${\bar{B}}_s\to {\mu }^{+}{\mu }^{-}$ decay in the Randall-Sundrum model

We investigate the ${\bar{B}}_s\to {\mu }^{+}{\mu }^{-}$ decay in the presence of a light stabilized radion in Randall-Sundrum model. The branching ratio $BR({\bar B_s} \to \mu^+ \mu^-)$inthestandardmodelisfoundtobe$3.17 \times 10^{-9}$ (two order smaller than the experimental upper bound) and raises the question whether some new physics can play a crucial role or not. We found that for a reasonable range of parameters (i.e. radion mass $m_{\varphi }$ and radion vev $\text{vphi}$), the above deficit between the experimental bound and the standard model result can well be accomodated. Using this upper bound on $BR({\bar B_s} \to \mu^+ \mu^-)$,weobtainthelowerboundon$\vphi$.