Dark-pion dark matter beyond leading order: unitarized chiral dynamics

Abstract

Dark pions are promising dark matter candidates, yet most analyses rely on leading-order (LO) chiral perturbation theory (ChPT). Motivated by the fact that, even for QCD pi-pi scattering, LO ChPT near threshold underestimates the isoscalar s-wave amplitude by an O(1) factor relative to high-precision dispersive results, we quantify how unitarization modifies the standard LO ChPT picture using the chiral unitary method, a nonperturbative resummation that implements the correct analytic structure with minimal input, and assess its impact on the phenomenology of dark-pion dark matter, taking SIMP and WIMP scenarios as canonical examples. We fix the subtraction constant to its natural estimate, interpreted as an effective cutoff at the chiral scale, so that the unitarized amplitudes depend only on the dark-pion mass and decay constant. We show that, depending on the coupling, the unitarized amplitudes develop resonance poles absent at LO, leading to sizable departures in 2-to-2 self-scattering, relevant for SIMP scenarios, and in annihilation including initial-state interaction effects, relevant for WIMP scenarios. These modifications, in turn, affect the viable parameter space. Although the subtraction constant is, from a model-building perspective, merely a parameter, a substantial deviation from its natural value would point to additional elementary resonances with the same quantum numbers.