Effective model of QCD magnetic monopoles from numerical study of one- and two-component Coulomb quantum Bose gases

Magnetic monopoles are suggested to play an important role in strongly coupled quark-gluon plasma (sQGP) near the deconfinement temperature. Until now, their many-body treatment has been studied classically; only their binary scattering has been solved in quantum mechanics. In this paper we start quantum many-body studies of the monopole ensembles. Specifically, we carry out numerical simulations of the path integral for one- and two-component Coulomb Bose systems. We determine the relation between the critical temperature for the Bose-Einstein condensation phase transition Tc and the Coulomb coupling strength using two methods, the classic finite-size scaling of the condensate and a lattice-tested method based on permutation cycles. For a one-component Coulomb Bose gas, we observe the same behavior of the critical temperature - initially rising slightly, then falling as interaction strength is increased - as seen in the case of hard spheres; we also observe the same behavior for a two-component Coulomb Bose gas. We then calculate sets of radial correlation functions between the like and unlike charged particles. By matching these with the correlation functions previously calculated on the lattice, we derive an effective quantum model of color magnetic monopoles in QCD. From this matched model, we are able to extract the monopole contribution to the QCD equation of state near Tc.