The LZ event with a two-state dark matter halo

Abstract

The LUX-ZEPLIN (LZ) experiment has reported a single nuclear-recoil candidate at $E_R \simeq 248$keV. LZ interprets it in terms of inelastic dark matter that scatters endothermically from its ground state, $χ_1 N \to χ_2 N$. In pseudo-Dirac models the excited state $χ_2$ can survive to the present day, and exothermic scattering, $χ_2 N \to χ_1 N$, is then also open. The published LZ intervals do not describe this case. We rebuild the LZ statistical inference and validate it against the published intervals. We then apply it to a halo that contains a fraction $f$ of $χ_2$. For $f \gtrsim 10^{-5}$--$10^{-2}$, depending on the mass splitting, the exothermic contribution dominates. For $f=1/2$ the cross section required by the candidate drops by factors of $80$ to $1.6\times10^4$ for $δ= 250$--$350$~keV, and the kinematic cutoff of the endothermic signal disappears. A benchmark that explains the event with $χ_1$ alone lies a factor of $30$ above the upper limit when half of the halo is $χ_2$.