LHCb sensitivity to the $B^0_{s}\to \mu^\pm \mu^\mp \gamma$ decay

We discuss here the LHCb sensitivity to the Flavor Changing Neutral Current (FCNC) $B^0_{s}\to \mu^+ \mu^- \gamma$ decay, as obtained from our analysis of DC06 Monte Carlo data (proton-proton interactions at $\sqrt{s}$ = 14 TeV). The Standard Model branching ratio receives contributions from both long distance (LD) and short distance (SD) physics. The SD physics can be described by the well known formalism of the effective Hamiltonian and is dominated by the penguin and the box diagram operators. If the regions in the $(\mu^+\mu^-)$ invariant mass spectrum of the resonance regions ($\phi$, $J/\Psi$, $\Psi^{\prime}$) are cut away, the dominant Feynman diagrams are those with a photon emission from the initial quark leg. Though this being a LD effect, its contribution is shown by various authors to be under theoretical control and leads to a branching ratio estimate within the Standard Model of $\leq 5\cdot 10^{-9}$; this value is of the same order of magnitude of the $B^0_{s}\to \mu^+\mu^-$ decay, since the photon emission removes the helicity suppression. This decay, as the other FCNC decays of b hadrons, is sensitive to physics beyond the Standard Model, which can enhance the branching ratio by an order of magnitude or more. No measurement of this channel was performed so far and only one upper limit was set on the corresponding $B^0_{d}$ decay from the B-factory data. Our study shows that the LHCb 90 % C.L. upper limit assu ming no signal is found is $(6.02^{+2.37}_{-1.39}) \cdot 10^{-9 }$ with 2 fb $^{-1}$. This study does not deal yet with the normalization issues or with systematic effects, that will be subject of further studies.