1. B physics at hadron collider
Polarization In
Decays
With PQCD Approach
沈月龙
中科院高能所
2019/1/14
B physics at hadron collider

2. B physics at hadron collider
Outline
Polarization problem in decays
Numerical analysis in PQCD approach.
Summary
2019/1/14
B physics at hadron collider

3. B physics at hadron collider
The decomposition of the amplitude for
2019/1/14
B physics at hadron collider

4. B physics at hadron collider
The helicity amplitude and power counting
Helicity flip suppression of the transverse polarization amplitude in the factorization assumption
Naïve counting rule
2019/1/14
B physics at hadron collider

5. B physics at hadron collider
Conflict between the experiment and theory
The perpendicular polarization is given by:
2019/1/14
B physics at hadron collider

6. B physics at hadron collider
Theoretical attempts to solve these puzzles
Nonperturbative corrections:
a) the charming penguin
b) the final state interactions ……
Currents that breaks the naïve cutting rule:
a) new physics
b) the magnetic penguin
c) the annihilation diagrams ……
2019/1/14
B physics at hadron collider

7. B physics at hadron collider
The annihilation diagram
Fierz Transformation
The S+P(S-P) current can break the counting rule, In the
annihilation diagram, the transverse and the longitudinal
polarization are at the same order .
2019/1/14
B physics at hadron collider

8. B physics at hadron collider
Endpoint singularity in collinear factorization
In QCD factorization approach, the annihilation diagram
can be parameterized as
2019/1/14
B physics at hadron collider

9. B physics at hadron collider
We introduce transverse momentum to regularize the endpoint
singularity
Then there is no endpoint singularity in factorization . but
large logarithm and are produced after
radiative corrections, they should be resummed to generate
the Sudakov form factor to improve the perturbation theory.
This is factorization formula in PQCD approach
2019/1/14
B physics at hadron collider

10. B physics at hadron collider
Annihilation diagrams in PQCD approach
The quark and gluon propagators can be on mass-shell,
so it may give a large imaginary part.
For helicity suppression(if the 4-quark operators are two left hand current), there is cancellation between the diagrams in which the gluon is attached to quark or an anti-quark, except for the perpendicular polarization part, but it is suppressed by a factor
The transverse and the longitudinal polarization in the
diagrams with (S+P)(S-P) current are at the same order,
they are suppressed by a factor
2019/1/14
B physics at hadron collider

11. B physics at hadron collider
Numerical analysis of some processes
C.H. Chen et al, PRD66,
C. D. Lu et al, hep-ph/
Y. Li et al, hep-ph/
J. Zhu et al, Phys.Rev. D72 (2005)
C. D. Lu, Eur.Phys.J. C41 (2005)
J. F. Cheng et al
J. Zhu, et al, hep-ph/
2019/1/14
B physics at hadron collider

12. B physics at hadron collider
Polarization in PQCD approach
In PQCD approach,
2019/1/14
B physics at hadron collider

13. B physics at hadron collider
Enhancement of the transverse polarization by the annihilation and hard spectator scattering diagrams
2019/1/14
B physics at hadron collider

14. B physics at hadron collider
A possible resolution within PQCD framework
The main contradiction between PQCD calculation and the experiments is the dominated modes,
Which is sensitive to the K* wave functions.
Recently, the reanalysis of the longitudinal polarized K*
distribution amplitude
shows it should be very close to the asymptotic form, we
can adopt asymptotic form as a test.
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B physics at hadron collider

15. B physics at hadron collider
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B physics at hadron collider

16. B physics at hadron collider
, which is sensitive to
is dominated by
the K* meson distribution amplitude.
If we fix at The longitudinal polarization of can be reduced to about 0.7
2019/1/14
B physics at hadron collider

17. B physics at hadron collider
and
is the first measured channel in Bs decays. which is
useful to determine the shape of the Bs wave function
Experiment:
2019/1/14
B physics at hadron collider

18. B physics at hadron collider
Summary
It is very difficult to resolve the polarization puzzle
in decays.
We perform the calculation for some channel with in PQCD
framework, which can enhance the transverse polarization for
penguin dominated decays, the problems still exist.
More precise experimental data and more involved theoretical
attempts are needed .
2019/1/14
B physics at hadron collider

19. B physics at hadron collider
Thank you !
2019/1/14
B physics at hadron collider