Test Z’ Model in Annihilation Type Radiative B Decays

Ying Li Yonsei University, KoreaYantai University, China

Based on J. Hua, C.S Kim, Y. Li, arxiv:1002.2531

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Outline

• Motivation

• Calculation of in the SM

• Calculation in the non-universal Z’ model

• Summary

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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

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• Annihilation type radiative B decays play important role in explaining CP violation and SU(3) asymmetry of BK*gamma,

Brho 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)

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Calculation in the SM

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The form factor FV has been defined as:

In order to calculate the form factor FV , we need two-particle light-cone projector for an initial B meson:

So we get:

With the parameterization:

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we write down the helicity amplitudes for these channels as:

We can get the averaged branching ratios as:

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The vertex correction diagrams:

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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.

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• 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

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• 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 [he

p-ph]; R. Mohanta and A. K. Giri, Phys. Rev. D 79, 057902 (200

9);• 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:

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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 Mz’ to the MW scale.

• We write the couplings of the Z’ boson to fermions as:

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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 describingthe 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.

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With the definition:

we can get:

Generally, one expects g0/g1~ 1, if both the U(1) gauge groups have the same origin from some grand unified theories, and MZ/MZ0~0.1 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.

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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.

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The contributions of new physics can be formulated as

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Considering the Z’ model for :

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SM

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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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