The LZ event with a two-state dark matter halo

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, ${\chi }_{1}N\to {\chi }_{2}N$. In pseudo-Dirac models the excited state ${\chi }_2$ can survive to the present day, and exothermic scattering, ${\chi }_{2}N\to {\chi }_{1}N$, 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 ${\chi }_2$. For $f\gtrsim {10}^{-5}$–${10}^{-2}$, depending on the mass splitting, the exothermic contribution dominates. For $f=1\mathrm{/}2$ the cross section required by the candidate drops by factors of $80$ to $1.6\times {10}^4$ for $\delta =250$–$350$~keV, and the kinematic cutoff of the endothermic signal disappears. A benchmark that explains the event with ${\chi }_1$ alone lies a factor of $30$ above the upper limit when half of the halo is ${\chi }_2$.