Effective field theory for resonant wino dark matter

TL;DR

This paper develops an effective field theory to accurately describe resonant wino dark matter interactions, including nonperturbative effects and Coulomb resummation, improving understanding of their annihilation rates and scattering properties.

Contribution

It introduces a novel effective field theory framework for SU(2)-triplet wino dark matter, incorporating nonperturbative zero-range interactions and long-range Coulomb effects.

Findings

Effective field theory accurately describes low-energy wino interactions.

Coulomb resummation improves the prediction of scattering observables.

The theory matches well with Schrödinger equation calculations.

Abstract

Enhancements in WIMP annihilation rates have been identified with a nonperturbative "Sommerfeld enhancement" arising from the exchange of light mediators. At certain critical values of the WIMP mass, the enhancement is increased dramatically due to a zero-energy resonance at the WIMP-pair threshold. For masses near these critical values, WIMP scattering processes are accurately described by an effective field theory where WIMPs have nonperturbative zero-range contact interactions. The effective field theory is controlled by a renormalization-group fixed point at which the WIMPs are degenerate in mass and their scattering length is infinite. If the WIMPs can exchange massless mediators, the resulting long-range interaction must also be treated nonperturbatively. We develop an effective field theory for SU(2)-triplet dark matter, which have short-range weak and long-range electromagnetic interactions. We refer to these dark matter particles as winos. The long-range Coulomb interaction between charged winos is resummed to all orders. The parameters of the effective field theory can be determined by matching wino-wino scattering amplitudes calculated by solving the Schr\"odinger equation with a potential describing exchange of electroweak gauge bosons. With Coulomb resummation, the effective field theory at leading order gives a good description of the low-energy two-body observables for winos.