Enhancement of p-wave dark matter annihilation by quasi-bound states

Abstract

We scrutinize the Sommerfeld enhancement in dark matter pair annihilation for p-wave and higher-ℓ partial waves. For the Yukawa potential these feature a super-resonant Breit-Wigner peak in their velocity-dependence close to Sommerfeld resonances as well as a universal scaling with velocity for all ℓ ≥ 1 that differs from the s-wave case. We provide a quantum mechanical explanation for these phenomena in terms of quasi-bound states sustained by the centrifugal barrier of the partial-wave potential, and give approximate WKB expressions capturing the main effects. The impact of quasi-bound states is exemplified for wino dark matter and models with light mediators, with a focus on indirect detection signals. We note that quasi-bound states can also explain similar peaks in the bound-state formation and self-scattering cross sections.