Leptophilic dark matter in $U(1)_{L_{i}-L_{j}}$ models: a solution to the Fermi-LAT Galactic Center Excess consistent with cosmological and laboratory observations

Abstract: The particle origin of dark matter (DM) remains elusive despite decades of direct, indirect, and collider searches. Several groups have reported a $\gamma$-ray excess toward the Galactic Centre, commonly referred to as the Galactic Centre Excess (GCE). Its spectrum is consistent with annihilation of weakly interacting massive particles (WIMPs) of mass $\mathcal{O}(10-100)$ GeV and a thermal-relic cross section. Although many concrete WIMP models reproduce the GCE spectrum, most are now excluded by direct detection experiments that are approaching the neutrino floor. We investigate a class of anomaly-free extensions of the Standard Model featuring gauged differences of lepton number, $U(1){L_i-L_j}$, and gauged baryon minus lepton number, $U(1){B-L}$. We show that these models can reproduce the GCE while remaining compatible with the observed relic abundance. We then impose collider and direct detection constraints, accounting for both tree-level and loop-induced kinetic mixing. The $L_\mu-L_e$ model gives the best fit to the GCE: a DM mass of $m_\chi\sim 40-50$ GeV remains consistent with the muon and electron magnetic moment anomalies, $(g-2){\mu,e}$, as well as current collider and direct detection limits, for mediator masses in the range $m{A'}\sim 70-86$ GeV and a DM-mediator coupling of $(1-5)\times10^{-2}$. By contrast, the $L_e-L_\tau$ and $L_\mu-L_\tau$ models yield poorer fits; satisfying both the relic density and experimental bounds forces the DM mass to lie very close to resonance (i.e., approximately half the mediator mass). Finally, while the $B-L$ model also matches the GCE well, its parameter space is almost entirely ruled out by strong direct detection limits, except for the narrow resonance region where $m_\chi$ should be equal to $m_{A'}/2$ requiring a fine-tuning at the few-percent level.