Residual excited-state abundance in the minimal dark-photon model

Determine the residual excited-state abundance of the Majorana state \(\chi_2\) across the parameter region favored by the endothermic LUX–ZEPLIN interpretation, including late-time \(\chi_1\leftrightarrow\chi_2\) conversion and subsequent \(\chi_2\) decay, in order to assess cosmological energy-injection and exothermic-scattering constraints on the minimal model.

Background

The model produces two nearly degenerate Majorana dark-matter states, with endothermic direct detection proceeding through χ1N→χ2N\chi_1 N\to\chi_2 N. The LUX–ZEPLIN-preferred mass splittings are below the e+e−e^+e^- threshold, so the excited state χ2\chi_2 cannot rapidly decay through the electron–positron channel and may survive to late times. Its abundance can be constrained by energy injection from decays and by exothermic down-scattering, χ2N→χ1N\chi_2N\to\chi_1N.

References

Moreover, we treat the present-day dominance of χ₁ as an assumption of the recoil analysis, leaving a detailed assessment of its consistency with the cosmological evolution of the two-state system for future work.

— ALP-mediated inelastic dark matter and the LUX-ZEPLIN high-recoil candidate event LZ230616  (2609.08893 - Yuan et al., 8 Sep 2026) in Section Discussion and Conclusions

A complete assessment of the minimal model therefore requires a dedicated calculation of the residual excited-state abundance, including late-time $\chi_1\leftrightarrow\chi_2$ conversion and subsequent decay. We leave this calculation for future work, and thus do not regard the minimal model as fully excluded by the present analysis.

— Endothermic dark matter with a light dark photon and the LUX--ZEPLIN high-energy nuclear-recoil candidate  (2609.09015 - Zhu et al., 8 Sep 2026) in Section Summary (Section \ref{sec:conclusions})

Nonetheless, precise quantitative statements require a dedicated analysis, which we leave for future work.

— A scalar-extended ${\rm U(1)_{L_μ-L_τ}}$ explanation of the LUX-ZEPLIN 248 keV excess  (2610.12443 - Pradhan et al., 8 Oct 2026) in Appendix, Section “BBN and CMB Consistency from Heavier Dark Scalar Decay”