V_{cb} and V_{ub} Determinations from Inclusive Semileptonic B Decays

a rXiv:h ep-ph/2105v11Oct221|V cb |and |V ub |Determinations from Inclusive Semileptonic B Decays Changhao Jin a a School of Physics,University of Melbourne,Victoria 3010,Australia The determinations of |V cb |and |V ub |from inclusive semileptonic B decays are reviewed.A comparison of the light-cone approach with the heavy quark expansion approach is made.The perspective for further improvement of the |V cb |and |V ub |determinations is discussed.1.INTRODUCTION |V cb |and |V ub |are two of the fundamental con-stants of the Standard Model.They need to be determined by experimental measurements.These can be done with leptonic,semileptonic,or nonleptonic decays of B mesons.In this talk I will discuss the determinations of |V cb |and |V ub |from inclusive semileptonic B decays.An observ-able in these processes is schematically related to |V cb |or |V ub |in the form observable =|V c (u )b |2·T,where T is a quantity derived from theory.The-ory may also be involved in the experimental analysis to obtain the observable.With the the-oretical relationship between the observable and |V cb |or |V ub |,the measured quantity can be con-verted into a value of |V cb |or |V ub |.The main ob-stacle in the theoretical description of the weakdecay processes is long-distance strong interac-tion effects.There are two classes of observ-ables:(1)routine observables,such as branching fractions and lifetimes,and (2)theory-motivated observables,such as the differential decay rate d Γ/dw at zero recoil (w =1)in the exclusive semileptonic decay B →D ∗lνfor determining |V cb |.The latter is motivated from theory because its relationship with |V cb |or |V ub |is theoretically clean and model-independent in some sense.2.THEORY OF INCLUSIVE SEMILEP-TONIC B DECAYSStrong interaction effects on inclusive semilep-tonic B decays are contained in the hadronic ten-sor W µν=−1M 2B W 2−iεµναβP αq βM 2B W 4+P µq ν+q µP ν28W2=[f(ξ+)−f(ξ−)],(5)ξ+−ξ−W4=0,(6) W5=W3,(7) whereξ±=(q0±d(y·P)4π3it decreases the total rate in the HQE approach. Therefore,there is significant duality violation in the HQE approach.In particular,it cannot in-clude the phase space effect.From the measured inclusive semileptonic branching fractions and the lifetime of the B meson,the LC approach would give rise to smaller values of|V cb|and|V ub|than the HQE approach,as I will discuss in more detail below.3.CONVENTIONAL METHODS Conventionally,the routine observables,the branching fractions and the lifetime of the B me-son,have been used to determine|V cb|and|V ub| from inclusive semileptonic B decays.These ob-servables are related to|V cb|or|V ub|in the form B(B→X c lν)τB=|V ub|2·γu.(11)Theory is needed to computeγc andγu.Be-sides parametric uncertainties,additional uncer-tainties in the theoretical calculations ofγc and γu stem from the assumption of quark-hadron du-ality in the HQE approach and the detailed shape of the distribution function,which is unknown at present,in the LC approach.The uncertainty due to the assumption of quark-hadron duality is irreducible.The errors usually quoted in the determinations of|V cb|and |V ub|from inclusive semileptonic B decays using the HQE calculations should be interpreted with caution.The significant uncertainty from the as-sumption of quark-hadron duality has not been included in the errors.In contrast,the uncer-tainty due to the shape of the distribution func-tion in the LC approach can be reduced.The distribution function is universal:It incorporates bound state effects in inclusive B decays,in-cluding semileptonic[1,2,3,4],radiative[5],and nonleptonic[17,18]inclusive B decays.Mea-surements of decay distributions and moments in these processes will impose constraints on the dis-tribution function.Especially,theξu spectrum [ξu=(q0+| q|)/M B]in B→X u lνand the photon energy spectrum in B→X sγare directly propor-Table1Kinematic cuts for suppressing the B→X c lνbackground.Fraction of events∼10%∼20%∼80%44.A NEW METHOD FOR THE PRE-CISE DETERMINATION OF|V ub|In the light-cone limit,y2→0,the b-quark number conservation leads to the sum rule[19,20] S≡ 10dξu1dξu=|V ub|2G2F M5B516.C.H.Jin,Phys.Lett.B448,119(1999).17.X.-G.He,C.H.Jin,and J.P.Ma,Phys.Rev.D64,014020(2001).18.C.H.Jin,Phys.Rev.D65,114009(2002).19.C.H.Jin,Mod.Phys.Lett.A14,1163(1999).20.C.H.Jin,Phys.Rev.D62,014020(2000).21.C.H.Jin,Phys.Lett.B520,92(2001).。