes,milk collection centers use lactometers instead ofdensity meters, but the use of a density meter provesmore accurate, reliable, repeatable and user-friendly.Therefore, the readings between two differentinstruments have to agree and deliver uniform testresults. This can be achieved with a customer specificmethod for DMA™ M (Figure 6).The formula [13]SNF [%] = 0.25D + 0.22f + 0.72for solid non-fat applies for liquid milk at 20 °C wheref = fat content in %w/w andD = (1000*density-1000).Formulas for the calculation of SNF can also be found elsewhere [14]. The milk fat is determined in the laboratory with the Gerber or Babcock test and subsequently entered into the DMA™ M for the SNF calculation (Figure 6). If the milk is warmer or colder, the SNF has to be corrected adding to D a factor of 0.24 for each degree above 20 °C and subtracting 0.24 for each degree below [13].9.3 Process solutionsAs described above, the fat content determined in thelaboratory is entered into the DMA™ M, and the CLR,TS, SNF and SG are automatically calculated anddisplayed. Anton Paar process instrumentation is ableto perform the same calculations as shown in Fig. 7,without the need to enter the laboratory milk fatcontent. This is accomplished by performing a skimmilk adjustment.Figure 7: Screen shot of an mPDS 5 Evaluation UnitThe calculation of the fat content of cream/whole milkis based on the density difference between skim milkand cream/whole milk. As the density of skim milkchanges with seasons and depends on the supplier ofthe raw milk, it is necessary to carry out a skim milkadjustment on a regular, automated basis.To accomplish this, the separator is briefly set toremove all fat from the milk and skim milk is runthrough the L-Dens 7400 density sensor for 1 minute.Once the value is stable, the temperature and densityare automatically stored, the separator returns tonormal production and the density difference ismonitored to calculate the fat content. Knowing thetemperature, density and fat content, all other valuesare calculated; density at 20 °C, density at a customerspecific temperature, specific gravity, solids-non-fat(SNF), corrected lactometer reading (CLR), and totalsolids (TS). Because both lab and processmeasurements use the same method, results arecomparable, repeatable and reliable.The frequency of the skim milk adjustment must befound out empirically. As long as the deviation to thelaboratory reference lays within acceptable limits noskim milk adjustment is necessary. Adjustmentfrequency depends on the customer, production sizeblending capabilities and milk quality and is typicallyperformed automatically every 20-40 minutes. Inaddition to the skim milk adjustment, it is possible toenter a constant milk fat content for the calculations. Aproduct specific adjustment is also possible.9.4 A process exampleThe raw milk flows to the separator and thepasteurizer and then to the milk or cream tank,respectively. The skim milk density and temperatureare measured and the values stored automatically.Once the skim milk values are saved, the separatorallows some of the cream to remain in thestandardized milk and the density difference of thesaved skim milk and standardized milk is used tocalculate the fat content. If the fat content, density andtemperature are known, the CLR, SNF and TS arecalculated using standard industry formulas.9.5 Lab and process working togetherThe following two examples illustrate the agreementbetween data obtained with laboratory and processinstrumentation. The laboratory results for % SNF and% TS were recorded with a DMA™ density meter, thelaboratory result for fat was obtained with a differentmethod.Figure 8 illustrates the calculated linear regression.Figure 9 compares laboratory and process data.10 References[1] Wattiaux, M.A., Milk composition and nutritional value, University of Wisconsin--Madison. Babcock Institute for International Dairy Research and Development, Babcock Institute for International Dairy Research and Development, 1995, pp 73 - 76 [2] /what_is_in_raw_ milk.html[3] Lorenz, W., Hoffer, W., Milchwirtschaftliche Berichte Folge 61/1979[4] /de/content/herstellungsverf ahren-nahrung-produktion/molkerei/milch/[5] Milchwirtschaftliche Berichte Folge 60/1979, pp 199-200[6] Goff, H.D., Hill A.R., "Dairy Chemistry and Physics", University of Guelph[7] Jost, R., Milk and Dairy Products, Ullmann´s Encyclopedia of Industrial Chemistry, 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim[8] Koestler, G., Zeitschrift für Untersuchung der Lebensmittel 52/4, 1926, pp 279-287[9] Töpel, A., Chemie und Physik der Milch: Naturstoff, Rohstoff, Lebensmittel, B. Behr‘s Verlag GmbH & Co. KG, 1. Auflage 2004[10] Michaelsen KF, Pedersen SB, Skafte L, Jaeger P, Peitersen B., J Pediatr Gastroenterol Nutr. 1988 Mar-Apr;7(2), pp 229-35[11] Lüning, O., Zeitschrift für Untersuchung der Nahrungs- und Genußmittel, sowie der Gebrauchsgegenstände 1920, Volume 39, Issue 3-4, pp 96-98[12] DMA™ 4100/4500/5000 M Instruction Manual and Safety Information, [13] Manuals of food quality control Volume 8: Food analysis FAO 1986 (reprinted 1997)[14] Rao, S.R.M., Bector, B.S., Indian Journal of Dairy Science 1980 Vol. 33 No. 1 pp 1-6Contact Anton Paar GmbH Tel: +43 316 257-0********************** ********************** Appendix: The milk production processMeasuring point 1: Raw milk receiving Why? Adulteration test (addition of water)What and how?Laboratory instrumentation:Density withDMA™ 35, DMA™ 501, DMA™ 1001, and (with pre-determined fat content) CLR, SNF, TS and fat with DMA™ 4100/4500/5000 MProcess instrumentation:Density withL-Dens 7400; mPDS 5Measuring point 2: Raw milk tankWhy? Quality check before processingWhat and how?Laboratory instrumentation:Density withDMA™ 35, DMA™ 501, DMA™ 1001, and (with pre-determined fat content) CLR, SNF, TS and fat with DMA™ 4100/4500/5000 MMeasuring point 3: Standardized milk processWhy? Process control, quality control and assurance What and how? Laboratory instrumentation:Density withDMA™ 35, DMA™ 501, DMA™ 1001, and (with pre-determined fat content) CLR, SNF, TS and fat with DMA™ 4100/4500/5000 MProcess instrumentation: Density and (with skim milk adjustment) CLR, SNF, TS and fat withL-Dens 7400, mPDS 5Measuring point 4: Standardized milk tank, pre-packagingWhy? Quality control pre-packagingWhat and how?Laboratory instrumentation:Density withDMA™ 35, DMA™ 501, DMA™ 1001, and (with pre-determined fat content) CLR, SNF, TS and fat with DMA™ 4100/4500/5000 MMeasuring point 5: Packaged products Why? Quality control of packaged productsWhat and how?Laboratory instrumentation:Density withDMA™35, DMA™ 501, DMA™ 1001 and (with pre-determined fat content) CLR, SNF, TS and fat with DMA™ 4100/4500/5000 M。
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a r X i v :h e p -e x /0607094v 1 28 J u l 2006B A B A R -PUB-06/010SLAC-PUB-11968Measurement of the Pseudoscalar Decay Constant f D s Using Charm-Tagged Events in e +e −Collisions at√R.Kroeger,49J.Reidy,49D.A.Sanders,49D.J.Summers,49H.W.Zhao,49S.Brunet,50D.Cˆo t´e,50M.Simard,50 P.Taras,50F.B.Viaud,50H.Nicholson,51N.Cavallo,52,‡G.De Nardo,52D.del Re,52F.Fabozzi,52,‡C.Gatto,52 L.Lista,52D.Monorchio,52P.Paolucci,52D.Piccolo,52C.Sciacca,52M.Baak,53H.Bulten,53G.Raven,53 H.L.Snoek,53C.P.Jessop,54J.M.LoSecco,54T.Allmendinger,55G.Benelli,55K.K.Gan,55K.Honscheid,55D.Hufnagel,55P.D.Jackson,55H.Kagan,55R.Kass,55T.Pulliam,55A.M.Rahimi,55R.Ter-Antonyan,55Q.K.Wong,55N.L.Blount,56J.Brau,56R.Frey,56O.Igonkina,56M.Lu,56R.Rahmat,56N.B.Sinev,56D.Strom,56J.Strube,56E.Torrence,56F.Galeazzi,57A.Gaz,57M.Margoni,57M.Morandin,57A.Pompili,57 M.Posocco,57M.Rotondo,57F.Simonetto,57R.Stroili,57C.Voci,57M.Benayoun,58J.Chauveau,58P.David,58 L.Del Buono,58Ch.de la Vaissi`e re,58O.Hamon,58B.L.Hartfiel,58M.J.J.John,58Ph.Leruste,58J.Malcl`e s,58 J.Ocariz,58L.Roos,58G.Therin,58P.K.Behera,59L.Gladney,59J.Panetta,59M.Biasini,60R.Covarelli,60 M.Pioppi,60C.Angelini,61G.Batignani,61S.Bettarini,61F.Bucci,61G.Calderini,61M.Carpinelli,61R.Cenci,61F.Forti,61M.A.Giorgi,61A.Lusiani,61G.Marchiori,61M.A.Mazur,61M.Morganti,61N.Neri,61E.Paoloni,61G.Rizzo,61J.Walsh,61M.Haire,62D.Judd,62D.E.Wagoner,62J.Biesiada,63N.Danielson,63P.Elmer,63u,63C.Lu,63J.Olsen,63A.J.S.Smith,63A.V.Telnov,63F.Bellini,64G.Cavoto,64A.D’Orazio,64E.Di Marco,64R.Faccini,64F.Ferrarotto,64F.Ferroni,64M.Gaspero,64L.Li Gioi,64M.A.Mazzoni,64S.Morganti,64G.Piredda,64F.Polci,64F.Safai Tehrani,64C.Voena,64M.Ebert,65H.Schr¨o der,65R.Waldi,65 T.Adye,66N.De Groot,66B.Franek,66E.O.Olaiya,66F.F.Wilson,66R.Aleksan,67S.Emery,67A.Gaidot,67 S.F.Ganzhur,67G.Hamel de Monchenault,67W.Kozanecki,67M.Legendre,67B.Mayer,67G.Vasseur,67 Ch.Y`e che,67M.Zito,67W.Park,68M.V.Purohit,68A.W.Weidemann,68J.R.Wilson,68M.T.Allen,69D.Aston,69R.Bartoldus,69P.Bechtle,69N.Berger,69A.M.Boyarski,69R.Claus,69J.P.Coleman,69M.R.Convery,69M.Cristinziani,69J.C.Dingfelder,69D.Dong,69J.Dorfan,69G.P.Dubois-Felsmann,69D.Dujmic,69W.Dunwoodie,69R.C.Field,69T.Glanzman,69S.J.Gowdy,69M.T.Graham,69V.Halyo,69C.Hast,69T.Hryn’ova,69W.R.Innes,69M.H.Kelsey,69P.Kim,69M.L.Kocian,69D.W.G.S.Leith,69S.Li,69J.Libby,69S.Luitz,69V.Luth,69H.L.Lynch,69D.B.MacFarlane,69H.Marsiske,69R.Messner,69D.R.Muller,69C.P.O’Grady,69V.E.Ozcan,69A.Perazzo,69M.Perl,69B.N.Ratcliff,69A.Roodman,69A.A.Salnikov,69R.H.Schindler,69J.Schwiening,69A.Snyder,69J.Stelzer,69D.Su,69M.K.Sullivan,69K.Suzuki,69S.K.Swain,69J.M.Thompson,69J.Va’vra,69N.van Bakel,69M.Weaver,69A.J.R.Weinstein,69 W.J.Wisniewski,69M.Wittgen,69D.H.Wright,69A.K.Yarritu,69K.Yi,69C.C.Young,69P.R.Burchat,70 A.J.Edwards,70S.A.Majewski,70B.A.Petersen,70C.Roat,70L.Wilden,70S.Ahmed,71M.S.Alam,71R.Bula,71 J.A.Ernst,71V.Jain,71B.Pan,71M.A.Saeed,71F.R.Wappler,71S.B.Zain,71W.Bugg,72M.Krishnamurthy,72 S.M.Spanier,72R.Eckmann,73J.L.Ritchie,73A.Satpathy,73C.J.Schilling,73R.F.Schwitters,73J.M.Izen,74I.Kitayama,74X.C.Lou,74S.Ye,74F.Bianchi,75F.Gallo,75D.Gamba,75M.Bomben,76L.Bosisio,76C.Cartaro,76F.Cossutti,76G.Della Ricca,76S.Dittongo,76S.Grancagnolo,nceri,76L.Vitale,76V.Azzolini,77F.Martinez-Vidal,77Sw.Banerjee,78B.Bhuyan,78C.M.Brown,78D.Fortin,78K.Hamano,78 R.Kowalewski,78I.M.Nugent,78J.M.Roney,78R.J.Sobie,78J.J.Back,79P.F.Harrison,tham,79G.B.Mohanty,79H.R.Band,80X.Chen,80B.Cheng,80S.Dasu,80M.Datta,80A.M.Eichenbaum,80K.T.Flood,80J.J.Hollar,80J.R.Johnson,80P.E.Kutter,80H.Li,80R.Liu,80B.Mellado,80A.Mihalyi,80A.K.Mohapatra,80Y.Pan,80M.Pierini,80R.Prepost,80P.Tan,80S.L.Wu,80Z.Yu,80and H.Neal81(The B A B A R Collaboration)1Laboratoire de Physique des Particules,F-74941Annecy-le-Vieux,France2Universitat de Barcelona,Facultat de Fisica Dept.ECM,E-08028Barcelona,Spain3Universit`a di Bari,Dipartimento di Fisica and INFN,I-70126Bari,Italy4Institute of High Energy Physics,Beijing100039,China5University of Bergen,Institute of Physics,N-5007Bergen,Norway6Lawrence Berkeley National Laboratory and University of California,Berkeley,California94720,USA7University of Birmingham,Birmingham,B152TT,United Kingdom8Ruhr Universit¨a t Bochum,Institut f¨u r Experimentalphysik1,D-44780Bochum,Germany9University of Bristol,Bristol BS81TL,United Kingdom10University of British Columbia,Vancouver,British Columbia,Canada V6T1Z111Brunel University,Uxbridge,Middlesex UB83PH,United Kingdom12Budker Institute of Nuclear Physics,Novosibirsk630090,Russia13University of California at Irvine,Irvine,California92697,USA14University of California at Los Angeles,Los Angeles,California90024,USA15University of California at Riverside,Riverside,California92521,USA16University of California at San Diego,La Jolla,California92093,USA17University of California at Santa Barbara,Santa Barbara,California93106,USA 18University of California at Santa Cruz,Institute for Particle Physics,Santa Cruz,California95064,USA 19California Institute of Technology,Pasadena,California91125,USA20University of Cincinnati,Cincinnati,Ohio45221,USA21University of Colorado,Boulder,Colorado80309,USA22Colorado State University,Fort Collins,Colorado80523,USA23Universit¨a t Dortmund,Institut f¨u r Physik,D-44221Dortmund,Germany24Technische Universit¨a t Dresden,Institut f¨u r Kern-und Teilchenphysik,D-01062Dresden,Germany25Ecole Polytechnique,LLR,F-91128Palaiseau,France26University of Edinburgh,Edinburgh EH93JZ,United Kingdom27Universit`a di Ferrara,Dipartimento di Fisica and INFN,I-44100Ferrara,Italy28Laboratori Nazionali di Frascati dell’INFN,I-00044Frascati,Italy29Universit`a di Genova,Dipartimento di Fisica and INFN,I-16146Genova,Italy30Harvard University,Cambridge,Massachusetts02138,USA31Universit¨a t Heidelberg,Physikalisches Institut,Philosophenweg12,D-69120Heidelberg,Germany32Imperial College London,London,SW72AZ,United Kingdom33University of Iowa,Iowa City,Iowa52242,USA34Iowa State University,Ames,Iowa50011-3160,USA35Johns Hopkins University,Baltimore,Maryland21218,USA36Universit¨a t Karlsruhe,Institut f¨u r Experimentelle Kernphysik,D-76021Karlsruhe,Germany37Laboratoire de l’Acc´e l´e rateur Lin´e aire,IN2P3-CNRS et Universit´e Paris-Sud11,Centre Scientifique d’Orsay,B.P.34,F-91898ORSAY Cedex,France38Lawrence Livermore National Laboratory,Livermore,California94550,USA39University of Liverpool,Liverpool L697ZE,United Kingdom40Queen Mary,University of London,E14NS,United Kingdom41University of London,Royal Holloway and Bedford New College,Egham,Surrey TW200EX,United Kingdom42University of Louisville,Louisville,Kentucky40292,USA43University of Manchester,Manchester M139PL,United Kingdom44University of Maryland,College Park,Maryland20742,USA45University of Massachusetts,Amherst,Massachusetts01003,USA 46Massachusetts Institute of Technology,Laboratory for Nuclear Science,Cambridge,Massachusetts02139,USA47McGill University,Montr´e al,Qu´e bec,Canada H3A2T848Universit`a di Milano,Dipartimento di Fisica and INFN,I-20133Milano,Italy49University of Mississippi,University,Mississippi38677,USA50Universit´e de Montr´e al,Physique des Particules,Montr´e al,Qu´e bec,Canada H3C3J751Mount Holyoke College,South Hadley,Massachusetts01075,USA52Universit`a di Napoli Federico II,Dipartimento di Scienze Fisiche and INFN,I-80126,Napoli,Italy53NIKHEF,National Institute for Nuclear Physics and High Energy Physics,NL-1009DB Amsterdam,The Netherlands 54University of Notre Dame,Notre Dame,Indiana46556,USA55Ohio State University,Columbus,Ohio43210,USA56University of Oregon,Eugene,Oregon97403,USA57Universit`a di Padova,Dipartimento di Fisica and INFN,I-35131Padova,Italy 58Universit´e s Paris VI et VII,Laboratoire de Physique Nucl´e aire et de Hautes Energies,F-75252Paris,France 59University of Pennsylvania,Philadelphia,Pennsylvania19104,USA60Universit`a di Perugia,Dipartimento di Fisica and INFN,I-06100Perugia,Italy 61Universit`a di Pisa,Dipartimento di Fisica,Scuola Normale Superiore and INFN,I-56127Pisa,Italy62Prairie View A&M University,Prairie View,Texas77446,USA63Princeton University,Princeton,New Jersey08544,USA64Universit`a di Roma La Sapienza,Dipartimento di Fisica and INFN,I-00185Roma,Italy65Universit¨a t Rostock,D-18051Rostock,Germany66Rutherford Appleton Laboratory,Chilton,Didcot,Oxon,OX110QX,United Kingdom67DSM/Dapnia,CEA/Saclay,F-91191Gif-sur-Yvette,France68University of South Carolina,Columbia,South Carolina29208,USA69Stanford Linear Accelerator Center,Stanford,California94309,USA70Stanford University,Stanford,California94305-4060,USA71State University of New York,Albany,New York12222,USA72University of Tennessee,Knoxville,Tennessee37996,USA73University of Texas at Austin,Austin,Texas78712,USA74University of Texas at Dallas,Richardson,Texas75083,USA75Universit`a di Torino,Dipartimento di Fisica Sperimentale and INFN,I-10125Torino,Italy76Universit`a di Trieste,Dipartimento di Fisica and INFN,I-34127Trieste,Italy77IFIC,Universitat de Valencia-CSIC,E-46071Valencia,Spain78University of Victoria,Victoria,British Columbia,Canada V8W3P679Department of Physics,University of Warwick,Coventry CV47AL,United Kingdom80University of Wisconsin,Madison,Wisconsin53706,USA81Yale University,New Haven,Connecticut06511,USA(Dated:February7,2008)Using230.2fb−1of e+e−annihilation data collected with the B A B A R detector at and near the peakof theΥ(4S)resonance,489±55events containing the pure leptonic decay D+s→µ+νµhave beenisolated in charm-tagged events.The ratio of partial widthsΓ(D+s→µ+νµ)/Γ(D+s→φπ+)ismeasured to be0.143±0.018±0.006allowing a determination of the pseudoscalar decay constantf D s=(283±17±7±14)MeV.The errors are statistical,systematic,and from the D+s→φπ+branching ratio,respectively.PACS numbers:13.20.He,14.40.Nd,14.60.FgMeasurements of pure leptonic decays of charmed pseu-doscalar mesons are of particular theoretical importance.They provide an unambiguous determination of the over-lap of the wavefunctions of the heavy and light quarkswithin the meson,represented by a single decay constant(f M)for each meson species(M).The partial width fora D+s meson to decay to a single leptonflavor(l)and itsaccompanying neutrino(νl),is given byΓ(D+s→l+νl)=G2F|V cs|2m2D s 2,(1)where m Ds and m l are the D+s and lepton masses,re-spectively,G F is the Fermi constant,and V cs is theCKM matrix element giving the coupling of the weakcharged current to the c and s quarks[1].The partialwidth is governed by two opposing terms in m2l.Thefirst term reflects helicity suppression in the decay of thespin-0meson,requiring the charged lepton to be in itsunfavored helicity state.The second term is a phase-space factor.As a result,the ratio ofτ:µ:e de-cays is approximately10:1:ttice calcula-tions have resulted in f Ds=(249±17)MeV and a ratiof Ds/f D=1.24±0.07[2].CLEO-c has recently measureda value for f D=(223±17)MeV[3].We present herein the most precise measurement todate of the ratioΓ(D+s→µ+νµ)/Γ(D+s→φπ+)andthe decay constant f Ds.The data(230.2fb−1)were col-lected with the B A B A R detector at the asymmetric-energye+e−storage ring PEP-II at and below theΥ(4S)reso-nance.The B A B A R detector is described in detail else-where[4].Briefly,the components used in this analysisare the tracking system composed of afive-layer siliconvertex detector and a40-layer drift chamber(DCH),theCherenkov detector(DIRC)for chargedπ–K discrim-ination,the CsI(Tl)calorimeter(EMC)for photon andelectron identification,and the18-layerflux return(IFR)located outside the1.5T solenoid coil and instrumentedwith resistive plate chambers for muon identification andhadron rejection.The analysis proceeds as follows.In order to measureD+s→µ+νµ,the decay chain D∗+s→γD+s,D+s→µ+νµis reconstructed from D∗+s mesons produced in the hardfragmentation of continuum c5FIG.1:Tag mass distribution,showing the signal and side-band regions,in events with a recoil muon.All tag modes are combined,scaling their mass and width to that of the D0→K−π+mode.Muons used in this analysis are identified with an average efficiency of≈70%,while the pion misidentification rateis≈2.5%.Clusters of energy in the EMC not associated with charged tracks are identified as photon candidates.The photon CM energy must exceed0.115GeV.The CM missing energy(E∗miss)and momentum( p∗miss) are calculated from the four-momenta of the incominge+e−,the tag four-momentum,and the four-momenta of all remaining tracks and photons in the event.The energy of the charged particles that do not belong tothe tag is calculated from the track momentum under a pion mass hypothesis.Assigning a mass according to the most likely particle hypothesis has negligible effecton the missing energy resolution.Since the neutrino in the signal decay leads to a large missing energy in theevent,the requirement E∗miss>0.38GeV is made. The neutrino CM four-momentum(p∗ν=(| p∗ν|, p∗ν)) is estimated from the muon CM four-momentum(p∗µ) and p∗miss,using a technique adopted from Ref.[5].Thedifference| p∗miss− p∗ν|is minimized,while the invariant mass of the neutrino-muon pair is required to be the known mass of the D+s[6].Studies of simulated decays of signal and background cc events it peaks at a negative value significantly separated from the signal.A requirement p corr>−0.06GeV/c is imposed.To reduce contributions from background events where particles are lost along the beam pipe in the forward direction,a requirement on the neutrino CM polar angleθ∗ν>38◦is made.The muon CM four-momentum(p∗µ)is combined with p∗νto form the D+s candidate.Unlike the signal D+s,a large num-ber of random D+s combinations have the muon candi-date aligned with the D+sflight direction.A requirement cos(αµ,Ds)<0.90is made on the angle between the muondirection in the D+s frame and the D+sflight direction in the CM frame.The D+s candidate is then combined with a photon candidate to form the D∗+s.The CM momen-tum of correctly reconstructed D∗+s is typically higher than that of random combinations;signal candidates are required to have| p∗D∗+s|>3.55GeV/c.The resulting sig-nal detection efficiency in tagged events isǫSig=8.13%.The selection requirements on E∗miss,αµ,Ds,p corr,θ∗ν, and| p∗D∗+s|are optimized using simulation to maximize the significance s/√c where the tag is incorrectly reconstructed. Although these events potentially contain the signal de-cay,they are also subtracted using the tag sidebands. These two sources amount to≈42%of the background. The second class of background events(≈26%)are correctly tagged cc fragmentation or indecays of D∗+(s),excluding the signal decay chain.If the photon used in the reconstruction originates from aπ0ofa D∗+(s)decay,the∆M distribution peaks sharply around 70MeV/c2;otherwise it isflat.A small background (≈1%)arises from decays D∗+s→γD+s→γτ+ντwith τ+→π+(π0)ντand the charged pion being misidentified as a muon.Its∆M distribution peaks close to that of the signal.Other backgrounds(≈10%)include signal events with an incorrectly chosen photon candidate,and hadronic c6FIG.2:∆M distribution of charm-tagged events passing thesignal selection.The tag can be from the tag signal region(solid lines)or the sidebands(dashed lines).In the bottomplot the signal muon is replaced with an electron to estimatethe semileptonic charm andτdecay background.usually aπ+or a K+,being misidentified as a muon.These backgrounds have aflat∆M distribution.Events that pass the signal selection are grouped intofour sets,depending on whether the tag lies in the sig-nal region or the sideband regions,and on whether thelepton is a muon or an electron(Fig.2).For each leptontype the sideband∆M distribution is subtracted.Theelectron distribution,scaled by the relative phase-spacefactor(0.97)appropriate to semileptonic charm mesondecays and leptonicτdecays is then subtracted fromthe muon distribution.The resulting∆M distributionisfitted with a function(N Sig f Sig+N Bkgd f Bkgd)(∆M),where f Sig and f Bkgd describe the simulated signal andbackground∆M distributions.The function f Sig is adouble Gaussian distribution.The function f Bkgd con-sists of a double and a single Gaussian distribution de-scribing the two peaking background components,anda function[7]describing theflat background component.The relative sizes of the background components,alongwith all parameters except N Sig and N Bkgd arefixed tothe values estimated from simulation.Theχ2fit yieldsN Sig=489±55(stat)signal events and has afit proba-bility of8.9%(Fig.3).The branching fraction of D+s→µ+νµcannot be de-termined directly,since the production rate of D(∗)+smesons in c7FIG.4:∆M distribution of selected D∗+s→γD+s→γφπ+ events after the tag sideband is subtracted.The solid line is thefitted signal and background distribution(Nφπfφπ+ NφπBkgd fφπBkgd),the dashed line is the background distribu-tion(NφπBkgd fφπBkgd)alone.pion to be at least0.8GeV/c.The efficiency-correctedD∗+s momentum distribution in data is compared to that of D∗+s in simulated D∗+s→γD+s→γφπ+events.A harder momentum spectrum is observed in data.The de-tection efficiencies for signal and D∗+s→γD+s→γφπ+ events are re-evaluated after weighting simulated events to match the D∗+s momentum distribution measured in data.The correction to the efficiency ratio is+1.5%. With both corrections applied,the partial width ra-tio is determined to beΓµν/Γφπ=(N/ǫ)Sig/(N/ǫ)φπ×B(φ→K+K−)=0.143±0.018(stat),with B(φ→K+K−)=49.1%[6].The combined systematic uncertainty due to the cor-rections applied,taken as half the size of each correction, is1.0%.The systematic error in the signal efficiency due to selection criteria insensitive to the D∗+s momentum is evaluated using reconstructed D∗0→γD0→γK−π+ events.The conditions present in the signal are emulated by removing the charged pion,taken to represent the neu-trino,from these events.The signal reconstruction and selection steps are repeated,and the selection efficiencies compared between simulated and data events.The as-signed systematic uncertainty is1.4%.For the D+s→φπ+selection,requirements on the D+s andφvertexfit probability contribute a systematic uncertainty of0.7%, estimated from comparisons of D+s→φπ+events in sim-ulation and data.Control samples of e+e−→µ+µ−γand D∗+→π+D0→π+K−π+events are used to mea-sure the particle identification efficiencies of muons and charged kaons and pions in data,and to correct the sim-ulated signal and D∗+s→γD+s→γφπ+efficiencies.An uncertainty of0.7%is associated with these corrections, mainly due to the limited statistics of the control sam-ples.The systematic uncertainties in the track recon-struction efficiency cancel partially in the D+s→µ+νµto D+s→φπ+ratio and contribute1.2%.An additional uncertainty of1.1%is due to the statistical limitations of the simulated signal and D+s→φπ+event samples.Simulation studies are used to evaluate the systematic uncertainties arising from a possible inadequate param-eterization of the signal(0.9%)and background(2.3%) shapes.Simulations are also used to determine the sys-tematic uncertainty associated with the subtraction of the electron sample(0.4%).The error on the branching ratio B(φ→K+K−)is1.2%,the uncertainty on the D+s→f0(980)π+background is1.1%.The total sys-tematic uncertainty onΓ(D+s→µ+νµ)/Γ(D+s→φπ+) is3.9%.Using the B A B A R average for the branching ratio B(D+s→φπ+)=(4.71±0.46)%[8][9],we obtain the branching fraction B(D+s→µ+νµ)=(6.74±0.83±0.26±0.66)×10−3and the decay constant f Ds=(283±17±7±14)MeV.Thefirst and second errors are statistical and systematic,respectively;the third is the uncertainty from B(D+s→φπ+).The ratio of our value for f D s to f D from the CLEO-c measurement,f Ds/f D=1.27±0.14, is consistent with lattice QCD.Using B(D+s→φπ+)PDG=(3.6±0.9)%[6],the branching fraction is B(D+s→µ+νµ)=(5.15±0.63±0.20±1.29)×10−3and the decay constant f Ds=(248±15±6±31)MeV.We are grateful for the excellent luminosity and ma-chine conditions provided by our PEP-II colleagues,and for the substantial dedicated effort from the computing organizations that support B A B A R.The collaborating institutions wish to thank SLAC for its support and kind hospitality.This work is supported by DOE and NSF(USA),NSERC(Canada),IHEP(China),CEA and CNRS-IN2P3(France),BMBF and DFG(Germany), INFN(Italy),FOM(The Netherlands),NFR(Norway), MIST(Russia),and PPARC(United Kingdom).Indi-viduals have received support from the Marie Curie EIF (European Union)and the A.P.Sloan Foundation.∗Also at Laboratoire de Physique Corpusculaire,Clermont-Ferrand,France†Also with Universit`a di Perugia,Dipartimento di Fisica, Perugia,Italy‡Also with Universit`a della Basilicata,Potenza,Italy[1]Charge conjugation is implied throughout this Letter.[2]C.Aubin et al.,Phys.Rev.Lett.95,122002(2005).[3]CLEO Collaboration,M.Artuso et al.,Phys.Rev.Lett.95,251801(2005).[4]B A B A R Collaboration,B.Aubert et al.,Nucl.Instrum.Methods Phys.Res.,Sect.A479,1(2002).[5]CLEO Collaboration,M.Chadha et al.,Phys.Rev.D58,032002(1998).[6]Particle Data Group,S.Eidelman et al.,Phys.Lett.B592,1(2004).[7]¯A(∆M|∆M0,a,b,c)= 1−exp −∆M−∆M0∆M0 a+b ∆M8to appear in Phys.Rev.D-Rapid Communications.091104(2005).[9]B A B A R Collaboration,B.Aubert et al.,hep-ex/0605036,。