Contributions Of Sterile Neutrino To Leptonic Decays Of The Pseudoscalar Mesons

The standard model of particle physics can successfully describe the weak interaction,strong interaction and electromagnetic interaction,almost all predictions have been tested by experiments and success in two aspects of theories and experiments.But it cannot be an ultimate theory,aslo have some questions.For example,neutrino mass,dark matter and dark energy.The pure and radiative leptonic decays of the pseudoscalar meson M are theoretically very clean.The only non-perturbation quantity involved in these decay processes is the meson de-cay constant F_M.The decays M→lνand M→vvare helicity suppressed in the SM,the radiative leptonic decays M→lνγare not subject to the helicity suppression,which might be comparable or even larger than the corresponding decay M→lν.Thus,all of these processes are sensitive to new physics effects,and is very important for the exploration of new physics beyond the standard model.Many new physics models giving the tiny neutrino masses pre-dict the existence of the sterile neutrinos with mass covering various mass ranges.Recently,the relatively light sterile neutrinos with masses at the GeV scale have been attracting some interests.We consider a scenario with only one sterile neutrino N,negligible mixing with the active neutrinosν_L,where its interactions with ordinary particles could be described in an effective theory,and the contributions of the sterile neutrino N to the pure leptonic decays M→lνandvv,and the radiative leptonic decays M→lνγwith M denoting the pseudoscalar mesons B,D and K.We find that the sterile neutrino N can indeed enhance the values of the branch-ing ratios Br（M→lν）predicted by the SM.However,for most of these decay processes,it can not make Br（M→lν）reach the experimental measurement value.The exception is Br（K⁺→μ⁺ν_μ）,which can exceed the corresponding current experimental up limit,thus might give new constraints on the free parametersα^′s and m_N.The contributions of the sterile neutrino N to the decays M⁺→e⁺ν_eγare very small and the values of the relative cor-rection parameter R^′（M⁺→e⁺ν_eγ）are smaller than one in a thousand.While it can pro-duce significant contributions to M⁺→μ⁺ν_μγ,which can make the values of the parameters R^′（B⁺→μ⁺ν_μγ）,R^′（K⁺→μ⁺ν_μγ）and R^′（D⁺→μ⁺ν_μγ）reach 1.08,5.87 and 2.72.All of the branching ratios Br（M→ν（?））can be significant enhanced by the sterile neutrino N.For the branching ratio Br（B_s→ν（?））,its value can reach 4.2×10^-10,which might approach the sensitivity of Belle Ⅱ.