Cosmological Constrained Axion-Portal Inelastic Dark Matter for the LZ Event

The recent high-recoil candidate event reported by LUX-ZEPLIN (LZ) motivates dark-matter scenarios with nonstandard kinematics and momentum-dependent interactions. We study a two-state inelastic dark-matter model in which χ 1 and χ 2 couple off-diagonally to an axion-like particle (ALP) that also couples to gluons and photons. Unlike treatments that assume only one dark-matter state is present today, we track the cosmological evolution of both states. The excited state χ 2 is sufficiently long-lived to survive to the present, with its relic fraction determined by the dark-sector conversion process χ 2χ 2 χ 1χ 1. We find that this fraction depends strongly on the Lorentz structure of the DM--ALP interaction: scalar transition couplings efficiently deplete χ 2, favoring endothermic χ 1 N toχ 2 N scattering, whereas pseudoscalar transition couplings preserve f 2 1/2, yielding recoil spectra dominated by exothermic χ 2 N toχ 1 N down-scattering. Benchmark spectra in all four scenarios can peak near the observed recoil energy of 250, keV. Our results demonstrate that the dominant direction of inelastic scattering in direct detection can be dynamically selected by the early-Universe evolution of the dark sector. With additional data, annual modulation measurements could distinguish these scenarios. We further show that the ALP portal can be directly probed at colliders.