Thermal extension of the screened massive expansion in the Landau gauge

Abstract: The massive screened expansion for pure SU(3) Yang-Mills theory is extended to finite temperature in the Landau gauge. All thermal integrals are evaluated analytically up to an external one-dimensional integration, yielding explicit integral representations of analytic functions which can be continued to the whole complex plane. The gluon propagator is first explored in the Euclidean space by making use of parameters obtained from first principles, which were already found to accurately reproduce the lattice data at zero temperature. Within such a scheme, the agreement with the lattice at $T\neq 0$ turns out to be only qualitative. The description improves provided that the parameters are tuned in a temperature-dependent way by a fit to the data, carried out separately for each component of the propagator; in particular, the transverse component closely follows the lattice data, while the agreement of the longitudinal component with the data is poor at small momenta and moderately high temperatures. The dispersion relations of the quasi-gluon are then extracted from the pole trajectory in the complex plane using the fitted parameters. A crossover is found for the mass, suppressed by temperature like an order parameter in the confined phase, while increasing like an ordinary thermal mass in the deconfined phase.