Exothermic dark matter and the 248 keV nuclear recoil in LUX-ZEPLIN

Abstract

The single 248-keV nuclear-recoil candidate reported by LZ is reproduced by dark matter that downscatters, with the relic in the excited state of a pseudo-Dirac pair and a splitting \delta\simeq-350\keV. Every interpretation so far advanced is endothermic and places the splitting within a few percent of the xenon kinematic ceiling, so that the predicted count changes from zero to 143 times its central value as the halo escape speed runs from 500 to 600 km/s. The downscattering branch has no threshold speed; the same variation changes its count by 0.3 %. The ratio of counts below 70 keV to those above is 0.011, so the null standard search follows from the kinematics. A weak-strength coupling overproduces the event by 8.9\times10^{5}, so the mediator is a dark-sector one, and longevity of the relic excited state requires |\delta|<2m_e. Solving the coupled Boltzmann system removes the one free normalization. Rotating to the eigenchannels of the off-diagonal potential gives \sigma_0=(\pi/k^2)\sin^2(\delta_+-\delta_-), whose phase difference is 0.03 to 1.3 rad, so the Born rate exceeds the s-wave unitarity bound where it is used. One event then requires \sigma_p\simeq2\times10^{-42} cm^2 and a kinetic mixing \epsilon\simeq1\times10^{-6} at m_{A'}=1\GeV, with beam-dump coverage below 0.6\GeV pushing the mediator above that value. The ground state upscatters endothermically through the same operator, which excludes |\delta|\lesssim300 keV and makes the published endothermic reading the small-splitting limit of one model. The decisive test is argon, whose first form-factor zero lies at 695 keV against 94.6 keV for xenon; argon yields 4 to 6 events per tonne-year near 250 keV, where the endothermic reading is forbidden at any exposure.