Penguin contribution to the phase of Bs-B¯s mixing and Bs→μμ in grand unified theories

We investigate the possibility of a large Bs-Bs¯ mixing phase in the context of grand unified theory (GUT) models, e.g., SO(10) and SU(5). In these models, we find that a large phase of Bs mixing is correlated with Br(b→sγ), Br(τ→μγ) and Br(Bs→μμ) for large tanβ. In the case of the SO(10) model, the large phase of Bs mixing is correlated with Br(b→sγ) and Br(Bs→μμ) and we find that a large Bs mixing corresponds to an enhanced Br(Bs→μμ) about to be probed by the Tevatron. In the case of the SU(5) model, the large phase is correlated with Br(τ→μγ) and Br(Bs→μμ). In this case, the Br(τ→μγ) constraint requires a smaller pseudo-scalar Higgs mass which in turn generates a large Br(Bs→μμ) almost at the edge of present experimental constraint. If the present observation of large phase of Bs mixing persists in the upcoming data, using all these branching ratios, we will be able to distinguish these models.