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

Run-Hui Yonsei2 Content  Introduction  in SM  Two NP scenarios  Summary  Angular distribution  BR, FBA, fL.  Brief introduction  Parameters obtained by fitting  Effect on the SM results

Run-Hui Yonsei3 Why B to K(K*,K 1,K 2 *) l + l - ? At quark level FCNC in SM (∆B=1) Loop effects in SM Ideal place to probe new physics Dominated by FCNC

Run-Hui Yonsei4  5 polarization states: Jz=-2 ， -1 ， 0 ， 1 ， 2  3 contribute to, Jz=-1, 0, 1, because of angular momentum conservation.  Simlilar to. About K 2 *

Run-Hui Yonsei5 Effective Hamiltonian The effective Hamiltonian for is given as The effective operators given as

Run-Hui Yonsei6 : Contributions to the decays Short-distance contributions Long-distance contributions Contribution s from the resonant states Contributions of effective operators at tree and one loop level A.J. Buras and M. Munz, Phys. Rev. D 52, 186(1995) 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.

Run-Hui Yonsei7 Effective Hamiltonian & Wilson coefficients Long distance contributions can be subtracted easily in experiments. Therefore, we only consider the short distance contributions.

Run-Hui Yonsei8 B to K 2 * l + l - decay Hadronic part

Run-Hui Yonsei9  Phenomenal parameters  Contains all the nonperturbative information. Form Factors

Run-Hui Yonsei10 Form Factors in PQCD approach W. Wang, PRD83, The parameterization formula Numerical results

Run-Hui Yonsei11 Angular distribution is decomposed into 11 terms Partial decay width

Run-Hui Yonsei12 Angular distribution

Run-Hui Yonsei13 Angular distribution 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.   Up to one-loop matrix element and resonances taken out, only contributes a small imaginary part.

Run-Hui Yonsei14 BRs, fL With the PQCD results for form factors Branching ratios: Polarization distributions:

Run-Hui Yonsei15 Forward and Backward Asymmetry The zero-crossing point of FBAs is determined by the equation

Run-Hui Yonsei16 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 free parameter The VQM effects can be absorbed into the Wilson coefficients C 9 and C 10 Lepton section in VQM is the same as in SM.

Run-Hui Yonsei17 NP scenario: Family non-universal Z’ model 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. Expand SM by simply including an additional U(1)’ symmetry. The current is 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. Too many free parameters. so we set in our analysis to reduce freedoms. Z’ also only affects C 9 and C 10 phenomenally:

Run-Hui Yonsei18 Constrain the NP parameters Data used for fitting Definition of Heavy Flavor Averaging Group, arXiv: ; Particle Data Group, J. Phys. G 37,

Run-Hui Yonsei19 VQM Constrain the NP parameters Phase less constrained Constrains on the Wilson coefficients with Z’ Assume as real with Both and are complex numbers. with has little effect on Combining the above results

Run-Hui Yonsei20 To illustrate the NP effects, we choose and as the reference points. NP effects in observables  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 Yonsei21  is investigated in SM.  Two NP scenarios (VQM, Z’ model) are investigated. Summary Angular distribution performed: could be chosen as window for NP : 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.