1. 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

2. 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

3. 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

4. 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

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

6. 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

7. seminar at Academia Sinica

8. 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

9. 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

10. 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

11. 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

12. 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

13. seminar at Academia Sinica

14. seminar at Academia Sinica

15. seminar at Academia Sinica

16. 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

17. 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

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

19. 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

20. 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

21. 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

22. seminar at Academia Sinica

23. seminar at Academia Sinica

24. seminar at Academia Sinica

25. seminar at Academia Sinica

26. seminar at Academia Sinica

27. 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

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

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

30. 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, (2001)
C-H.Chen and H-n.Li,
PRD63, (2000)
E.Kou and A.I.Sanda,
PLB525,240 (2002)
C-D.Lu and K.Ukai,
hep-ph/
S.Mishima,
PLB521,252 (2001)
C-H.Chen, Y-Y.Keum
and H-n.Li,
PRD66, (2002)
H.Hayakawa,K.Hasokawa
and T.Kurimoto,
hep-ph/
seminar at Academia Sinica

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

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