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

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.