Probing the Glashow resonance at electron-positron colliders

The Glashow resonance is a rapid enhancement of the cross section for scattering of electron antineutrinos on electrons at the $W^-$ boson production threshold due to the $s$-channel contribution. This resonance is being searched for at large volume neutrino detectors in which the reaction $\bar\nu_ee^-\rightarrow W^-$ to be initiated by cosmic ray antineutrinos of energies about 6.3 PeV. The relatively small neutrino flux reaching the Earth together with the necessity of analyzing ultra-high-energy final states make such searches challenging. We argue here that the Glashow resonance may contribute to the process $e^+e^-\rightarrow~W^+W^-$. By extending the method of the effective (equivalent) particles to the neutral leptons, we relate the distribution of the effective neutrinos in the electron to the total cross section for $e^+e^-\rightarrow~W^+W^-$. Our approach gives a good fit to existing experimental data measured at the collider LEP at CERN and allows one to interpret these measurements as an observation of the Glashow resonance. We also discuss an advantage of future electron-positron colliders for probing the resonance.