Haipeng An, Fei Gao, Jia Liu, Minghao Liu, Changlong Xu
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 $χ_2χ_2\leftrightarrowχ_1χ_1$. 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 $f_2\simeq1/2$, 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 $250\,\mathrm{keV}$. 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.