procedure of factorization and practical application to b decays in pqcd
DESCRIPTION
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. Brief explanation about factorization approach. - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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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
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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
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What is Factorization ?
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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
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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
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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
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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 ?
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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
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PQCD
factorizable nonfactorizablegluon
parton transverse momentum is introduced
Consider in the impact parameter space
NO end-point singularityfactorizable and nonfactorizable
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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
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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
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IR regulator for a parton-level diagram
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∞
∞+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
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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
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Especially, Especially,
Direct CP violation may appear from the interference of
b → c with b → u transition
Effective Hamiltonian
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QCD sum rule
B→D form factor
B→πform factor
NormalizationConstants
shapeparameters
shapeparameters
there are three kinds of wave functions
Numerical analysis
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Direct CP violation
together with their conjugate
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measurement of φ3
strong phase
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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)
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Summary
In near future, two approaches will be discriminated by experiments
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Results within PQCD are consistent with experimental dataAccording to the studies of other decay modes,