Decaying Dark Matter for the Exothermic Recoil at LZ

The LUX-ZEPLIN (LZ) experiment has reported a single nuclear-recoil candidate at $248\pm 23(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 23(\mathrm{s}\mathrm{y}\mathrm{s})$ keV. We suggest that it comes from a GeV-scale dark state ${\chi }_1$ that downscatters exothermically, ${\chi }_{1}A\to {\chi }_{2}A$, and is continuously replenished in the halo by the slow decay ${\chi }_0\to {\chi }_1{\chi }_1$ of a long-lived parent. Because the recoil energy is supplied by the mass splitting rather than by the halo velocity, the event is a narrow line with no low-energy tail. Kinematics requires $m_{{\chi }_1}\gtrsim 247$ MeV and fixes the splitting for each $m_{{\chi }_1}$. The same line should appear at 700$-$810 keV in argon for $m_{{\chi }_1}=0.3-10$ GeV. Normalizing to one LZ event also fixes the local rate of the radiative decay ${\chi }_1\to {\chi }_2\gamma \gamma$, up to the mediator’s photon coupling. A rough $\gamma$-ray estimate then requires this coupling to be $\lesssim {10}^{-2}$ of a proton-loop reference at $m_{{\chi }_1}=10$ GeV, but $\lesssim {10}^{-9}$ at 0.3 GeV, which favours daughters near 10 GeV.