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

A bstract 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 ππ 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 DM, taking SIMP and WIMP scenarios as canonical examples. We fix the subtraction constant to its natural estimate, interpreted as an effective cutoff at Λ χ = 4 πf π , so that the unitarized amplitudes depend only on m π and f π . We show that, depending on the coupling m π / f π , the unitarized amplitudes develop resonance poles absent at LO, leading to sizable departures in 2 → 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.