A Peccei-Quinn Origin for Inelastic Electroweak Dark Matter after LUX-ZEPLIN

Abstract

The LUX-ZEPLIN (LZ) experiment has reported one nuclear recoil event reconstructed at $E_R=248\pm 23_{\mathrm{stat}}\pm 23_{\mathrm{sys}}\mathrm{keV}$ in a search extending to $E_R\simeq 270\mathrm{keV}$. 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 $v_S=4.4\times 10^{11}\mathrm{GeV}$ and Majorana mass $M_N\simeq 50\mathrm{TeV}$, the relation $M_N=y_S{v}_S/\sqrt{2}$ 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 $M_D=286.9$, $376.1$, and $509.1\mathrm{GeV}$, ${\delta }_{\chi }\simeq 307-348\mathrm{keV}$, and ${\xi }_{\chi }\simeq 0.068-0.214$, 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 $3\times 10^{-2}\mathrm{s}$ and a decay length of order $20\mathrm{km}$, leaving the LZ topology as a single nuclear recoil while enabling a complementary luminous signal after terrestrial upscattering.

Comments: 11 pages, 1 figure. Revised the vectorlike EW doublet scattering normalization and numerical analysis; incorporated recent work