Study of the Yang-Mills and Quark-Gluon Plasma Equations of State thanks to Quasiparticle Approaches

Understanding QCD at finite temperature and baryonic potential is nowadays a fascinating topic.
Indeed, from the experimental side, SPS, RHIC and LHC have pointed out several evidences of the
existence of a deconfined matter : the Quark-Gluon Plasma (QGP).
From a theoretical point of view, studying the QCD phase diagram and all its implications is a
challenging subject in itself and has motivated many approaches and developments. In particular, in
this seminar, we will focus on two quasiparticle approaches and their comparisons with lattice QCD
data.
In the first approach, the thermodynamics of the Yang-Mills matter in the confined phase is
addressed thanks to a hadron resonance gas model. Its particularity is to obtain equations of state
(EoS) for any gauge groups.
In the second approach, the Dashen, Ma and Bernstein formulation of statistical mechanics is used
in order to produce EoS for QCD matter in the deconfined regime. This formulation has the
advantage to formally take into account many-body interactions. In our developments, we limited
ourself to two-body interactions; These latter being computed within a T-matrix formalism. Then,
the thermodynamics of the Yang-Mills matter (for arbitrary gauge groups), the QGP and a
supersymmetric medium with one supersymmetric generator have been studied.