Run-Hui Li Yonsei University

1. Run-Hui Li Yonsei University Mainly based on R.H. Li, C.D. Lu, and W. Wang, PRD83:034034.

2. Content • Introduction • in SM • Two NP scenarios • Summary • About K2* meson • Why ? • Effective Hamiltonian and Wilson coefficients • Angular distribution • BR, FBA, fL. • Brief introduction • Parameters obtained by fitting • Effect on the SM results Run-Hui Li @ Yonsei

3. About K2* • 5 polarization states: Jz=-2，-1，0，1，2 • 3 contribute to , Jz=-1, 0, 1, because of angular momentum conservation. • Simlilar to K* mesons. formulism can be got by some substitution in formulism in pQCD approach. Run-Hui Li @ Yonsei

4. Why B to K(K*,K1,K2*) l+ l- ? Loop effects in SM Dominated by FCNC At quark level Ideal place to probe new physics FCNC in SM (∆B=1) Run-Hui Li @ Yonsei

5. Effective operator Effective Hamiltonian & Wilson coefficients In B meson decays, W, Z, top, … are very heavy, and never appear in the external lines. Integrate them out to get effective operators. Example of charged current Run-Hui Li @ Yonsei

6. Wilson coefficient Charged Current Effective Hamiltonian & Wilson coefficients The effective Hamiltonian has the form Run-Hui Li @ Yonsei

7. Effective Hamiltonian & Wilson coefficients The effective Hamiltonian for is given as The effective operators given as Run-Hui Li @ Yonsei

8. : Contributions to the decays Short-distance contributions A.J. Buras and M. Munz, Phys. Rev. D 52, 186(1995) Long-distance contributions C.S. Kim, T. Morozumi and A.I. Sanda, Phys. Lett. B 218,343 A. Ali, T. Mannel and T. Morozumi, Phys. Lett. B 273,505. Contributions of effective operators at tree and one loop level Contributions from the resonant states Run-Hui Li @ Yonsei

9. Effective Hamiltonian & Wilson coefficients Long distance contributions can be subtracted easily in experiments. Therefore, we only consider the short distance contributions. Run-Hui Li @ Yonsei

10. B to K2* l+ l- decay Hadronic part Run-Hui Li @ Yonsei

11. Form Factors • Phenomenal parameters • Contains all the nonperturbative information. Run-Hui Li @ Yonsei

12. Form Factors in PQCD approach The parameterization formula Numerical results W. Wang, PRD83,014008 Run-Hui Li @ Yonsei

13. Partial decay width is decomposed into 11 terms Angular distribution Run-Hui Li @ Yonsei

14. Angular distribution Run-Hui Li @ Yonsei

15. Angular distribution • Up to one-loop matrix element and resonances taken out, only contributes a small imaginary part. Without higher order QCD corrections They could be chosen as the window to observe those effects that can change the behavior of the Wilson coefficients, such as NP effects. Run-Hui Li @ Yonsei

16. BRs, fL With the PQCD results for form factors Branching ratios: Polarization distributions: Run-Hui Li @ Yonsei

17. Forward and Backward Asymmetry The zero-crossing point of FBAs is determined by the equation Run-Hui Li @ Yonsei

18. New Physics part How does NP enter low energy processes, such as B decays? If light, new particles observed directly. If heavy, new particles can not be generated directly, effect the Wilson coefficients like the W, Z, and top. Run-Hui Li @ Yonsei

19. free parameter NP scenario: Vector-like quark model (VQM) Expanding SM with including a SU(2)L singlet down type quark, Yukawa section of SM is modified to This modification brings FCNC for the mass eigenstates at tree level. The interaction for b-s-Z in VQM is with which the effective Hamiltonian for is given as The VQM effects can be absorbed into the Wilson coefficients C9 and C10 Lepton section in VQM is the same as in SM. Run-Hui Li @ Yonsei

20. Too many free parameters. so we set in our analysis to reduce freedoms. NP scenario: Family non-universal Z’ model Expand SM by simply including an additional U(1)’ symmetry. The current is which couples to a family non-universal Z’ boson. After rotating to the mass eigen basis, FCNC appears at tree level in both LH and RH section. Interaction for b-s-Z’ is given as The effective Hamiltonian for is given as Different from VQM, the couplings in both the quark and lepton section are free parameters. Z’ also only affects C9 and C10 phenomenally: Run-Hui Li @ Yonsei

21. Definition of Constrain the NP parameters Data used for fitting Heavy Flavor Averaging Group, arXiv:1010.1589; Particle Data Group, J. Phys. G 37,075021. Run-Hui Li @ Yonsei

22. Constrain the NP parameters VQM Phase less constrained Constrains on the Wilson coefficients with Assume as real Z’ with Both and are complex numbers. with has little effect on Combining the above results Run-Hui Li @ Yonsei

23. NP effects in observables To illustrate the NP effects, we choose and as the reference points. • Br may be enhanced, however, large uncertainties. • Zero-crossing point of AFB may be changed obviously. In this parameter space, is consistent with the recent measurement. D0 collaboration, PLB 693,539. Run-Hui Li @ Yonsei

24. Summary • is investigated in SM. • Two NP scenarios (VQM, Z’ model) are investigated. could be chosen as window for NP Angular distribution performed: : expected to be observed in future Exp. FBA, polarization fractions, etc, are investigated, with small uncertainties. Parameter space constrained with data of and . NP effects on are investigated. Zero-crossing point of FBA can be changed dramatically, which can be used for NP effects observation. Thank you very much for your attention. Run-Hui Li @ Yonsei