Decaying Dark Matter for the Exothermic Recoil at LZ

Abstract

The LUX-ZEPLIN (LZ) experiment has reported a single nuclear-recoil candidate at $248\pm23\,(\mathrm{stat})\pm23\,(\mathrm{sys})$ keV. We suggest that it comes from a GeV-scale dark state $χ_1$ that downscatters exothermically, $χ_1A\toχ_2A$, and is continuously replenished in the halo by the slow decay $χ_0\toχ_1χ_1$ 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 $m_{χ_1}\gtrsim247$ MeV and fixes the splitting for each $m_{χ_1}$. The same line should appear at 700$-$810 keV in argon for $m_{χ_1}=0.3-10$ GeV. Normalizing to one LZ event also fixes the local rate of the radiative decay $χ_1\toχ_2γγ$, up to the mediator's photon coupling. A rough $γ$-ray estimate then requires this coupling to be $\lesssim10^{-2}$ of a proton-loop reference at $m_{χ_1}=10$ GeV, but $\lesssim10^{-9}$ at 0.3 GeV, which favours daughters near 10 GeV.