Signature of GW from the Hidden Sector in light of the Recent LZ Event

Abstract

The LZ collaboration has recently reported a single nuclear-recoil event at $E_R=248\pm23_\text{stat}\pm23_\text{sys}$ keV, observed in a 2.84 tonne-year exposure with a local significance of $3.4σ$, pointing towards an inelastic dark matter (DM) interpretation. We explain this event within a gauged $U(1)_X$ hidden-sector model, spontaneously broken by a singlet scalar whose vacuum expectation value (VEV) gives rise to: \textit{(i)} gauge boson mass, \textit{(ii)} a small Majorana mass for the vector-like singlet fermion, the DM candidate, charged under the new symmetry, which splits the fermion into two pseudo-Dirac states (mass splitting proportional to the scalar VEV) thus resulting in a purely off-diagonal vector current, \textit{(iii)} the frequency and the amplitude of the GW signal arising from the hidden sector symmetry breaking via first-order phase transition (FOPT). The symmetry-breaking scale thus provides a multi-messenger probe connecting terrestrial direct-detection kinematics at the LZ and early-universe FOPT thermodynamics while obtaining thermal DM relic abundance. We delineate the viable parameter space compatible with the LZ event, correct relic density, and detectable GW signals in the low frequency regimes at future interferometers like $μ{\rm ARES}$ and THEIA while satisfying existing cosmological, astrophysical, and terrestrial bounds.