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

Leptophilic dark matter (DM) is a well-motivated thermal WIMP framework that can evade stringent nuclear-recoil searches while remaining testable via DM-induced heating of neutron stars (NS). In this work, we study leptophilic scalar DM in a ${\mathrm{U}(1)}_{L_{\mu }-L_{\tau }}$ 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 ${\mathrm{U}(1)}_{L_{\mu }-L_{\tau }}$ 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 ${\mathrm{U}(1)}_{L_{\mu }-L_{\tau }}$ 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. Assuming maximal capture in NSs, we find that the remaining parameter space can be tested by near-infrared observations of NSs, providing sensitivity complementary to terrestrial searches in regions that are currently weakly constrained.