Analytical study of a gas of gluonic quasiparticles at high temperature: effective mass, pressure and trace anomaly

The thermodynamical properties of a pure Yang-Mills theory SU(N) is described by a gas of gluonic quasiparticles with temperature dependent mass $m(T)$ and a bag function $B(T)\mathrm{.}$ The analytic behavior of $m(T)$ and the pressure $p$ at high $T$ are derived and constraints on the parameters defining $B(T)$ are discussed. The trace anomaly $\theta =\rho -3p$ is evaluated in the high $T$ domain: it is dominated by a quadratic behavior $\theta =nK{T}^2,$ where $n=2(N^2-1)$ is the number of degrees of freedom and $K$ is an integration constant which does not depend on the bag function $B(T)$. This is a general result which is in very good agreement with recent lattice simulations.