Glueballs and the Yang-Mills plasma in a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi></mml:math>-matrix approach

Abstract

The strongly coupled phase of Yang-Mills plasma with arbitrary gauge group is studied in a $T$ matrix approach. The existence of lowest-lying glueballs, interpreted as bound states of two transverse gluons (quasiparticles in a many-body setup), is analyzed in a nonperturbative scattering formalism with the input of lattice-QCD static potentials. Glueballs are actually found to be bound up to 1.3 ${T}_{c}$. Starting from the $T$-matrix, the plasma equation of state is computed by resorting to a formulation of statistical mechanics (Dashen et al.) and favorably compared to quenched lattice data. Special emphasis is put on $\mathrm{SU}(N)$ gauge groups, for which analytical results can be obtained in the large-$N$ limit, and predictions for a ${G}_{2}$ gauge group are also given in this work.