Constraining active-sterile neutrino mixing via lepton flavor violating decays of mesons

As a hypothetic particle, a sterile neutrino can exist in types of new physics models. In this work by investigating flavor violating semileptonic and leptonic decays of K,D, and B mesons induced by the GeV scale sterile neutrino, we explore its allowed regions in parameter space. Analytically, we derive branching fractions of semileptonic decay \(M^{+}_{h}\to M_{l}^{+}\ell _{1}^{+}\ell _{2}^{-}\) and leptonic decay \(M^{0}\to \ell _{1}^{-}\ell _{2}^{+}\), including the contribution from a new box diagram contribution due to the massive sterile neutrino. Imposing its mass ranges, we numerically analyze the active-sterile neutrino mixings in corresponding regions. We find that when the sterile neutrino mass is located in between pion and kaon mass, K⁺→π⁺e^±μ^∓ gives the strongest constraint while B⁺→π⁺e^±μ^∓ provides the dominated constraint when its mass in between of kaon and B meson. If the sterile neutrino is even heavier than Bmesons, the LHCb \(B^{0}_{s}\to \mu ^{\pm } e^{\mp }\) results gives the strongest constraint.