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Supernova neutrino boosted dark matter (SN$\nu$ BDM) and its afterglow effecthave been shown to be a promising signature for beyond Standard Model (bSM)physics. The time-evolution feature of SN$\nu$ BDM allows for %the possiblydirect inference of DM mass $m_\chi$, and results in significant backgroundsuppression with improving sensitivity. This paper extends the earlier studyand provides a general framework for computing the SN$\nu$ BDM fluxes for asupernova that occurs at any location in our galaxy. A bSM$U(1)_{L_\mu-L_\tau}$ model with its gauge boson coupling to both DM and thesecond and third generation of leptons is considered, which allows for bothDM-$\nu$ and DM-$e$ interactions. Detailed analysis of the temporal profile,angular distribution, and energy spectrum of the SN$\nu$ BDM are performed.Unique signatures in SN$\nu$ BDM allowing extraction of $m_\chi$ and detailfeatures that contain information of the underlying interaction type arediscussed. Expected sensitivities on the above new physics model fromSuper-Kamiokande, Hyper-Kamiokande, and DUNE detections of BDM events inducedby the next galactic SN are derived and compared with the existing bounds.

Signatures of afterglows from light dark matter boosted by supernova neutrinos in current and future large underground detectors