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 \((L_e - Lμ)\) and \((Lμ - Lτ)\) in various realizations. We explore diverse manifestations of the atlas to understand their impact on explaining the muon \((g-2)μ\) 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 ~ 10~MeV and non-universal couplings as indicated successfully mediates interactions in the fermion and dark matter sectors in such a way that (g-2)μ 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~ GeV order mass and a strong dark coupling (gχ ~ 0.3, much stronger than the lepton's couplings g'ₗ 10⁻⁴) to be a successful scenario to unravel astrophysical small scale problems.