Procedure of factorization and Practical application to B decays in PQCD

1. 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

2. 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 In this talk, summary seminar at Academia Sinica

3. Introduction B-B mixing 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 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

4. specific input parameters depending on the framework higher loop corrections nonperturbative effects stemming from strong interactions source on the theoretical side What is the source of this uncertainty? Beyond SM In EW 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 isFactorization seminar at Academia Sinica

5. What is Factorization ? seminar at Academia Sinica

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

9. 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

10. 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

11. QCDF based on collinear factorization B → M1 M2 factorizable nonfactorizable There is only longitudinal degrees of freedom factorizable NOparton 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

12. 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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16. 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 SCEF Effective Theory same order contributions SCET: It is argued that soft and hard contributions are same order seminar at Academia Sinica

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

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

19. 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

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

21. 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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27. 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

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

29. measurement of φ3 strong phase seminar at Academia Sinica

30. PQCD has been applied to various exclusive decay modes Branching ratio 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

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

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