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Run-Hui Li
Yonsei University
Mainly based on R.H. Li, C.D. Lu, and W. Wang, PRD83:034034.
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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
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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
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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*
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Effective Hamiltonian
The effective Hamiltonian for is given as
The effective operators given as
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: 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.
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Effective Hamiltonian & Wilson coefficients
Long distance contributions can be subtracted easily in experiments. Therefore, we only consider the short distance contributions.
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B to K2* l+ l- decay
Hadronic part
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Phenomenal parameters Contains all the
nonperturbative information.
Form Factors
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Form Factors in PQCD approach
W. Wang, PRD83,014008
The parameterization formula
Numerical results
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Angular distribution
is decomposed into 11 terms
Partial decay width
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Angular distribution
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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.
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BRs, fLWith the PQCD results for form factors
Branching ratios:
Polarization distributions:
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Forward and Backward Asymmetry
The zero-crossing point of FBAs is determined by the equation
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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.
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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:
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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.
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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
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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.
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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.