A Peccei-Quinn Origin for Inelastic Electroweak Dark Matter after LUX-ZEPLIN
The LUX-ZEPLIN (LZ) experiment has reported one nuclear recoil event reconstructed at $E_R=248\pm23_{\rm stat}\pm23_{\rm sys}{\rm\,keV}$ in a search extending to $E_R\simeq270{\rm\,keV}$. We investigate an inelastic electroweak (EW) doublet interpretation in which spontaneous Peccei-Quinn (PQ) breaking leaves a residual parity that stabilizes the lighter neutral state and generates the Majorana splitting. A PQ-charged singlet fermion acquires its Majorana mass from the PQ-breaking vacuum expectation value and, after being integrated out, induces the dimension-five operator that splits a vectorlike EW doublet. A minimal KSVZ colored sector supplies the QCD anomaly. For a representative PQ-breaking scale $v_S=4.4\times10^{11}{\rm\,GeV}$ and Majorana mass $M_N\simeq50{\rm\,TeV}$, the relation $M_N=y_Sv_S/\sqrt{2}$ gives $y_S\simeq1.6\times10^{-7}$, while the splitting relevant for LZ requires a Higgs-doublet Yukawa coupling $y\simeq0.023$. In a standard thermal history, the EW doublet constitutes only a subcomponent of the dark matter. A rate estimate probing the high velocity tail gives representative benchmarks with $M_D=286.9$, $376.1$, and $509.1{\rm\,GeV}$, $\delta_\chi\simeq307-348{\rm\,keV}$, and $\xi_\chi\simeq0.068-0.214$, each yielding an order-one LZ event count under the standard thermal assumption. The remaining abundance is supplied by the QCD axion through vacuum misalignment for suitable $v_S$ and initial angle. The excited state has a radiative lifetime of order $3\times10^{-2}{\rm\,s}$ and a decay length of order $20{\rm\,km}$, leaving the LZ topology as a single nuclear recoil while enabling a complementary luminous signal after terrestrial upscattering.