Dark matter scattering cross section and dynamics in dark Yang-Mills theory

TL;DR

This paper computes the dark matter candidate glueball scattering cross section in $SU(2)$ Yang-Mills theory using lattice methods, providing insights into dark matter interactions and constraints on the theory's scale.

Contribution

First calculation of glueball scattering cross section in $SU(2)$ Yang-Mills theory using lattice QCD techniques, linking theory with dark matter observational constraints.

Findings

Lower bound on the $SU(2)$ Yang-Mills scale parameter: $ ext{Lambda} > 60$ MeV.

Determined low-energy effective Lagrangian for glueballs.

Estimated dark matter self-scattering cross section compatible with observations.

Abstract

We calculate for the first time the scattering cross section between lightest glueballs in $SU(2)$ pure Yang-Mills theory, which are good candidates of dark matter. In the first step, we evaluate the interglueball potential on lattice using the HAL QCD method, with several lattice spacings ($\beta = 2.1, 2.2, 2.3, 2.4$, and 2.5). The systematics associated with nonzero angular momentum effect is removed by subtracting the centrifugal force. The statistical accuracy is improved by employing the cluster-decomposition error reduction technique and by using all space-time symmetries. We then determine the low energy glueball effective Lagrangian and the scattering cross section at low energy, which is compared with the observational constraint on the dark matter self-scattering. We derive the lower bound on the scale parameter of the $SU(2)$ Yang-Mills theory, as $\Lambda > 60$ MeV.