Lepton Flavour Violation and $B_s$ Leptonic Final States at the LHC

An overview of ATLAS and CMS studies of B_s leptonic decays providing constraints on the lepton flavour violation phenomenon is presented. Except direct lepton flavour violating final states B_s -> l_1^+ l_2^-, constraints can also be set by a measurement of B_s -> mu^+ mu^- decay, whose branching ratio in some theoretical models correlates with a branching ratio of B_s -> l_1^+ l_2^-, tau -> 3mu and some other lepton flavour violating decays. In this paper, the feasibility of measurements of B_s -> mu^+ mu^- decay is described, including the present status, the trigger and the offline analysis strategies and the expected reach in the branching ratio measurement. The ATLAS and CMS experiments foresee to provide 3-sigma evidence of Standard Model B_s -> mu^+ mu^- branching ratio by the end of LHC low-luminosity stage (30 fb^(-1)). Also a CMS study of the tau -> 3mu decay and an initial particle-level based study of the B_s -> tau mu decay are presented. A sensitivity of ~10^(-8) for the tau -> 3mu branching ratio measurement is predicted by CMS.