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 SUðNÞ 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.

We discuss the dependence of pure Yang-Mills equation of state on the choice of gauge algebra.In the confined phase, we generalize to an arbitrary simple gauge algebra Meyer's proposal of modelling the Yang-Mills matter by an ideal glueball gas in which the high-lying glueball spectrum is approximated by a Hagedorn spectrum of closed-bosonic-string type. Such a formalism is undefined above the Hagedorn temperature, corresponding to the phase transition toward a deconfined state of matter in which gluons are the relevant degrees of freedom. Under the assumption that the renormalization scale of the running coupling is gauge-algebra independent, we discuss about how the behavior of thermodynamical quantities such as the trace anomaly should depend on the gauge algebra in both the confined and deconfined phase. The obtained results compare favourably with recent and accurate lattice data in the su(3) case and support the idea that the more the gauge algebra has generators, the more the phase transition is of first-order type. *

The Lagrange-mesh method is a very accurate procedure for computing eigenvalues and eigenfunctions of a two-body quantum equation written in the configuration space. Using a Gauss quadrature rule, the method only requires the evaluation of the potential at some mesh points. The eigenfunctions are expanded in terms of regularized Lagrange functions, which vanish at all mesh points except one. Using the peculiarities of the method, it is shown that the Fourier transform of the eigenfunctions, computed in the configuration space, can easily be obtained with good accuracy in the physical domain of the momentum space. Also, observables in this space can easily be computed with good accuracy only using matrix elements and eigenfunctions computed in the configuration space.

We propose a quasiparticle approach allowing to compute the equation of state of a generic gauge theory with gauge group SU(Nc) and quarks in an arbitrary representation. Our formalism relies on the thermal quasiparticle masses (quarks and gluons) computed from perturbative techniques, in which the standard two-loop running coupling constant is used. Our model is minimal in the sense that we do not allow any extra ansatz concerning the temperature-dependence of the running coupling. We first show that it is able to reproduce the most recent equations of state computed on the lattice for temperatures typically higher than 2 Tc. Well above Tc indeed, an ideal gas framework with thermal masses is indeed expected to be relevant. Then we study the accuracy of various inequivalent large-Nc limits concerning the description of the QCD results, as well as the equivalence between the QCDAS limit and the N = 1 SUSY Yang-Mills theory.PACS. 12.38.Mh -11.15.Pg 1 Remark that a quasiparticle description of hypothetical quark stars has been proposed historically as an application of the quark hypothesis, see [6].

The strongly-coupled phase of the quark-gluon plasma (QGP) is studied here by resorting to a T -matrix formulation in which the medium is seen as a non-ideal gas of quasiparticles (quarks, antiquarks and gluons) interacting nonpertubatively. In the temperature range under study, (1-5) T c , where T c is the temperature of deconfinement, the interactions are expected to be strong enough to generate bound states. The dissociation temperature of such binary bound states is thus computed here. The more the quasiparticles involved in the binary system are heavy, the more the bound state is likely to survive significantly above T c . Then, the QGP equations of state at zero and small baryonic potential are computed for N f = 2 and N f = 2 + 1 by resorting to the Dashen, Ma and Bernstein formulation of statistical mechanics. Comparisons with current lattice QCD data are presented. *