A comparative lattice analysis of \(SU(2)\) dark gluebal

We study the mass and scattering cross section of \(SU(2)\) glueballs as dark matter candidates using lattice simulations. We employ both naive and improved \(SU(2)\) gauge actions in \(3+1\) dimensions with several \(\beta\) values, and adopt both the traditional Monte Carlo method and the flow-based model based on machine learning techniques to generate lattice configurations. The mass of dark scalar glueball with \(J^{PC}=0^{++}\) and the NBS wave function are calculated. Using a coupling constant of \(\beta=2.2\) as an illustration, we compare the dark glueball mass calculated from the configurations generated from the two methods. While consistent results can be achieved, the two methods demonstrate distinct advantages. Using the Runge-Kutta method, we extract the glueball interaction potential and two-body scattering cross section. From the observational constraints, we obtain the lower bound of the mass of scalar glueball as candidates of dark matter.