Implications of the KM3NeT ultrahigh-energy event on neutrino self-interactions

Neutrino self-interactions ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>ν</a:mi> <a:mi>SI</a:mi> </a:mrow> </a:math> ) mediated by light bosonic particles can produce characteristic spectral dips in astrophysical neutrino fluxes, thereby altering the expected energy spectrum. The high-energy astrophysical neutrino spectrum has been extensively used to probe <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>ν</c:mi> <c:mi>SI</c:mi> </c:math> models through these distinctive features. The recent detection of the ultrahigh-energy event KM3-230213A presents a new opportunity to explore <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>ν</e:mi> <e:mi>SI</e:mi> </e:math> phenomenology at extreme energies. In this work, we investigate two implications of this observation, assuming the event originates from a diffuse power-law spectrum. First, we find that <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>ν</g:mi> <g:mi>SI</g:mi> </g:math> -induced spectral distortions can mildly alleviate the tension between the KM3-230213A detection and the previous nonobservation of PeV-scale neutrinos in IceCube data. Second, we derive the strongest constraints on the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>τ</i:mi> </i:math> -flavored <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>ν</k:mi> <k:mi>SI</k:mi> </k:math> coupling strength for mediator masses around 100 MeV. Our analysis shows that neutrino telescopes can surpass existing collider bounds in this mass range. In the near future, IceCube-Gen2 is expected to significantly enhance <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>ν</m:mi> <m:mi>SI</m:mi> </m:math> sensitivity, including regions relevant to alleviating the Hubble and neutrino mass tensions.