1. Calculation of Pure Annihilation Type B Decay in PQCD Approach
Ying Li
Institute of High Energy Physics
2019/5/23
Chang Ping, Bei Jing (昌平)

2. Chang Ping, Bei Jing (昌平)
Outline
Motivation
Framework
Numerical Evaluation
Conclusion
2019/5/23
Chang Ping, Bei Jing (昌平)

3. Chang Ping, Bei Jing (昌平)
Motivation
Many rare B decays are being measured in B factories.
Rare B decays are important windows in searching for new physics.
Pure annihilation is difficult to calculate in other factorization approaches.
Pure annihilation decays have been measured in B- factories since 2001.
2019/5/23
Chang Ping, Bei Jing (昌平)

4. Pure Annihilation Type B Decay
The four quarks
in final States are
different from the ones in B meson.
2019/5/23
Chang Ping, Bei Jing (昌平)

5. Chang Ping, Bei Jing (昌平)
SM Picture
vacuum
2019/5/23
Chang Ping, Bei Jing (昌平)

6. Chang Ping, Bei Jing (昌平)
Naive Factorization (B.S.W)
Generalized Factorization
(Ali, C.-D. Lu, H.-Y. Cheng)
BBNS-Factorization
(BBNS, Du, Yang, Xiao,…)
Perturbative QCD approach
(H.-N. Li, Sanda, Lu, …)
Soft-collinear effective theory (SCET)
(Stewart, Bauer, Pirjol, Li,…)
2019/5/23
Chang Ping, Bei Jing (昌平)

7. Chang Ping, Bei Jing (昌平)
PQCD Approach
PQCD is a successful effective approach in calculating B meson two body decay.
Sudakov factor can suppress the contribution of non-perturbative contribution effectively.
Non-factorization and annihilation diagrams play important roles in studying B meson two body non-leptonic decay.
The introduction of kT kills the endpoint singularity.
2019/5/23
Chang Ping, Bei Jing (昌平)

8. Chang Ping, Bei Jing (昌平)
Many decay models calculated in PQCD agree with experimental data: . .
C.-D Lü,Ukai,Yang, PRD63, (2001)
Keum, Li, Sanda, PRD63, (2001)
Y.-Y.Keum, et.al, PRD69, (2004)
C.-D.Lü,Ukai, EPJC28, 305 (2003)
Y. Li, C.-D.Lü, hep-ph/
...…
...…
2019/5/23
Chang Ping, Bei Jing (昌平)

9. Effective theory and Operator Expansion
2019/5/23
Chang Ping, Bei Jing (昌平)

10. Chang Ping, Bei Jing (昌平)
Considering the QCD corrections:
Effective
vertexes
If we don’t consider QCD
corrections, there is no
O_1 operator.
2019/5/23
Chang Ping, Bei Jing (昌平)

11. Chang Ping, Bei Jing (昌平)
Considering the Penguins :
Current-current:
QCD-Penguins:
2019/5/23
Chang Ping, Bei Jing (昌平)

12. Chang Ping, Bei Jing (昌平)
Electroweak penguins:
Magnetic penguins:
In our work, we ignore the magnetic penguins because their effects may be small .
2019/5/23
Chang Ping, Bei Jing (昌平)

13. Chang Ping, Bei Jing (昌平)
PQCD Picture of Decay
2019/5/23
Chang Ping, Bei Jing (昌平)

14. Chang Ping, Bei Jing (昌平)
The four quarks in final states are different from the ones in B -meson.
The gluon is a hard one, we can deal with it in perturbation theory.
2019/5/23
Chang Ping, Bei Jing (昌平)

15. Chang Ping, Bei Jing (昌平)
F.A Fail ?
Decay
constant
Form factor
This form factor at
can not be calculated.
2019/5/23
Chang Ping, Bei Jing (昌平)

16. Chang Ping, Bei Jing (昌平)
Scales Involved
Harder Part
Hadronization
Hard Part
One method to treat the multi-scales problem is factorization .
2019/5/23
Chang Ping, Bei Jing (昌平)

17. Chang Ping, Bei Jing (昌平)
Factorization
Hadronization of
quark and anti-quark
Hard part
(six-quark operator )
Harder part. Result from
the radiative corrections
at short distance.
2019/5/23
Chang Ping, Bei Jing (昌平)

18. Chang Ping, Bei Jing (昌平)
Wave Functions
Wave function describes hadronization of the quark and anti-quark to the meson. It is independent of the specific processes.
Wave function is decomposed in terms of spin structure and twists.
Wave function comes from QCD-Sum Rules or Lattice QCD
2019/5/23
Chang Ping, Bei Jing (昌平)

19. Light-cone Wave Function
This figure shows that most of
momentum is taken by b quark, and light quark takes very small fraction.
2019/5/23
Chang Ping, Bei Jing (昌平)

20. Chang Ping, Bei Jing (昌平)
Transverse Momentum-
Two Propagators
♣ Quark Propagator
♣ Gluon Propagator
Endpoint
singularity
We can not drop K_T away because there are in denominator!
2019/5/23
Chang Ping, Bei Jing (昌平)

21. Chang Ping, Bei Jing (昌平)
Sudakov Factor
The double logarithm from the overlap of collinear and soft gluon corrections.
2019/5/23
Chang Ping, Bei Jing (昌平)

22. Chang Ping, Bei Jing (昌平)
Exp[-S(Q,b)]
The Sudakov form factor suppresses the
soft dynamics effectively, this practically
make PQCD approach applicable.
2019/5/23
Chang Ping, Bei Jing (昌平)

23. The only part we need to calculate is the hard part.
Trace over Dirac and color indices.
The only part we need to calculate is the hard part.
Wave Functions
Wilson Coefficients
Threshold Resummation
Sudakov factor
2019/5/23
Chang Ping, Bei Jing (昌平)

24. Chang Ping, Bei Jing (昌平)
For Decay
2019/5/23
Chang Ping, Bei Jing (昌平)

25. Chang Ping, Bei Jing (昌平)
Meson color singlet
2019/5/23
Chang Ping, Bei Jing (昌平)

26. Chang Ping, Bei Jing (昌平)
2019/5/23
Chang Ping, Bei Jing (昌平)

27. Chang Ping, Bei Jing (昌平)
Comments
The vertexes involve all electroweak information.
We can get some information about
CP violation. This is different from QCD improved factorization.
2019/5/23
Chang Ping, Bei Jing (昌平)

28. Chang Ping, Bei Jing (昌平)
Numerical Evaluation
Results:
C.-D Lu, Ukai , Eur. Phys. J. C 28, 305 (2003)
Y. Li, C.-D Lu, J. Phy.G29, 2115 (2003)
Experiments:
2019/5/23
Chang Ping, Bei Jing (昌平)

29. Chang Ping, Bei Jing (昌平)
New Physics?
Results:
C.-D Lu, Ukai , Eur. Phys. J. C 28, 305 (2003)
Y. Li, C.-D Lu, J. Phy.G29, 2115 (2003)
Y. Li, C.-D Lu, hep-ph/
2019/5/23
Chang Ping, Bei Jing (昌平)

30. Chang Ping, Bei Jing (昌平)
Have a try :
Y.Li, C.D. Lu and Zh-J,Xiao, J.Phys.G31,273,2005 , hep-ph/
2019/5/23
Chang Ping, Bei Jing (昌平)

31. Chang Ping, Bei Jing (昌平)
Y. Li ,C. D. Lu, Z.J. Xiao and X.Q. Yu, PRD70, (2004)
2019/5/23
Chang Ping, Bei Jing (昌平)

32. Chang Ping, Bei Jing (昌平)
Uncertainty Origin
The wave functions
The decay constants
CKM matrix elements
High order corrections
2019/5/23
Chang Ping, Bei Jing (昌平)

33. The Hadronic Picture
Our results show this interaction may be unimportant.
2019/5/23
Chang Ping, Bei Jing (昌平)

34. Chang Ping, Bei Jing (昌平)
Summary
We calculated many rare decays using PQCD approach based on -factorzation.
Some decays have been measured, and some will be measured in B factories and LHC-b.
These rare decays may help us to study SM and search for new physics.
2019/5/23
Chang Ping, Bei Jing (昌平)

35. Chang Ping, Bei Jing (昌平)
Thank You
2019/5/23
Chang Ping, Bei Jing (昌平)