Explaining lepton-flavor non-universality and self-interacting dark matter with L${}_{\mu }$-L${}_{\tau }$

Experimental hints for lepton-flavor universality violation in the muon's magnetic moment as well as neutral- and charged-current B-meson decays require Standard-Model extensions by particles such as leptoquarks that generically lead to unacceptably fast rates of charged lepton flavor violation and proton decay. We propose a model based on a gauged U(1)${}_{L_{\mu }-L_{\tau }}$ that eliminates all these unwanted decays by symmetry rather than finetuning and efficiently explains (g-2)${}_{\mu }$, R${}_{K^{(\ast )}}$, R${}_{D^{(\ast )}}$, and neutrino masses. The U(1)${}_{L_{\mu }-L_{\tau }}$ furthermore acts as a stabilizing symmetry for dark matter and the light Z${}^{\prime }$ gauge boson mediates velocity-dependent dark-matter self-interactions that resolve the small-scale structure problems. Lastly, even the Hubble tension can be ameliorated via the light Z${}^{\prime }$ contribution to the relativistic degrees of freedom.