Exothermic Dark Matter with a Dark Higgs: The LZ 248 keV Event and the Galactic Center Excess

LUX-ZEPLIN (LZ) reported a $248\mathrm{k}\mathrm{e}\mathrm{V}$ nuclear-recoil event. Exothermic dark matter can explain it in a dark $U(1)$ model whose dark Higgs generates the dark photon mass and the mass splitting. A computed excited-state fraction gives two branches with dark photon masses near $1$ and $26\mathrm{G}\mathrm{e}\mathrm{V}$ for kinetic mixing $\epsilon ={10}^{-4}$. INTEGRAL/SPI limits on excited-state decays bound the LZ rate, and cosmic microwave background limits exclude the lighter branch at its likelihood minimum. For a dark Higgs boson near the dark photon mass, the heavier branch agrees with the southern-sky Galactic Center $\gamma$-ray excess.