Penguin Contribution to the Phase of B_s-bar B_s Mixing and B_s -> mu mu in Grand Unified Theories

We investigate the possibility of a large B_s-\bar B_s 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 B_s mixing is correlated with Br(b -> s gamma), Br(tau -> mu gamma) and Br(B_s -> mu mu) for large tan beta. In the case of the SO(10) model, the large phase of B_s mixing is correlated with Br(b -> s gamma) and Br(B_s -> mu mu) and we find that a large B_s mixing corresponds to an enhanced Br(B_s -> mu mu) about to be probed by the Tevatron. In the case of the SU(5) model, the large phase is correlated with Br(tau -> mu gamma) and Br(B_s -> mu mu). In this case, the Br(tau -> mu gamma) constraint requires a smaller pseudo-scalar Higgs mass which in turn generates a large Br(B_s -> mu mu) almost at the edge of present experimental constraint. If the present observation of large phase of B_s mixing persists in the upcoming data, using all these branching ratios, we will be able to distinguish these models.