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

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
2019/6/23
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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.
2019/6/23
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4. Ideal place to probe new physics
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)
2019/6/23
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5. 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
Effective operator
2019/6/23
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6. Effective Hamiltonian & Wilson coefficients
Charged Current
Wilson coefficient
The effective Hamiltonian has the form
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7. Effective Hamiltonian & Wilson coefficients
The effective Hamiltonian for is given as
The effective operators given as
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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
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9. 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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10. B to K2* l+ l- decay
Hadronic part
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11. Form Factors Phenomenal parameters
Contains all the nonperturbative information.
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12. Form Factors in PQCD approach
The parameterization formula
Numerical results
W. Wang, PRD83,014008
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13. Angular distribution Partial decay width is decomposed into 11 terms
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14. Angular distribution
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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.
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16. BRs, fL With the PQCD results for form factors Branching ratios:
Polarization distributions:
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17. Forward and Backward Asymmetry
The zero-crossing point of FBAs is determined by the equation
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18. How does NP enter low energy processes, such as B decays?
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.
2019/6/23
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19. 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
free parameter
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.
2019/6/23
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20. 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.
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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21. Constrain the NP parameters
Data used for fitting
Heavy Flavor Averaging Group, arXiv: ;
Particle Data Group, J. Phys. G 37,
Definition of
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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
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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.
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24. Thank you very much for your attention.
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.
2019/6/23
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