Calculation of Pure Annihilation Type B Decay in PQCD Approach

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Presentation transcript:

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

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

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)

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)

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

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)

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)

Chang Ping, Bei Jing (昌平) Many decay models calculated in PQCD agree with experimental data: . . C.-D Lü,Ukai,Yang, PRD63, 074009 (2001) Keum, Li, Sanda, PRD63, 054008 (2001) Y.-Y.Keum, et.al, PRD69, 094018 (2004) C.-D.Lü,Ukai, EPJC28, 305 (2003) Y. Li, C.-D.Lü, hep-ph/0508032 ...… ...… 2019/5/23 Chang Ping, Bei Jing (昌平)

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

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)

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

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)

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

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

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

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)

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)

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/0305278 2019/5/23 Chang Ping, Bei Jing (昌平)

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/0308243. 2019/5/23 Chang Ping, Bei Jing (昌平)

Chang Ping, Bei Jing (昌平) Y. Li ,C. D. Lu, Z.J. Xiao and X.Q. Yu, PRD70, 034009(2004) 2019/5/23 Chang Ping, Bei Jing (昌平)

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)

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

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)

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