We calculate the scattering cross section between two 0 þþ glueballs in SUð2Þ Yang-Mills theory on a lattice at β ¼ 2.1, 2.2, 2.3, 2.4, and 2.5 using the indirect (HAL QCD) method. We employ the clusterdecomposition 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 Λ as σ ϕϕ ¼ ð2-51ÞΛ −2 (stat þ sys). From the observational constraints of galactic collisions, we obtain the lower bound of the scale parameter as Λ > 60 MeV. We also discuss the naturalness of the Yang-Mills theory as the theory explaining dark matter.
We report Lee-Yang zeros behavior at finite temperature and density. The quark number densities, n , are calculated at the pure imaginary chemical potential iµ qI , where no sign problem occurs. Then, the canonical partition functions, Z C (n, T, V ), up to some maximal values of n are estimated through fitting theoretically motivated functions to n , which are used to compute the Lee-Yang zeros. We study the temperature dependence of the distributions of the Lee-Yang zeros around the pseudo-critical temperature region T /T c = 0.84 -1.35.In the distributions of the Lee-Yang zeros, we observe the Roberge-Weiss phase transition at T /T c ≥ 1.20. We discuss the dependence of the behaviors of Lee-Yang zeros on the maximal value of n, so that we can estimate a reliable infinite volume limit.
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