Model-Independent Sideband Constraints on Inelastic Dark Matter at the LZ High-Recoil Candidate

The LUX-ZEPLIN experiment has reported one nuclear-recoil event at $248\pm {23}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {23}_{\mathrm{s}\mathrm{y}\mathrm{s}}\mathrm{k}\mathrm{e}\mathrm{V}$ in a $2.84\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{n}\mathrm{e}\text{-}\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}$ exposure, with a local significance of $3.4\sigma$. Inelastic (endothermic) dark matter is a natural candidate: its kinematic threshold suppresses low-energy recoils and shifts the signal toward higher recoil energies. We perform a model-independent analysis of the LZ data using two sidebands, without specifying an ultraviolet completion, so our results apply broadly to inelastic dark matter with coherent spin-independent nuclear scattering. For each $(m_{\chi },\delta )$ we compute $N_{\mathrm{l}\mathrm{o}\mathrm{w}}\mathrm{/}{N}_{\mathrm{s}\mathrm{i}\mathrm{g}}$ and $N_{\mathrm{h}\mathrm{i}}\mathrm{/}{N}_{\mathrm{s}\mathrm{i}\mathrm{g}}$—predicted count ratios in the sidebands $[14,225)\mathrm{k}\mathrm{e}\mathrm{V}$ and $(271,800]\mathrm{k}\mathrm{e}\mathrm{V}$ relative to the signal region $[225,271]\mathrm{k}\mathrm{e}\mathrm{V}$. The two ratios vary in opposite directions with $\delta$ and are simultaneously optimized at a unique splitting ${\delta }^{\star }$. For $m_{\chi }=1\mathrm{T}\mathrm{e}\mathrm{V}$, ${\delta }^{\star }=339\mathrm{k}\mathrm{e}\mathrm{V}$ with a combined Poisson tension of $\approx 1.9\sigma$; over $500\mathrm{G}\mathrm{e}\mathrm{V}$–$3\mathrm{T}\mathrm{e}\mathrm{V}$, the tension at ${\delta }^{\star }$ rises from $\lesssim 1.3\sigma$ to $\approx 2.5\sigma$. Additional suppression arises from the Helm form factor: $\mathrm{\mid }{F}_{\mathrm{X}\mathrm{e}}^{\mathrm{H}\mathrm{e}\mathrm{l}\mathrm{m}}{\mathrm{\mid }}^2\simeq 3\times {10}^{-4}$ at $248\mathrm{k}\mathrm{e}\mathrm{V}$, near its second diffraction zero. A dedicated LZ search over $271<E_R<800\mathrm{k}\mathrm{e}\mathrm{V}$ would provide a decisive test of inelastic dark matter with $\delta \gtrsim 330\mathrm{k}\mathrm{e}\mathrm{V}$.