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Experimental hints for lepton-flavor universality violation in the muon'smagnetic moment as well as neutral- and charged-current $B$-meson decaysrequire Standard-Model extensions by particles such as leptoquarks thatgenerically lead to unacceptably fast rates of charged lepton flavor violationand 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 finetuningand efficiently explains $(g-2)_\mu$, $R_{K^{(*)}}$, $R_{D^{(*)}}$, andneutrino masses. The $U(1)_{L_\mu-L_\tau}$ furthermore acts as a stabilizingsymmetry for dark matter and the light $Z'$ gauge boson mediatesvelocity-dependent dark-matter self-interactions that resolve the small-scalestructure problems. Lastly, even the Hubble tension can be ameliorated via thelight $Z'$ contribution to the relativistic degrees of freedom.

Explaining lepton-flavor non-universality and self-interacting dark matter with $L_\mu-L_\tau$