Novel bounds on neutrino portal dark matter from leptonic meson decays

Abstract

We investigate the potential of leptonic meson decays $M \to \ell \bar\nu_\ell$, where $M$ is a pseudo-scalar meson, as a probe of neutrino portal dark matter. The model of our focus features a neutral fermion $\psi$ and scalar $\phi$, which are coupled predominantly to neutrinos in the form ${\cal L} \supset \lambda\,\overline\nu_L\,\phi\,\psi_R$. This interaction generates two corrections to the $M \to \ell \bar\nu_\ell$ observables. The first one is a novel three-body decay process $M \to \ell \bar\psi\phi$. This process is enabled by the splitting of the off-shell anti-neutrino $\bar\nu_\ell$ into $\psi$ and $\phi$ in the $M \to \ell \bar\nu_\ell$ diagram. The helicity suppression in $M \to \ell \bar\nu_\ell$ is absent in the three-body process, thereby forming a potentially large contribution to real experimental results, provided $\psi$ and $\phi$ are invisible. The second one is one-loop radiative corrections to the weak vertex $W\ell \bar\nu_\ell$, which do not modify the charged lepton spectrum but lead to enhancement or suppression of the partial $M \to \ell \bar\nu_\ell$ decay width. To demonstrate the ability of the leptonic meson decays to probe the neutrino portal dark matter, we compute two corrections analytically and compare the modified meson branching ratios with the experimental data on the lepton flavor universality of pion and Kaon decays. The resulting constraints turn out to surpass the existing bounds in a large part of parameter spaces.