The Inert Doublet Model of Dark Matter and the LUX-ZEPLIN High-Recoil Event

The recent LUX-ZEPLIN (LZ) search reported a nuclear-recoil event near $248\mathrm{k}\mathrm{e}\mathrm{V}$. Such a high-recoil event can be interpreted in terms of endothermic inelastic dark matter scattering, which typically requires a mass splitting of order a few hundred keV between the initial and final dark states. The inert doublet model (IDM) provides a natural realization of this scenario through the $Z$-mediated transition $H+N\to A+N$. In this work, we systematically examine whether this interpretation can be consistently realized in the IDM under the relevant theoretical constraints and existing experimental bounds. We perform a detailed profile-likelihood analysis of the LZ event, and find a viable high-mass IDM region with a profile best fit at $m_H=1080\mathrm{G}\mathrm{e}\mathrm{V}$ and $m_A-m_H=369\mathrm{k}\mathrm{e}\mathrm{V}$.