Linking the KM3-230213A Neutrino Event to Dark Matter Decay and Gravitational Wave signals

Abstract

The KM3NeT collaboration recently reported the detection of an ultra-high-energy (UHE) neutrino event, dubbed KM3-230213A. This is the first observed neutrino event with energy of the order of $\mathcal{O}(100) {\rm PeV}$, the origin of which remains unclear. In this paper, we interpret this high energy neutrino event in terms of the Dirac fermion dark matter (DM) $\chi$ decays via the right-handed (RH) neutrino portal assuming the Type-I seesaw mechanism for neutrino masses and mixings. Furthermore, the Dirac fermion dark matter $\chi$ is assumed to be charged under $U(1)_X$ dark gauge symmetry, which is spontaneously broken by the vacuum expectation value (VEV) of the dark Higgs $\Phi$. In this scenario, DM can decay into a pair of Standard Model (SM) particles, such as neutrinos, leptons, and gauge bosons via the RH neutrino portals for $v_\Phi \gg m_\chi$. Then we can reply on the HDMSpectra package to generate the neutrino and $\gamma$-ray spectra from heavy DM decays. If the DM mass is around $440\ {\rm PeV}$ with a lifetime $5\times 10^{29}$ sec, it can account for the KM3-230213A event. However, such heavy DM cannot be produced through the thermal freeze-out mechanism due to overproduction and violation of unitarity bounds. We focus on the UV freeze-in production of DM through a dimension-5 operator, which helps in producing the DM dominantly in the early Universe. Finally, the large value of the dark Higgs field VEV opens up the intriguing possibility of generating gravitational waves (GWs) spectra from cosmic strings. We have found a reasonable set of parameter values that can address the KM3NeT signal, yield the correct value of the DM relic density through freeze-in mechanism, and allow for the possible detection of GW signal at the future detectors.