Leptophilic scalar dark matter in U(1)$_{L_μ-L_τ}$: Evading direct detection and prospective neutron star heating

Abstract

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 $\mathrm{U(1)}_{L_μ-L_τ}$ 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 $\mathrm{U(1)}_{L_μ-L_τ}$ 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 $\mathrm{U(1)}_{L_μ-L_τ}$ 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.

Figures (7)

• Figure 1: Loop corrections to the trilinear Higgs-portal couplings.
• Figure 2: Constraints and prospective sensitivities for the secluded scalar DM model in the $m_{\mathrm{DM}}$--$\xi_X$ plane, with $\sqrt{Q_{\mathrm{DM}}}g_X$ fixed to $0.1$ (left panel) and $0.3$ (right panel). The light blue shaded regions are excluded by the LZ direct detection experiment. The solid cyan, green, and orange curves indicate the parameter space reproducing the correct thermal relic density ($\Omega_{\mathrm{DM}} h^2 \approx 0.12$) for specific charge assignments: $Q_{\mathrm{DM}}=15, 30, 50$ (left) and $Q_{\mathrm{DM}}=4, 6, 8$ (right). The vertical color shaded bands on the left represent the exclusion limits from Fermi-LAT indirect detection corresponding to each $Q_{\mathrm{DM}}$ value. The red solid and dashed curves illustrate the prospective sensitivity reach from NS heating for two benchmark neutron star masses, BM-1 ($1.5 M_\odot$) and BM-2 ($1.9 M_\odot$), assuming the maximal heating scenario.
• Figure 3: Constraints and prospective sensitivities for pNGB DM model A. The top panels display the results in the $m_{\mathrm{DM}}$--$m_{h_2}$ plane with $m_X=1.5m_{h_2}$, fixing $v_\phi=3m_{h_2}$ (left) and $v_\phi=2m_{h_2}$ (right). The bottom panel projects the constraints onto the $m_{\mathrm{DM}}$--$v_\phi$ plane for fixed masses $m_{h_2}=0.6$ TeV and $m_X=4m_{h_2}$. The light blue and pink shaded regions represent the parameter space excluded by the LZ direct detection and neutrino trident production experiments, respectively. The solid cyan, green, and orange curves indicate the regions reproducing the correct thermal relic density ($\Omega_{\mathrm{DM}} h^2 \approx 0.12$) for scalar mixing parameters $t_\theta=0.05, 0.1$, and $0.2$, respectively. The corresponding color shaded bands denote the regions excluded by Fermi-LAT indirect detection limits for each $t_\theta$. The red solid and dashed lines illustrate the prospective sensitivity reach from NS heating for the BM-1 ($1.5 M_\odot$) and BM-2 ($1.9 M_\odot$) neutron star models, assuming maximal heating.
• Figure 4: Constraints and prospective sensitivities for pNGB DM model B in the $m_{\mathrm{DM}}$--$\xi$ plane, where the mass ratio is defined as $\xi \equiv m_X/m_{h_2}$. The fixed parameters are $v_\phi=1.2$ TeV and $m_{h_2}=0.6$ TeV across all panels. The four subplots correspond to different combinations of the DM charge $Q_{\mathrm{DM}}$ (top row: $Q_{\mathrm{DM}}=3$; bottom row: $Q_{\mathrm{DM}}=1$) and the UV matching scale ratio $r_{UV}$ (left column: $r_{UV}=10$; right column: $r_{UV}=10^3$). The light blue and pink shaded regions represent the parameter space excluded by the LZ direct detection and neutrino trident production experiments, respectively. The solid cyan, green, and orange curves trace the regions reproducing the correct thermal relic density ($\Omega_{\mathrm{DM}} h^2 \approx 0.12$) for scalar mixing parameters $t_\theta=0.1, 0.15$, and $0.2$. The corresponding color shaded bands denote the regions excluded by Fermi-LAT indirect detection limits for each $t_\theta$. The red solid and dashed curves illustrate the prospective sensitivity reach from NS heating for the BM-1 ($1.5 M_\odot$) and BM-2 ($1.9 M_\odot$) neutron star models, respectively, assuming the maximal heating scenario.
• Figure 5: Constraints and prospective sensitivities for pNGB DM model B projected onto the $m_{\mathrm{DM}}$--$m_{h_2}$ plane. The gauge boson mass is fixed to $m_X=4m_{h_2}$ and the VEV is set to $v_\phi=1.2$ TeV across all panels. Similar to Fig. \ref{['figmodelB1']}, the panels represent four benchmark combinations of $Q_{\mathrm{DM}}$ (3 for the top row, 1 for the bottom row) and $r_{UV}$ (10 for the left column, $10^3$ for the right column). The light blue and pink shaded regions correspond to exclusions from LZ and neutrino trident production, respectively. The cyan, green, and orange curves indicate the correct relic density for $t_\theta=0.1, 0.15$, and $0.2$, accompanied by their corresponding color Fermi-LAT exclusion bands. The red solid (BM-1) and dashed (BM-2) lines denote the prospective reach of NS heating.