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

We calculate the scattering cross section between two 0(++ )glueballs in SU(2) Yang-Mills theory on a 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 the 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.