Super heavy dark matter origin of the PeV neutrino event: KM3-230213A (2503.04464v1)

Abstract: The recent observation of the ultra-high-energy neutrino event KM3-230213A by the KM3NeT experiment offers a compelling avenue to explore physics beyond the Standard Model. In this work, we explore a simplest possibility that this event originates from the decay of a super-heavy dark matter (SHDM). We consider a minimal extension of the type-I seesaw by including a singlet scalar and a singlet fermion DM, both being odd under a $Z_2$ symmetry. At high scale, the $Z_2$ symmetry is spontaneously broken by the vev of the $Z_2$ odd scalar, leading to i) mixing between DM and heavy right-handed neutrinos and ii) formation of domain walls (DW). In the former case, the decay of the DM to $\nu,h$ can give rise to the PeV neutrino event KM3-230213A. While, in the latter case, the disappearance of the DW can give rise to stochastic gravitational waves. We derive constraints on the DM lifetime as a function of DM mass ensuring consistency with IceCube, Auger upper limits and the observed KM3-230213A event. We found that KM3-230213A gives stringent constraint on DM mass ranging from $1.7\times10^8$ GeV to $5.5\times10^9$ GeV with lifetime $6.3\times10^{29}$ s to $3.6\times10^{29}$ s.

• The paper proposes a model where super-heavy dark matter (SHDM) decay, within a type-I seesaw extension, explains the ultra-high-energy KM3-230213A neutrino event observed by KM3NeT.
• The analysis constrains the SHDM mass consistent with the event and other limits to a range of 1.7 imes 10^8 GeV to 5.5 imes 10^9 GeV, with corresponding lifetimes around 10^{29} seconds.
• The model predicts potential stochastic gravitational waves from associated domain wall decay, providing a multi-messenger pathway to test the proposed dark matter and neutrino mass framework.

The paper explores the possibility that the ultra-high-energy (UHE) neutrino event KM3-230213A, recently observed by the KM3NeT experiment, could originate from the decay of super-heavy dark matter (SHDM). The authors propose a minimal extension to the type-I seesaw model, incorporating a singlet scalar ($S$) and a singlet fermion ($\chi$) representing the DM, both odd under a $Z_2$ symmetry. The spontaneous breaking of this $Z_2$ symmetry, through the vacuum expectation value (vev) of $S$, leads to mixing between the DM and heavy right-handed neutrinos (RHN) and the formation of domain walls (DW). The DM decays into a neutrino ($\nu$) and a Standard Model Higgs boson ($h$), potentially explaining the KM3-230213A event, while the DWs' disappearance could generate stochastic gravitational waves (GW).

The paper constrains the DM lifetime as a function of its mass, ensuring consistency with IceCube and Auger upper limits, as well as the observed KM3-230213A event. The analysis reveals that KM3-230213A places a stringent constraint on the DM mass, ranging from $1.7 \times 10^8$ GeV to $5.5 \times 10^9$ GeV, with a corresponding lifetime of $6.3 \times 10^{29}$ s to $3.6 \times 10^{29}$ s.

Key aspects of the analysis include:

• Neutrino and Gamma-Ray Flux Calculation: The differential neutrino (gamma ray) flux per energy per unit solid angle from a decaying DM within an observational volume is expressed as:

  $$\frac{d^2\Phi_{\nu(\gamma)}^{\rm G}}{dE_{\nu(\gamma)}d\Omega}=\frac{1}{\tau_{\rm DM}}\frac{\mathcal{D}}{4\pi M_{\rm DM}}\frac{dN_{\nu(\gamma)}}{dE_{\nu(\gamma)}}$$,

  where:

  • $\Phi_{\nu(\gamma)}^{\rm G}$ is the neutrino (gamma ray) flux from galactic sources
  • $E_{\nu(\gamma)}$ is the energy of the neutrino (gamma ray)
  • $\Omega$ is the solid angle
  • $\tau_{\rm DM}$ is the DM lifetime
  • $\mathcal{D}$ is the D-factor which is related to the DM density profile
  • $M_{\rm DM}$ is the mass of the DM
  • $N_{\nu(\gamma)}$ is the neutrino (gamma ray) energy spectrum

  The D-factor, $\mathcal{D}$, is defined as:

  $$\mathcal{D}=\frac{1}{\Delta\Omega}\int_{\Delta\Omega} d\Omega\int_0^{s_{\rm max}}ds\rho(\sqrt{R_{\rm sc}^2-2sR_{\rm sc}\cos\psi+s^2})$$,

  where: * $\Delta\Omega$ is the angular region of observation * $s$ is the distance along the line of sight * $s_{\rm max}$ is the maximum distance along the line of sight * $\rho(r)$ is the DM density at a distance $r$ from the galactic center * $R_{\rm sc}$ is the distance from the solar system to the Galactic Center * $\psi$ are galactic coordinates

  The extragalactic neutrino (gamma ray) flux is given by:

  $$\frac{d\Phi_{\nu(\gamma)}^{\rm EG}}{dE}=\frac{1}{4\pi M_{\rm DM}\tau_{\rm DM}}\int_{0}^{\infty}\frac{\rho_0c/H_0}{\sqrt{\Omega_m(1+z)^3+\Omega_\Lambda}}\frac{1}{1+z}\frac{dN_{\nu(\gamma)}}{dE_{\nu(\gamma)}}dz$$,

  where: * $\Phi_{\nu(\gamma)}^{\rm EG}$ is the neutrino (gamma ray) flux from extragalactic sources * $E$ is the energy * $M_{\rm DM}$ is the mass of the DM * $\tau_{\rm DM}$ is the DM lifetime * $\rho_0$ is the average cosmological DM density at the present epoch * $c$ is the speed of light * $H_0$ is the Hubble constant * $\Omega_m$ is the contribution of matter to the total energy density of the Universe * $\Omega_\Lambda$ is the contribution of vacuum energy to the total energy density of the Universe * $z$ is the redshift * $N_{\nu(\gamma)}$ is the neutrino (gamma ray) energy spectrum

• Dark Matter Model: The seesaw model is extended with a singlet scalar $S$ and a singlet fermion $\chi$. The relevant Lagrangian includes terms for RHN ($N$), lepton doublet ($L$), Higgs doublet ($H$), and the DM candidate $\chi$. After $S$ acquires a vev ($v_S$), $N$ and $\chi$ mix, resulting in mass eigenstates $\chi_1$ and $\chi_2$. The DM, dominantly $\chi_2$, decays into $\nu$ and $h$, potentially explaining the KM3NeT event.
• Neutrino and Gamma-Ray Fluxes from DM Decay: The DM decays to neutrino via mixing with RHN, specifically through the $\chi \rightarrow \nu h$ channel. The IceCube limits constrain the UHE neutrino flux, which is used to constrain the DM lifetime. The neutrino flux is calculated using Eq. (3) for a DM mass of $4.5 \times 10^8$ GeV, showing that the flux fits the KM3NeT observation for a lifetime of $5 \times 10^{29}$ s.
• Gamma-Ray Constraints: Although DM can decay into gamma rays via the $h \rightarrow 2\gamma$ channel, the branching fraction is small, resulting in a suppressed gamma-ray flux. The paper uses data from HESS, LHAASO, CASA-MIA, and Auger to constrain the flux, confirming that it remains below current observational bounds.
• Stochastic Gravitational Waves (GW): The spontaneous breaking of the $Z_2$ symmetry leads to the formation of DWs. These DWs can decay and produce GWs. The frequency range of the GWs could be detectable at various GW detectors such as BBO, CE, DECIGO, NANOGrav, EPTA , PPTA , ET, GAIA, IPTA , LISA, SKA, THEIA, aLIGO , aVIRGO, $\mu$ARES.

In conclusion, the paper presents a compelling framework for explaining the KM3-230213A event through the decay of SHDM within a type-I seesaw extension. The model not only accommodates neutrino observations but also predicts potential GW signals, offering a multi-messenger approach to probe the nature of dark matter and neutrino masses.