Procedure of factorization and Practical application to B decays in PQCD

seminar at Academia Sinica 1

Procedure of factorization and Practical application to B decays in PQCD

Makiko NagashimaNTU Department of Physics

Particles and Fields Seminars at Institute of Physics, Academia Sinica

May, 23, 2003


In this talk,

Brief explanation about factorization approach

Difference between QCDF and PQCD

Procedure of factorization in PQCD

Demonstration of simple exampleconsidering the process πγ*→γ

Practical application to B decay

B→DK

summary


Introduction

Interesting subject How to reduce the theoretical uncertaintiesHow to reduce the theoretical uncertaintiesfrom predictions in B-physics from predictions in B-physics

Study of B-physics is important for determining of Standard Model (SM) parameters 　　　　　　 for testing the SM　

Unitarity triangle

three side

three angle

more precise predictions

need to reduce theoretical uncertainties

b →c lν

B →Ds π

b →u lν

B-B mixing

B →J/ψ KsB →φKs

B → ππ

B → DK

preciseness is necessary


What is the source of this uncertainty?

source on thetheoretical side

Beyond SM

higher loopcorrections

most important

BUT HOW do we tackle this problem?

specific input parameters

depending on the framework

nonperturbative effects

stemming from strong interactions

In EW

B decays

These effects make calculation of hadronic matrix element to be more complicated !

One solution is Factorization


What is Factorization ?


The first step of Factorization is

extracting of the nonperturbative dynamics

reflected by

infrared divergencesof radiative corrections in perturbation theory

There are two types ofinfrared divergences

Soft divergences

Collinear divergences


also

How distinguish them ??

How many soft gluon How collinear

quark lineImpressively

We want to push such an ambiguity in one piece

distribution amplitudeImportant

feature


The idea of FactorizationThe idea of Factorizationhas been developed and improvedhas been developed and improved

Recently, two assumptions have been proposed

QCD-improved Factorization (QCDF)

perturbative QCD (PQCD)

What differences are there between two approaches ?

To know this, Another singularity so-called end-point singularity


end-point singularity

When collinear (soft) factorization approachis applied to B meson decays without any stratagem,

B → X transition quark-level process

x : parton momentum fraction x is large region

x is small

No problem

What can we do ?


factorizable nonfactorizable

based on collinear factorization QCDFB → M1 M2

There is only longitudinal degrees of freedom

factorizable NO parton momentum fraction parton transverse momentum nonperturbative effects still exist in form factor

Not calculableInput (from exp.)

nonfactorizableparton transverse degrees of freedom are neglected

A complete expansion in transverse momenta has been done and dropped


PQCD

factorizable nonfactorizablegluon

parton transverse momentum is introduced

Consider in the impact parameter space

NO end-point singularityfactorizable and nonfactorizable


hardsoft

same order contributions

FactorizationAssumption

Effective Theory

Different picture for separating nonperturbative effects

QCDF dominant

PQCD dominant

QCDF: form factor (Fj) involves singularity → not calculable but dominant

PQCD: from factor (H) involves NO singularity → calculable and dominant

SCEF

SCET: It is argued that soft and hard contributions are same order


Procedure of Factorization in PQCD

Process is simple

π

πγ*→γ

lowest order diagram

momentum assignment

initial-state pion

final-state photon

on-shell parton has no kT

acquire kT throughcollinear gluon exchanges

Using the Fierz transformationCollecting the leading contributions,

do not depend onTransverse momentum


IR regulator for a parton-level diagram


∞

∞+b

y

The path for the Wilson link

This procedure is applied to all-order and approved extending to B→γlν

be composed of three pieces

0→ ∞ along the direction

∞ → ∞+b

∞+b → y along the direction

reproduced


Practical Application to B decay in PQCD

Analysis of B→DK

Charged B decays

Neutral B decays

Lowest orderContributions come from only tree level diagrams

stemming from two diagrams

stemming fromone diagram


Especially, Especially,

Direct CP violation may appear from the interference of

b → c with b → u transition

Effective Hamiltonian


QCD sum rule

B→D form factor

B→πform factor

NormalizationConstants

shapeparameters

shapeparameters

there are three kinds of wave functions

Numerical analysis


Direct CP violation

together with their conjugate


measurement of φ3

strong phase


PQCD has been applied to various exclusive decay modes

Decay mode Exp. PQCD

Branching ratio

E.Kou and A.I.Sanda,PLB525,240 (2002)

S.Mishima,PLB521,252 (2001)

C-H.Chen, Y-Y.Keumand H-n.Li,PRD66,054013 (2002)

C-H.Chen and H-n.Li,PRD63,014003 (2000)

H.Hayakawa,K.Hasokawaand T.Kurimoto, hep-ph/0212095

C-D.Lu and K.Ukai,hep-ph/0210206

Y-Y.Keum, H-n.Li andA.I.Sanda,PRD63,054008 (2001)


Summary

In near future, two approaches will be discriminated by experiments


Results within PQCD are consistent with experimental dataAccording to the studies of other decay modes,

Procedure of factorization and Practical application to B decays in PQCD

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