Signals of a New Gauge Boson from IceCube and Muon $g-2$

A $Z^{\mathrm{\prime }}$ boson associated with a broken $U(1{)}_{L_{\mu }-L_{\tau }}$ gauge symmetry offers an economical solution to the long-standing $g_{\mu }-2$ anomaly, confirmed and strengthened by recent measurements at Fermilab. Here, we revisit the impact of such a $Z^{\mathrm{\prime }}$ on the spectrum of high-energy astrophysical neutrinos, as measured by the IceCube experiment. This spectrum has been observed to exhibit a dip-like feature at $E_{\nu }\sim 0.2-1\mathrm{P}\mathrm{e}\mathrm{V}$, which could plausibly arise from the physics of the sources themselves, but could also be the consequence of high-energy neutrinos resonantly scattering with the cosmic neutrino background, mediated by a $Z^{\mathrm{\prime }}$ with a mass on the order of $m_{Z^{\mathrm{\prime }}}\sim 10\mathrm{M}\mathrm{e}\mathrm{V}$. In this study, we calculate the impact of such a $Z^{\mathrm{\prime }}$ on the high-energy neutrino spectrum for a variety of model parameters and source distributions. For couplings that can resolve the $g_{\mu }-2$ anomaly, we find that this model could self-consistently produce a spectral feature that is consistent with IceCube’s measurement, in particular if the neutrinos observed by IceCube predominantly originate from high-redshift sources.