Interpreting the KM3-230213A PeV Neutrino Event via Vector Dark Matter Decay and Its Multi-Messenger Signatures

The KM3NeT Collaboration recently reported the detection of an ultra-high-energy neutrino event KM3-230213A with a reconstructed energy of $220^{+570}_{-110}$ PeV, the most energetic astrophysical neutrino ever detected. The absence of convincing electromagnetic counterparts motivates exploration of exotic origins beyond standard astrophysical processes. We present a vector dark matter model based on a new $U(1)_X$ gauge symmetry to interpret this event through superheavy dark matter decay. Our analysis demonstrates that dark matter lifetimes in the range $7.3 \times 10^{28}$ to $2.9 \times 10^{30}$ s can successfully account for the KM3-230213A event while satisfying stringent constraints from gamma-ray observations. Moreover, the spontaneous breaking of $U(1)_X$ in our model naturally predicts cosmic string formation, generating a stochastic gravitational wave background with string tension $4.5 \times 10^{-11} \lesssim G\mu \lesssim 1.2 \times 10^{-10}$, consistent with recent pulsar timing array observations. This multi-messenger consistency across neutrinos, gamma-rays, and gravitational waves validates our vector dark matter interpretation of the KM3-230213A event while providing testable predictions for upcoming multi-wavelength experiments.