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

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

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

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

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

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

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

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

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

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

B physics at hadron collider Numerical analysis of some processes C.H. Chen et al, PRD66, 054013 C. D. Lu et al, hep-ph/0508080 Y. Li et al, hep-ph/0508032 J. Zhu et al, Phys.Rev. D72 (2005) 054015 C. D. Lu, Eur.Phys.J. C41 (2005) 311-317 J. F. Cheng et al J. Zhu, et al, hep-ph/0506316 2019/1/14 B physics at hadron collider

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

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

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. 2019/1/14 B physics at hadron collider

B physics at hadron collider 2019/1/14 B physics at hadron collider

B physics at hadron collider , which is sensitive to is dominated by the K* meson distribution amplitude. If we fix at 0.32. The longitudinal polarization of can be reduced to about 0.7 2019/1/14 B physics at hadron collider

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

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

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