seminar at Academia Sinica Procedure of factorization and Practical application to B decays in PQCD Makiko Nagashima NTU Department of Physics Particles and Fields Seminars at Institute of Physics, Academia Sinica May, 23, 2003 seminar at Academia Sinica

seminar at Academia Sinica In this talk, Brief explanation about factorization approach Difference between QCDF and PQCD Procedure of factorization in PQCD Demonstration of simple example considering the process πγ*→γ Practical application to B decay B→DK summary seminar at Academia Sinica

seminar at Academia Sinica Introduction Interesting subject How to reduce the theoretical uncertainties from predictions in B-physics Study of B-physics is important for determining of Standard Model (SM) parameters 　　　　　　for testing the SM　 Unitarity triangle B → ππ B →Ds π b →u lν three side B-B mixing three angle B → DK B →J/ψ Ks B →φKs preciseness is necessary b →c lν more precise predictions need to reduce theoretical uncertainties seminar at Academia Sinica

seminar at Academia Sinica What is the source of this uncertainty? Beyond SM In EW specific input parameters depending on the framework higher loop corrections source on the theoretical side nonperturbative effects stemming from strong interactions B decays most important These effects make calculation of hadronic matrix element to be more complicated ! BUT HOW do we tackle this problem? One solution is Factorization seminar at Academia Sinica

seminar at Academia Sinica What is Factorization ? seminar at Academia Sinica

seminar at Academia Sinica The first step of Factorization is extracting of the nonperturbative dynamics reflected by infrared divergences of radiative corrections in perturbation theory There are two types of infrared divergences Soft divergences Collinear divergences seminar at Academia Sinica

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seminar at Academia Sinica Impressively quark line also How many soft gluon How collinear How distinguish them ?? We want to push such an ambiguity in one piece Important feature distribution amplitude seminar at Academia Sinica

seminar at Academia Sinica The idea of Factorization has been developed and improved Recently, two assumptions have been proposed QCD-improved Factorization (QCDF) perturbative QCD (PQCD) What differences are there between two approaches ? Another singularity so-called end-point singularity To know this, seminar at Academia Sinica

seminar at Academia Sinica end-point singularity When collinear (soft) factorization approach is applied to B meson decays without any stratagem, B → X transition quark-level process x is large No problem x : parton momentum fraction region x is small What can we do ? seminar at Academia Sinica

seminar at Academia Sinica QCDF based on collinear factorization B → M1 M2 factorizable nonfactorizable There is only longitudinal degrees of freedom factorizable NO parton momentum fraction parton transverse momentum Not calculable Input (from exp.) nonperturbative effects still exist in form factor nonfactorizable parton transverse degrees of freedom are neglected A complete expansion in transverse momenta has been done and dropped seminar at Academia Sinica

seminar at Academia Sinica PQCD gluon nonfactorizable factorizable parton transverse momentum is introduced Consider in the impact parameter space factorizable and nonfactorizable NO end-point singularity seminar at Academia Sinica

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seminar at Academia Sinica Different picture for separating nonperturbative effects soft hard QCDF dominant Factorization Assumption PQCD dominant QCDF: form factor (Fj) involves singularity → not calculable but dominant PQCD: from factor (H) involves NO singularity → calculable and dominant Effective Theory SCEF same order contributions SCET: It is argued that soft and hard contributions are same order seminar at Academia Sinica

seminar at Academia Sinica Procedure of Factorization in PQCD πγ*→γ on-shell parton has no kT acquire kT through collinear gluon exchanges π lowest order diagram Process is simple momentum assignment initial-state pion final-state photon Using the Fierz transformation Collecting the leading contributions, do not depend on Transverse momentum seminar at Academia Sinica

seminar at Academia Sinica IR regulator for a parton-level diagram seminar at Academia Sinica

seminar at Academia Sinica The path for the Wilson link be composed of three pieces 0→ ∞ along the direction ∞+b ∞ ∞ → ∞+b y reproduced ∞+b → y along the direction This procedure is applied to all-order and approved extending to B→γlν seminar at Academia Sinica

seminar at Academia Sinica Practical Application to B decay in PQCD Analysis of B→DK Charged B decays Neutral B decays Lowest order Contributions come from only tree level diagrams stemming from two diagrams stemming from one diagram seminar at Academia Sinica

seminar at Academia Sinica Especially, Direct CP violation may appear from the interference of b → c with b → u transition Effective Hamiltonian seminar at Academia Sinica

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seminar at Academia Sinica Numerical analysis shape parameters there are three kinds of wave functions QCD sum rule Normalization Constants B→D form factor shape parameters B→πform factor seminar at Academia Sinica

seminar at Academia Sinica Direct CP violation together with their conjugate seminar at Academia Sinica

seminar at Academia Sinica measurement of φ3 strong phase seminar at Academia Sinica

seminar at Academia Sinica PQCD has been applied to various exclusive decay modes Branching ratio Decay mode Exp. PQCD Y-Y.Keum, H-n.Li and A.I.Sanda, PRD63,054008 (2001) C-H.Chen and H-n.Li, PRD63,014003 (2000) E.Kou and A.I.Sanda, PLB525,240 (2002) C-D.Lu and K.Ukai, hep-ph/0210206 S.Mishima, PLB521,252 (2001) C-H.Chen, Y-Y.Keum and H-n.Li, PRD66,054013 (2002) H.Hayakawa,K.Hasokawa and T.Kurimoto, hep-ph/0212095 seminar at Academia Sinica

seminar at Academia Sinica Summary In near future, two approaches will be discriminated by experiments seminar at Academia Sinica

seminar at Academia Sinica According to the studies of other decay modes, Results within PQCD are consistent with experimental data seminar at Academia Sinica