Search for $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ charged dark matter with neutrino telescope

We study a simple Dirac fermion dark matter model in $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ theory. The new light gauge boson X plays important roles in both dark matter physics and the explanation for the muon g − 2 anomaly. The observed dark matter relic density is realized by a large $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ charge without introducing a resonance effect of the X boson. As a by-product of the model, characteristic neutrino signatures from sub-GeV dark matter ψ are predicted depending on the mass spectrum. We formulate the analysis of $$ \psi \overline{\psi}\to \nu \overline{\nu} $$ , and of $$ \psi \overline{\psi}\to XX $$ followed by $$ X\to \nu \overline{\nu} $$ in a model independent way. The energy spectrum of neutrinos in the former process is monochromatic while in the latter process is bowl-shape. We also evaluate sensitivity at Super-Kamiokande and future Hyper-Kamiokande detectors. The analysis is finally applied to the $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ dark matter model.