Discovery potential of the Glashow resonance in an air shower neutrino telescope*

Abstract

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 $E^{}_{\rm \nu} = 6.3~{\rm PeV}$ arising from the $W$-boson production. There are many proposals in the next few decades that observe cosmic tau neutrinos with extensive air showers, also known as tau neutrino telescopes. As has been recognized, the air shower telescope is in principle sensitive to the Glashow resonance via the channel $W \to \tau \nu^{}_{\tau}$ followed by the tau decay in the air, such as TAMBO with a geometric area around $500~{\rm km^2}$. With a thorough numerical analysis, we find that the discovery significance can be up to $90\%$ with a TAMBO-like setup if PeV neutrinos mainly 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 a rather advanced proposal like TAMBO to discriminate the Glashow resonance induced by $\overline{\nu}^{}_{e}$ from the intrinsic $\nu^{}_{\tau}/\overline{\nu}^{}_{\tau}$ background. We have identified several limitations for those telescopes on hunting the resonance compared to the in-ice or in-water telescope: (i) a suppressed branching ratio of $11\%$ for the decay $W \to \tau \nu^{}_{\tau}$; (ii) the smearing effect and the reduced acceptance because the daughter neutrino takes away $\langle y \rangle \sim 75\%$ of the energy from the $W$ decay; (iii) a large attenuation effect for Earth-skimming neutrinos with the resonance.