Glueball scattering cross section in lattice SU(2) Yang-Mills theory

TL;DR

This study computes the glueball scattering cross section in lattice SU(2) Yang-Mills theory using the HAL QCD method, providing insights into dark matter models and setting bounds on the theory's scale parameter.

Contribution

It introduces a lattice calculation of glueball scattering cross sections with improved techniques and connects the results to dark matter phenomenology.

Findings

Derived the interglueball potential and phase shifts.

Established a lower bound on the scale parameter,  > 60 MeV.

Proposed implications for dark matter naturalness.

Abstract

We calculate the scattering cross section between two $0^{++}$ glueballs in $SU(2)$ Yang-Mills theory on lattice at $\beta = 2.1, 2.2, 2.3, 2.4$, and 2.5 using the indirect (HAL QCD) method. We employ the cluster-decomposition error reduction technique and use all space-time symmetries to improve the signal. In the use of the HAL QCD method, the centrifugal force was subtracted to remove the systematic effect due to nonzero angular momenta of lattice discretization. From the extracted interglueball potential we determine the low energy glueball effective theory by matching with the one-glueball exchange process. We then calculate the scattering phase shift, and derive the relation between the interglueball cross section and the scale parameter $\Lambda$ as $\sigma_{\phi \phi} = (2 - 51) \Lambda^{-2}$ (stat.+sys.). From the observational constraints of galactic collisions, we obtain the lower bound of the scale parameter, as $\Lambda > 60$ MeV. We also discuss the naturalness of the Yang-Mills theory as the theory explaining dark matter.