Dark matter in the scale-invariant 3-3-1-1 model

Abstract

We propose a novel scale-invariant model with the 3-3-1-1 gauge symmetry featuring a universal see-saw mechanism for all fermion masses, which, through the inclusion of additional vector-like quarks, provides a partial explanation for the observed fermion mass hierarchies. A discrete remnant of the gauge group, the matter parity ($P_M$), stabilises a fermionic dark matter candidate, and the scalar sector includes two triplets (minimal for 3-3-1 breaking) and two scalar singlets. We identify the lightest $ P_M $-odd fermion, $f_d$, as a viable dark matter candidate. Our analysis shows that $f_d$ satisfies the observed relic density constraint within the mass range 220 GeV $< m_{f_d}$ 555 GeV , primarily due to resonant annihilation via the new scalar $H_2$. While this mass range depends on the symmetry-breaking scale $v_\chi$, which has a lower bound of $ v_\chi \gtrsim 3.6$ TeV from LEP constraints on the $\rho_0$ parameter, we adopt a more conservative lower bound of $v_\chi > 10$ TeV. This choice is made to ensure that the $Z'$ boson mass remains above approximately $ 4$ TeV, and is motivated by recent LHC results and future projections for Z' boson searches, which provide more stringent constraints than previous bounds or those from the $\rho_0$ parameter. Spin-independent (SI) interactions dominate the direct detection phenomenology of $f_d$. We calculate the SI elastic scattering cross-section and find that parameter points satisfying the relic density constraint are consistent with current experimental limits from LZ and PandaX-4T for certain parameter choices, particularly depending on the $\alpha_{12}$ angle. Some regions of the viable parameter space lie below the neutrino floor. Prospects for detection by future experiments like XLZD and PandaX-xT are also presented and discussed.