Discovery potential of the Glashow resonance in an air shower neutrino telescope* * Project Supported by the ``CUG Scholar'' Scientific Research Funds at China University of Geosciences (Wuhan) (2024014)

The in-ice or in-water Cherenkov neutrino telescope, such as IceCube, has already proved its power in measuring the Glashow resonance by searching for the bump around arising from the W-boson production. There are many proposals for the next few decades for observations of cosmic tau neutrinos with extensive air showers, also known as tau neutrino telescopes. The air shower telescope is, in principle, sensitive to the Glashow resonance via the channel followed by the tau decay in the air (e.g., TAMBO, which has a geometric area of approximately ). Using a thorough numerical analysis, we find that the discovery significance can be up to 90% with a TAMBO-like setup if PeV neutrinos primarily originate from neutron decays, considering the flux parameters measured by IceCube as the input. The presence of new physics affecting the neutrino flavor composition can also increase the significance. However, if ultrahigh-energy neutrinos are dominantly produced from meson decays, it will be statistically difficult for an advanced proposal such as TAMBO to discriminate the Glashow resonance induced by from the intrinsic background. We have identified several limitations for such advanced telescopes, in comparison with the in-ice or in-water telescope, when measuring resonances: (i) a suppressed branching ratio of 11% for the decay ; (ii) the smearing effect and reduced acceptance because the daughter neutrino takes away 75% of the energy from the W decay; and (iii) a large attenuation effect for Earth-skimming neutrinos with the resonance.