Large phase of Bs-(B)overbars mixing in supersymmetric grand unified theories

We consider the impact of a large phase of B-s-(B)overbar(s) mixing in supersymmetric SU(5) and SO(10) models. In the models, the magnitude of this phase is correlated with the branching ratio of tau ->mu gamma, and we find that in the SU(5) model, the phase is bound to be small. In the case of SO(10) models, this correlation can be relaxed and a large phase can be obtained. We predict the sparticle mass ranges for the LHC for these models once the recent result which shows evidence of large phase is accommodated and discuss the dark matter and the anomalous magnetic moment constraints on this analysis. We show that the upcoming results of Fermilab will be very useful to decipher these important grand unified theory symmetries.