Novel bounds on neutrino portal dark matter from leptonic meson decays

TL;DR

This work investigates neutrino portal dark matter via leptonic meson decays $M \to \ell \overline{\nu}_\ell$, focusing on the interaction ${\cal L} \supset -\lambda_\ell \overline{\nu_L}_\ell \phi \psi_R$. The authors compute two corrections: (i) a novel three-body decay $M \to \ell \overline{\psi} \phi$ enabled by off-shell neutrino splitting, which can be enhanced when $\psi$ and $\phi$ are invisible due to the absence of helicity suppression, and (ii) one-loop radiative corrections to the weak vertex $W \ell \overline{\nu}_\ell$ that subtly modify the two-body width through a renormalized vertex. By comparing the predicted lepton-flavour-universal ratios $R^{(M)}_{e/\mu}$ for $K$ and $\pi$ decays with experimental data, they derive strong bounds on the couplings $|\lambda_e|$ and $|\lambda_\mu|$, with particularly stringent constraints when the three-body channel is kinematically allowed. The results show that these meson-decay probes can exceed existing bounds in large regions of parameter space and can test sub-GeV DM thermal freeze-out scenarios, while also highlighting the potential of spectral analyses to further enhance sensitivity.

Abstract

We investigate the potential of leptonic meson decays $M \to \ell \barν_\ell$, where $M$ is a pseudo-scalar meson, as a probe of neutrino portal dark matter. The model of our focus features a neutral fermion $ψ$ and scalar $φ$, which are coupled predominantly to neutrinos in the form ${\cal L} \supset λ\,\overlineν_L\,φ\,ψ_R$. This interaction generates two corrections to the $M \to \ell \barν_\ell$ observables. The first one is a novel three-body decay process $M \to \ell \barψφ$. This process is enabled by the splitting of the off-shell anti-neutrino $\barν_\ell$ into $ψ$ and $φ$ in the $M \to \ell \barν_\ell$ diagram. The helicity suppression in $M \to \ell \barν_\ell$ is absent in the three-body process, thereby forming a potentially large contribution to real experimental results, provided $ψ$ and $φ$ are invisible. The second one is one-loop radiative corrections to the weak vertex $W\ell \barν_\ell$, which do not modify the charged lepton spectrum but lead to enhancement or suppression of the partial $M \to \ell \barν_\ell$ 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.

Figures (4)

• Figure 1: Feynman diagram for the three-body meson decay $M \to \ell\, \overline{\psi} \,H$
• Figure 2: One-loop corrections to the weak-vertex $W \ell\,\overline{\nu}_\ell$ in our model. The decay of a meson $M$ is induced from attaching the $W$ boson to $\overline{u}$ and $d$ external lines like in fig.\ref{['fig:three-body']}.
• Figure 3: The constraints from the lepton universality measurements of $K\to\ell\bar{\nu}$ (top) and $\pi\to\ell\bar{\nu}$ (bottom) in the electro-philic case, where $\lambda_e\neq0$ and $\lambda_\mu=\lambda_\tau=0$. The $2\sigma$ exclusion regions are shaded with $m_\psi=m_H$ (gray) and $m_\psi=2m_H$ (red). The solid lines correspond to the predictions in the thermal freeze-out scenario with $m_H=m_\psi$ (gray) and $m_H=2 m_\psi$ (red). The thermal relic abundance of the DM candidate agrees with the Planck observation $\Omega h^2=0.12$ on those lines.
• Figure 4: The constraints from the lepton universality measurements of $K\to\ell\bar{\nu}$ (top) and $\pi\to\ell\bar{\nu}$ (bottom) in the muon-philic case, where $\lambda_\mu\neq0$ and $\lambda_e=\lambda_\tau=0$. The $2\sigma$ exclusion regions are shaded with $m_\psi=m_H$ (gray) and $m_\psi=2m_H$ (red). The two regions almost overlap. The solid lines correspond to the predictions for the thermal freeze-out production with $m_H=m_\psi$ (gray) and $m_H=2 m_\psi$ (red). The thermal relic abundance of the DM candidate agrees with the Planck observation $\Omega h^2=0.12$ on those lines.