  The ATLAS, CMS and LHCb experiments will perform extensive searches for
physics Beyond the Standard Model (BSM). The investigation of decays of beauty
hadrons represents an alternative and complementary approach to the direct BSM
searches. A particularly promising observable for the search of New Physics
(NP) in $B-$hadron decays, is the measurement of the branching ratio of the
decay $B_S\to \mu^{+} \mu^{-}$. This observable is sensitive to physics BSM
with new scalar or pseudoscalar effective operators, such as theories involving
an extended Higgs sector. Here the prospects of the ATLAS, CMS and the LHCb
experiments for such a measurement are discussed. In particular the LHCb
experiment, thanks to its good particle identification and momentum resolution,
has the potential for an early discovery of this decay.
