Study Majorana Neutrino Contribution to B-meson Semi-leptonic Rare Decays

B meson semi-leptonic rare decays are sensitive to new physics beyond standard model. We study the $B^{-}\to \pi^{-}\mu^{+}\mu^{-}$ process and investigate the Majorana neutrino contribution to its decay width. The constraints on the Majorana neutrino mass and mixing parameter are obtained from this decay channel with the latest LHCb data. Utilizing the best fit for the parameters, we study the lepton number violating decay $B^{-}\to \pi^{+}\mu^{-}\mu^{-}$, and find its branching ratio is about $6.4\times10^{-10}$, which is consistent with the LHCb data reported recently.