1. 𝐵→ 𝐾 1 𝑙 + 𝑙 − Decays in a Family Non-Universal Z′ Model
Ying Li
YanTai University

2. Outline Introduction: motivation & history
Remarks on 𝐾 1 (1270) and 𝐾 1 (1400)
Formulae
Results and Discussion
Summary

3. Introduction
FCNC process 𝑏→𝑠 𝑙 + 𝑙 − forbidden in the standard model (SM) at the tree level, are the most sensitive and stringiest test for the SM. Many processes, such as B->K* 𝑙 + 𝑙 − , have been explored by many groups in SM and extensions beyond of it.
Q-S Yan, et.al , PRD’98
W-J Li, et.al, EPJC’04
G-H Zhu, et.al EPJC, 06
T Huang, et.al , PRD’10
Y-D Yang, et.al , JHEP’09
K-C Yang, et.al , PRD’08
Y-M Wang, et.al , PRD’08
R-M Wang, et.al, PRD’08
R-H Li, et.al, PRD’09
Q Chang, et.al , NPB’11
C-W Chiang, et.al, CPC,11

4. Similar to B->K* 𝑙 + 𝑙 − , once 𝐵→𝐾 1 𝑙 + 𝑙 − could be measured well, they will offer another useful test of the SM and of its extensions.
Generally, in order to find the new physics signals, the relevant branching ratios, the di-lepton invariant mass distributions, the forward-backward asymmetries and lepton polarization asymmetries should be calculated in the SM and new physics models, before the possible new particles produce directly at the collides.

5. To make predictions of these exclusive decays, one requires the additional knowledge about form factors.
PQCD Approach
[Li, PRD,09]
QCD Sum Rules
[Dig,PRD’10]
Light front quark model
[Cheng, et.al, PRD’09]
Light-cone QCD Sum Rules
[Yang, PRD’08; Huang, PRD’11]

6. In some new physics models beyond of SM, Z’ could be naturally derived in certain string constructions , E6 by adding additional U(1)’ gauge symmetries.
Among many Z’ models, the simplest one is the family non-universal Z’ model. It is of interest to note that it could lead to FCNC at tree level as well as introduce new weak phases, which play important roles in explaining the CP asymmetries in the current high energy experiments.
Langacker, PRD’00; Cheung, PLB’07; Chiang, JHEP’06;
Barger, PLB’04,PLB,04; JHEP’09; Chang, JHEP’08, JHEP’09;
Barger, PRD’09; Chen, arxiv: ; Li, PLB’10, EPJC’10
Chiang, arXiv: ; Li, CPC’11, ……

7. Remarks on 𝐾 1 (1270) and 𝐾 1 (1400) 3P1 1P1
In SU(3) limit, K1A & K1B do not get mixed. However, they have admixture
due to strange and light quark mass difference
PDG ⇒ |K|  45o
Strong decays K1(1270), K1(1400) K,K* and their masses
⇒ K= 32,56
add: K 34, [CHY, arXiv: ]
Sign of K depends on the phase convention of states. It can be inferred from B→ K1 decays (HYC,Chua, PRD’05) We will use K=-34 13.

8. Remarks on 𝐾 1 (1270) and 𝐾 1 (1400)

9. [Yang, PRD’08]

10. Formulae A. The Effective Hamiltonian for 𝑏→𝑠 𝑙 + 𝑙 − in SM
The effective Hamiltonian responsible for the 𝑏→𝑠 𝑙 + 𝑙 − transitions is given as
The quark decay amplitude can also receive additional contributions from the matrix element of four-quark operators, which are usually absorbed into the effective Wilson coefficients

11. B. The Effective Hamiltonian for 𝑏→𝑠 𝑙 + 𝑙 − in Z’ model
Assuming that the couplings of right-handed quark flavors with Z’ boson are diagonal and ignoring Z-Z’ mixing, the Z’ part of the effective Hamiltonian for 𝑏→𝑠 𝑙 + 𝑙 − can be written as

12. The constraint of the parameters has been done by many groups in the past few years.
Combining the constraints from 𝑩 𝑺 − 𝑩 𝑺 mixing, and 𝐁→𝐊𝛑, 𝛒𝐊 decays, 𝑩 𝒔𝒃 𝑳 have been strictly constrained by Chang et. Al.
They also give the constraints of 𝑩 𝒍𝒍 𝑳 and 𝑩 𝒍𝒍 𝑹 from 𝐁→ 𝑿 𝒔 𝐥𝐥, 𝑲 ∗ 𝝁 + 𝝁 − and 𝑩 𝒔 → 𝝁 + 𝝁 − decays.
Recently, there have been more data from Tevatron and LHC on decay processes mentioned above. Many of them might afford stronger upper bounds than before, but the new parameters have not been fitted.
In the current work, we will adopt the parameters fitted by Chang et.al ,so as to probe contribution of new physics with the most possibility.

13. In order to show the maximal strength of Z’, with permitted range in S1, we choose the extreme values
More details about fitting can be seen in Chang’s talk.

14. C. Formula of Observables

15. D. The lepton polarization asymmetry
The lepton polarization asymmetry 𝐏 𝐢 (i = L;N;T) can be obtained by calculating

16. Results and Discussion

23. Summary
We studied the contributions of family non-universal Z’ model at the tree level in semi-leptonic B decays involving axial-vector meson K1 in the final states.
We found the 𝐵→ 𝐾 1 (1400)𝑙 + 𝑙 − is sensitive to the mixing angle.
The 𝐵→ 𝐾 1 (1270)𝑙 + 𝑙 − is not sensitive to mixing angle, and sensitive to the new physics effect.
The Zero position of FBA is a good probe of new physics contribution.
The ratio of branching ratios could be used to constrain the mixing angle.