The KM3NeT 220 PeV event: a neutrino messenger from the grand unification scale?

Abstract

The 220~PeV neutrino KM3-230213A, in tension with IceCube and Auger unless narrow, admits a two-body reading: relic decay $X\to \nu \bar{\nu }$ with $m_X\approx 4.4\times 10^8$~GeV. Consistency with neutrino and $\gamma$-ray bounds sets $\tau /f\approx 10^{29}$--$10^{30}$~s, lifetime over relic fraction. For a flavored ${}^1{S}_0$ onium, the operator scale lands in the Majorana-mass range of unified models: one Higgs insertion gives a singlet mediator, $M/|C_7{|}^{1/3}\approx 10^{14}$--$10^{16}$~GeV across the allowed relic fraction; two give the seesaw window; Dirac or Majorana neutrinos select the branch. We give the construction and its decisive tests.