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 $E_R=248\pm {23}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {23}_{\mathrm{s}\mathrm{y}\mathrm{s}}$,keV in a search extending to $E_R\simeq 270$,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 $v_S=4.4\times {10}^{11}$,GeV and Majorana mass $M_N\simeq 50$,TeV, the relation $M_N=y_S{v}_S\mathrm{/}\sqrt{2}$ gives $y_S\simeq 1.6\times {10}^{-7}$, while the splitting relevant for LZ requires a Higgs–doublet Yukawa coupling $y\simeq 0.023$. 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 $M_D\simeq 380$–$420$,GeV, $\text{dchi}\simeq 323$–$330$,keV, and ${\xi }_{\chi }\simeq 0.12$–$0.15$ 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 $3\times {10}^{-2}$,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.