1. Test Z’ Model in Annihilation Type Radiative B Decays Ying Li Yonsei University, Korea Yantai University, China Based on J. Hua, C.S Kim, Y. Li, arxiv:1002.2531

2. 2 Outline Motivation Calculation of in the SM Calculation in the non-universal Z’ model Summary

3. 3 Motivation The SM is just an effective theory of a more fundamental one yet to be discovered. B physics plays an important role in searching for new physics signals. Additional U(1)’ gauge symmetries and associated Z’ gauge bosons could appear in several well motivated extensions of the SM. I would like to check the Z’ effect in the annihilation type radiative B decays

4. 4 Annihilation type radiative B decays play important role in explaining CP violation and SU(3) asymmetry of B  K*gamma, B  rho gamma. A. Ali and A. Parkhomenko, arXiv:hep-ph/0610149. S. W. Bosch and G. Buchalla, Nucl. Phys. B 621, 459 (2002) P. Ball, G. W. Jones and R. Zwicky, Phys. Rev. D 75, 054004 (2007) W. Wang, R. H. Li and C. D. Lu, arXiv:0711.0432 [hep-ph]. Some annihilation type radiative decays, such as B->phi gamma and B->J/psi gamma, have been analyzed in the QCD factorization approach and in the perturbative QCD approach. X. Q. Li, et..al, Eur. Phys. J. C 36, 97 (2004) G. R. Lu, et.al, Eur. Phys. J. C 34, 291 (2004) Y. Li and C. D. Lu, Phys. Rev. D 74, 097502 (2006)

5. 5 Calculation in the SM

6. 6 The form factor F V has been defined as: In order to calculate the form factor F V, we need two-particle light-cone projector for an initial B meson: So we get: With the parameterization:

7. 7 we write down the helicity amplitudes for these channels as: We can get the averaged branching ratios as:

8. 8 The vertex correction diagrams:

9. 9

10. 10 Branching Ratios: CP Asymmetries: The above ratios can not be observed in the current running machines now. If the factories found any signals, we could say that we find the new physics.

11. 11 Additional heavy neutral Z’ gauge bosons are amongst the best motivated extensions of the standard model, or its supersymmetric extension. In particular, they often occur in grand unified theories, superstring theories, and theories with large extra dimensions. In traditional GUTs, the scale of the Z ′ mass is arbitrary. However, many researches imply that the Z’ mass should be less than around a TeV. There is thus both theoretical and experimental motivation for an additional Z’, most likely in the range 500 GeV - 1 TeV. If true, there should be a good chance to observe it at RUN II at the Tevatron, and certainly at the LHC. The collider signals of Z’ have been explored by many groups. Introduction to Z’ Model

12. 12 P. Langacker et. al,, Phys. Rev. D 62, 013006 (2000) ; P. Langacker, arXiv:0801.1345; V. Barger, et. al, Phys. Lett. B 580, 186 (2004) ; V. Barger, et. al, Phys. Lett. B 598, 218 (2004) ; V. Barger, et. al, arXiv:0906.3745 ; V. Barger, et. al, Phys. Rev. D 80, 055008 (2009) ; K. Cheung, et. al, Phys. Lett. B 652, 285 (2007) ; C. W. Chiang, et. al, JHEP 0608, 075 (2006); C. H. Chen, et. al, Phys. Rev. D 73, 075003 (2006); C. H. Chen, arXiv:0911.3479 [hep-ph]; C. W. Chiang, R. H. Li and C. D. Lu, arXiv:0911.2399 [hep-ph]; R. Mohanta and A. K. Giri, Phys. Rev. D 79, 057902 (2009); Q. Chang, X. Q. Li and Y. D. Yang, JHEP 0905, 056 (2009) Q. Chang, X. Q. Li and Y. D. Yang, arXiv:0907.4408 [hep-ph] …… The effects of Z ’ in B sector have been investigated by many groups:

13. 13 Introduction to Z’ Model We will consider the model in which the interaction between the Z’ boson and fermions are flavor non-universal for left handed couplings and flavor diagonal for right handed couplings. In our work, we neglected the mixing between the Z and Z’ and the evolution effect from the high scale M z’ to the M W scale. We write the couplings of the Z ’ boson to fermions as:

14. 14 After rotating to the physical basis, FCNCs generally appear at tree level in both left handed and right handed sectors. Moreover, these couplings may contain CP-violating phases beyond that of the SM. The effective Hamiltonians describing the transition mediated by the Z ’ boson have the form as: with denote the left (right) handed effective Z’ couplings of the quarks i and j at the weak scale.

15. 15 With the definition : we can get : Generally, one expects g 0 /g 1 ~ 1, if both the U(1) gauge groups have the same origin from some grand unified theories, and M Z /M Z0 ~0.1 for a TeV scale neutral Z ’ boson, which yields y~10 −2. However, if assuming a small mixing between Z −Z ’ bosons, the value of y is taken as y~10 −3.

16. 16 It has been shown that the mass difference of Bs −Bs bar mixing can be explained if. The CP asymmetry anomaly in B->phi K, phi K* can be resolved if. So, we assume that : It is noted that the other Wilson coefficients may also receive contributions from the Z’ boson through renormalization group (RG) evolution.

17. 17 The contributions of new physics can be formulated as

18. 18 Considering the Z’ model for :

19. 19

20. 20

21. 21 SM

22. 22 Summary The smallness of these decays in the standard model makes them sensitive probes of flavor physics beyond the standard model. Within the allowed parameter space, the branching ratios of these decay modes can be enhanced remarkably in the non-universal Z ’ model These branching ratios are large enough for LHC-b and/or Super B-factories to detect those channels in near future. Moreover, we also predict large CP asymmetries in suitable parameter space. The observation of these modes could in turn help us to constrain the Z ’ mass within the model.

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