Run-Hui Li Yonsei University

Run-Hui Li

Yonsei University

Mainly based on R.H. Li, C.D. Lu, and W. Wang, PRD83:034034.

23/4/22 Run-Hui Li @ Yonsei 2

Content Introduction in SM

Two NP scenarios

Summary

Angular distribution BR, FBA, fL.

Brief introduction Parameters obtained by fitting Effect on the SM results


Why B to K(K*,K1,K2*) l+ l- ?

At quark level

FCNC in SM (∆B=1)

Loop effects in

SM

Ideal place to probe new physics

Dominat

ed by

FCNC


5 polarization states: Jz=-2 ， -1 ， 0 ， 1 ， 2

3 contribute to , Jz=-1, 0, 1, because of angular momentum conservation.

Simlilar to .

About K2*


Effective Hamiltonian

The effective Hamiltonian for is given as

The effective operators given as


: Contributions to the decays

Short-distance contributions

Long-distance contributions

Contributions from the resonant states

Contributions from the resonant states

Contributions of effective operators at tree and one loop level

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.


Effective Hamiltonian & Wilson coefficients

Long distance contributions can be subtracted easily in experiments. Therefore, we only consider the short distance contributions.


B to K2* l+ l- decay

Hadronic part


Phenomenal parameters Contains all the

nonperturbative information.

Form Factors


Form Factors in PQCD approach

W. Wang, PRD83,014008

The parameterization formula

Numerical results


Angular distribution

is decomposed into 11 terms

Partial decay width





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.


BRs, fLWith the PQCD results for form factors

Branching ratios:

Polarization distributions:


Forward and Backward Asymmetry

The zero-crossing point of FBAs is determined by the equation


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 C9 and C10

Lepton section in VQM is the same as in SM.


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 C9 and C10 phenomenally:


Constrain the NP parameters

Data used for fitting

Definition of

Heavy Flavor Averaging Group, arXiv:1010.1589;Particle Data Group, J. Phys. G 37,075021.


VQM

Constrain the NP parameters

Phase less constrained

Constrains on the Wilson coefficients

with

Z’ Assume as real withBoth and are complex numbers.

with

has little effect on

Combining the above results


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.


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.

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Run-Hui Li Yonsei University