The L_μ-L_τ solution to the IceCube Ultra High Energy neutrino deficit in light of NA64

In this work we analyze the scenario where a MeV scale $L_\mu - L_\tau$ gauge boson can explain the deficit in the diffuse ultra high energy (UHE) astrophysical neutrino spectrum observed in IceCube, as well as the discrepancy between experimental and $e^+e^-$ dispersion data driven SM calculations of the muon anomalous magnetic moment. We map the parameter space of the model where the elastic resonant s-channel scattering of UHE neutrinos with the cosmic neutrino background, mediated by the new Z', can improve the description of the observed cascade and track spectra over the no-scattering hypothesis. Comparing to recent NA64$\mu$ results, we find that some part of the parameter space remains unexplored, but at a data volume of $10^{11}$ muons on target NA64$\mu$ will completely probe this region.