In light of the recent Muon g − 2 experiment data from Fermilab, we investigate the implications of a gauged Lµ − Lτ model for high energy neutrino telescopes. It has been suggested that a new gauge boson at the MeV scale can both account for the Muon g −2 data and alleviate the tension in the Hubble parameter measurements. It also strikes signals at IceCube from the predicted resonance scattering between high-energy neutrinos and the cosmic neutrino background. We revisit this model based on the latest IceCube shower data, and perform a four-parameter fit to find a preferred region. While the data are consistent with the absence of resonant signatures from secret interactions, we find the preferred region consistent with the muon g − 2 anomaly and Hubble tension. We demonstrate that future neutrino telescopes such as IceCube-Gen2 can probe this unique parameter space, and point out that successful measurements would infer the neutrino mass with 0.05 eV <~ Σmν <~ 0.3 eV.
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