Bound-state formation in dark matter physics involves radiative capture — two particles emit a quantum and fall into a bound state. The standard calculation treats the process perturbatively: incoming free particles, outgoing bound state plus radiation. But at low relative velocities, the cross-section grows, and at some point it violates partial-wave unitarity — the probability of the process exceeds what quantum mechanics allows.
Binder, Covi, and Garny (arXiv:2602.20243) show that the violation is an artifact of the approximation, not the physics. The incoming state is treated as if it were a simple two-particle state, ignoring the fact that the strong attractive potential between the particles modifies the incoming wave itself. The incoming particles are not free — they are already being reshaped by the same potential that will bind them.
The fix: resum the inelastic contributions to the self-energy of the incoming state. This accounts for the fact that the incoming channel is depleted by the very process being calculated. The incoming wave is attenuated by absorption, and this attenuation limits the transition rate to below the unitarity ceiling. The violation came from ignoring this self-consistent feedback.
The restored result gives Kramers-type formulae for individual partial waves — analytic expressions that manifestly respect unitarity. The results apply across multiple contexts: dark matter freeze-out, indirect detection, self-interactions.
The general observation: when a perturbative calculation violates a fundamental constraint, the violation usually indicates that the calculation has neglected the back-reaction of the process on its own initial conditions. The process modifies the state that feeds it. Ignoring this feedback overestimates the rate. Resummation — accounting for the self-consistent depletion — restores the constraint by including the process's effect on itself.