The LUX-ZEPLIN (LZ) collaboration recently reported one candidate nuclear-recoil event near 250 keV. That energy is hard to get from the simplest, momentum-independent dark-matter scattering. This paper explores a different idea: dark matter that comes in two nearly equal-mass states, χ1 (lighter) and χ2 (excited), which interact through an axion-like particle (ALP). The authors show that how many excited particles survive from the early Universe can change whether today’s collisions absorb energy (endothermic) or release it (exothermic), and that either possibility can produce recoil spectra that peak near 250 keV in benchmark cases.

The model has two main ingredients. First, the ALP couples to gluons and photons: the gluon coupling drives scattering off atomic nuclei in detectors, while the photon coupling controls the slow decay of the excited state χ2. Second, the two dark states couple to the ALP “off-diagonally,” so direct transitions between χ1 and χ2 occur. Rather than assuming only the lighter state exists today, the authors follow the cosmological history of both states. They find that for the ALP and coupling values relevant to the LZ signal, χ2 is long-lived—its decay lifetime is much longer than the age of the Universe—so its present-day abundance is set not by decay but by conversion reactions inside the dark sector.

The key process that sets the excited-state fraction f2 is χ2χ2 ↔ χ1χ1, an exothermic conversion that can still occur even when the dark particles are very cold because the small mass difference provides a fixed momentum kick. Whether that conversion efficiently removes χ2 or leaves a large fraction behind depends strongly on the Lorentz structure of the transition coupling. If the transition is of scalar type, conversions are efficient and χ2 is largely depleted, favoring endothermic scattering where χ1 is kicked up to χ2 in a detector. If the transition is pseudoscalar, conversions are inefficient and roughly half the dark matter remains in χ2, favoring exothermic down-scattering χ2→χ1. The authors calculate these effects for four benchmark combinations (Majorana or Dirac fermions with scalar or pseudoscalar transitions) and map out the resulting present-day f2.