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 $E_R=248\pm23_{\rm stat}\pm23_{\rm sys}$\,keV in a search extending to $E_R\simeq270$\,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 $v_S=4.4\times10^{11}$\,GeV and Majorana mass $M_N\simeq50$\,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 $M_D\simeq380$--$420$\,GeV, $\dchi\simeq323$--$330$\,keV, and $ξ_χ\simeq0.12$--$0.15$ yielding an order-one LZ event count. 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 $3\times10^{-2}$\,s and a decay length of order $20$\,km, leaving the LZ topology as a single nuclear recoil while enabling a complementary luminous signal after terrestrial upscattering.