Self-Interacting Dark Matter and flavor anomalies in an atlas of leptophilic models

We consider an atlas of leptophilic models with non-universal charges that combine the quantum numbers $(L_e-L_{\mu })$ and $(L_{\mu }-L_{\tau })$ in various realizations. We explore diverse manifestations of the atlas to understand their impact on explaining the muon $(g-2{)}_{\mu }$ anomaly, as well as the origin of self-interacting dark matter, which serves as a feasible explanation for the small-scale challenges of cold dark matter. We found that a single vector gauge boson with mass range of $\sim 10\mathrm{M}\mathrm{e}\mathrm{V}$ and non-universal couplings as indicated successfully mediates interactions in the fermion and dark matter sectors in such a way that $(g-2{)}_{\mu }$ additional contribution agrees with experimental constraints and the self-interacting dark matter fluid behaves as suggested by observations at different astrophysical length scales. Furthermore, the model requires a dark matter candidate within $10-100\mathrm{G}\mathrm{e}\mathrm{V}$ order mass and a strong dark coupling ($g_{\chi }\sim 0.3$, much stronger than the lepton’s couplings $g_l^{\mathrm{\prime }}\lesssim {10}^{-4}$) to be a successful scenario to unravel astrophysical small scale problems.