Constraining secret gauge interactions of neutrinos by meson decays

Secret coupling of neutrinos to a new light vector boson, Z′, with a mass smaller than 100 MeV is motivated within a myriad of scenarios which are designed to explain various anomalies in particle physics and cosmology. Due to the longitudinal component of the massive vector boson, the rates of three-body decay of charged mesons (M) such as the pion and the kaon to the light lepton plus neutrino and Z′ (M→lνZ′) are enhanced by a factor of (mM/mZ′)2. On the other hand, the standard two body decay M→lν is suppressed by a factor of (ml/mM)2 due to chirality. We show that in the case of (M→eνZ′), the enhancement of mM4/me2mZ′2∼108–1010 relative to two-body decay (M→eν) enables us to probe very small values of gauge coupling for νe. The strongest bound comes from the RK≡Br(K→e+ν)/Br(K→μ+ν) measurement in the NA62 experiment. The bound can be significantly improved by customized searches for signals of three-body charged meson decay into the positron plus missing energy in the NA62 and/or PIENU data.