Inelastic Signatures of Electroweak Dark Matter

Minimal electroweak dark matter (DM) extended by a Majorana (M) and a Dirac (D) multiplet coupled through Higgs interactions provides a predictive framework for high-energy inelastic nuclear recoils. We show that this setup can account for the type of event recently reported by the LUX-ZEPLIN (LZ) Collaboration. At the custodial point, electroweak symmetry breaking induces a neutral-state splitting $\delta$ and an off-diagonal $Z$ interaction. For the coupled multiplets $3_M{2}_D$, $5_M{4}_D$, $7_M{6}_D$, $9_M{8}_D$, ${11}_M{10}_D$, and ${13}_M{12}_D$, both the splitting and the leading inelastic interaction are universal at fixed $(m_{\chi },y)$, independent of the electroweak representation. The observed high recoil energy points to splittings of a few hundred keV, while the fixed $Z$-mediated rate allows us to determine a mass-dependent ${\delta }_{\mathrm{L}\mathrm{Z}}(m_{\chi })$ by requiring one expected inelastic event in the LZ exposure, with a two-sided $90\mathrm{\%}$ Poisson band. This defines a universal region in the $(m_{\chi },y)$ plane. Intersecting it with the representation-dependent thermal relic trajectories selects a benchmark for each multiplet. The corresponding electroweak representation then predicts a correlated loop-induced elastic spin-independent signal at lower recoil energies.