Leptophilic scalar dark matter in U(1)$_{L_\mu-L_\tau}$: Evading direct detection and prospective neutron star heating

Abstract

Leptophilic dark matter (DM) is a well-motivated thermal weakly interacting massive particle framework that can evade stringent nuclear-recoil searches while remaining testable via DM-induced heating of neutron stars (NSs). In this work, we study leptophilic scalar DM in a $U(1)_{L_\mu-L_\tau}$ gauge extension of the Standard Model, which provides a common leptophilic portal for all scenarios considered. To reproduce the observed relic abundance while suppressing direct-detection signals, we investigate three benchmark realizations: (i) a secluded DM scenario in which the relic density is set by annihilation into $U(1)_{L_\mu-L_\tau}$ gauge bosons and two pseudo-Nambu-Goldstone boson (pNGB) DM models based on (ii) an $SO(4)$ symmetry and (iii) an $SO(3)$ symmetry. In the $SO(4)$ pNGB model, the DM mass arises at tree level from a soft breaking term, while the elastic scattering amplitude is suppressed by a symmetry-protected cancellation. In the $SO(3)$ pNGB model, the DM mass is generated radiatively at one loop via the $U(1)_{L_\mu-L_\tau}$ gauge interaction, and we show that this gauging preserves the same cancellation mechanism, maintaining compatibility with direct-detection null results. We perform a systematic parameter scan imposing relic density, direct and indirect detection, and neutrino trident constraints and identify viable sub-TeV to TeV DM candidates. Under the optimistic maximal-heating assumption that the capture rate reaches the geometric limit and that the captured DM population efficiently thermalizes and attains capture-annihilation equilibrium inside NSs, we find that the remaining parameter space can be tested by near-infrared observations of old NSs, providing sensitivity complementary to terrestrial searches in regions that are currently weakly constrained.