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

Sarif Khan, Jongkuk Kim, Pyungwon Ko

TL;DR

This paper addresses the KM3NeT KM3-230213A ultra-high-energy neutrino event by proposing decaying heavy Dirac dark matter χ in a $U(1)_X$ gauge framework with a dark Higgs VEV $v_φ$. χ decays via a right-handed neutrino portal, with two-body SM final states dominating for $v_φ \\gg m_χ$, yielding a neutrino spectrum peaked at $E_ν \\sim M_χ/2$ and calculable fluxes using HDMSpectra; the relic density is achieved through UV freeze-in at a high reheat temperature $T_R$ and a heavy RH neutrino $N$, avoiding thermal overproduction. The large $v_φ$ also enables cosmic strings that generate a gravitational-wave background with tension $G μ$ in the accessible range for future detectors, providing a correlated multi-messenger scenario. The study identifies viable regions with $M_χ \sim 440$ PeV, $τ_χ \sim 5×10^{29}$ s, $v_φ$ in the range $10^{8}$–$10^{14}$ GeV, and $G μ$ between $10^{-11}$ and $10^{-19}$, linking high-energy neutrinos, DM production, and GW observations for a multi-messenger test.

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) $χ$ 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 $χ$ 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 $Φ$. 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 $v_Φ\gg m_χ$. Then we can reply on the HDMSpectra package to generate the neutrino and $γ$-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.

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

TL;DR

This paper addresses the KM3NeT KM3-230213A ultra-high-energy neutrino event by proposing decaying heavy Dirac dark matter χ in a gauge framework with a dark Higgs VEV . χ decays via a right-handed neutrino portal, with two-body SM final states dominating for , yielding a neutrino spectrum peaked at and calculable fluxes using HDMSpectra; the relic density is achieved through UV freeze-in at a high reheat temperature and a heavy RH neutrino , avoiding thermal overproduction. The large also enables cosmic strings that generate a gravitational-wave background with tension in the accessible range for future detectors, providing a correlated multi-messenger scenario. The study identifies viable regions with PeV, s, in the range – GeV, and between and , linking high-energy neutrinos, DM production, and GW observations for a multi-messenger test.

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 , 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) 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 is assumed to be charged under dark gauge symmetry, which is spontaneously broken by the vacuum expectation value (VEV) of the dark Higgs . 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 . Then we can reply on the HDMSpectra package to generate the neutrino and -ray spectra from heavy DM decays. If the DM mass is around with a lifetime 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.

Paper Structure

This paper contains 7 sections, 38 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Dark $U(1)_X$ model
  3. Neutrino Flux from DM decay
  4. Gravitational waves from cosmic string
  5. Dark Mater Production
  6. Conclusion
  7. Dark Matter Decay Width

Figures (4)

  • Figure 1: Neutrino (left-panel) and Gamma-ray (right-panel) spectra from DM $\chi$ decay with $M_\chi=440\mathrm{PeV}$ and lifetime $\tau_\chi =1/\Gamma = 5\times 10^{29}$s. In the left panel, bounds come from IceCube IceCube:2018fhmIceCube:2020wum. Blue cross corresponds to KM3NeT with $3\sigma$ C.L KM3NeT:2025npi. It presents the galactic (blue dotted curve) and extragalactic (red dotted curve) neutrino flux. In the right panel, orange crosses correspond to gamma-ray constraints from LHAASO-KM2A LHAASO:2023gne whereas EAS-MSU Fomin:2017ypo and PAO Castellina:2019huz limits are shown in brown and green arrows, respectively.
  • Figure 2: Variation of relic GW density with frequency for different values of string tension. Different colours represent the sensitivity prospects of various future GW detectors. EPTA data excludes cosmic string tensions $G\mu > 2 \times 10^{-11}$.
  • Figure 3: In the left panel (LP), we show the scatter plot in the $(M_{\chi},~\frac{\kappa^{2}}{M_{N}})$ plane, whereas the right panel (RP) displays the scatter plot in the $(M_{N},~y)$ plane. The color gradient in the LP represents different values of the reheating temperature $T_R$, while in the RP, it corresponds to different values of the coupling $\kappa$. The other parameters, which are not shown, have been varied as listed in Eq. \ref{['range-parameter']}.
  • Figure 4: The LP and RP show scatter plots in the $(G\mu,~y)$ and $(f_{\chi},~\tau_{\chi})$ planes, respectively. In the LP, the color gradient represents different values of $\tau_{\chi}$, while in the RP, it corresponds to values of $\kappa^{2}/M_{N}$.