Abstract :
[en] According to our current knowledges, all phenomena in nature are well described by only
four fundamental forces, namely the gravitation and the electromagnetic, weak and strong
interactions. Within my thesis, I have mainly studied one of them: the strong interaction.
As its name suggests it, it is the strongest one in nature but it only acts at the nuclear level
and on certain particles: the quarks, the antiquarks and the gluons. These particles have the
peculiarity to carry colour charges that make them sensitive to the strong interaction in the same
way as particles carrying electric charges are sensitive to the electromagnetic force. For this reason,
the theory underlying the strong interaction is called Quantum Chromodynamics (QCD).
QCD exhibits two essential features : the confinement and the asymptotic freedom. These
properties can be understood thanks to the behaviour of its running coupling constant that measures
the strength of the interaction between coloured particles. Indeed, this latter observable is a
decreasing (increasing) function in terms of the energy (distance) scale. This means that, provided
that the energy increases (or the distance decreases), a coloured particle feels less and less attracted
by the other ones, leading to the concept of asymptotic freedom. On the other hand, at low energy
(high distance), the strength of the interaction is so strong that colour particles are confined inside
bigger structures called hadrons (as for instance the protons and the neutrons). This important
particularity of QCD is expressed in the fact that observed hadrons are colourless, i.e. made of
coloured particles that combine their charges in a neutral way. It comes that quarks, antiquarks and
gluons can not exist as free particles in a confined regime, that is to say at low temperature and
baryonic potential.
However, when the temperature and the baryonic potential increase, a phase transition from
a confined to a deconfined world can occur because of the asymptotic freedom property. For
instance, at high enough temperatures, a weakly-coupled plasma phase (wQGP), whom the real
degrees of freedom are quarks and gluons, is then theoretically expected since in such temperature
range, the QCD coupling constant has to be small.
Understanding the different phases that QCD exhibits is thus nowadays a fascinating topic,
intensively studied both theoretically and experimentally. The creation of a deconfined state, the
quark-gluon plasma (QGP), was first announced at SPS (CERN) in 2000 and confirmed by RHIC
(BNL) in 2004 and by LHC (CERN) in 2010. One of the main observation of these two latter
experiments is that the QGP behaves like a nearly-perfect liquid with a low ratio viscosity over
entropy just above the critical temperature of deconfinement, Tc. This suggests that strong
interactions remain important around Tc. Therefore, it is much more some screening effects that
seem to produce the QGP. This state is then referred as a strongly-coupled QGP (sQGP).
From the theoretical side, many approaches are obviously considered in order to investigate
various aspects of QCD at finite temperature and baryonic potential. In particular, many lattice
QCD computations are developed in parallel to phenomenological approaches.
During my Ph.D. work, we have mainly studied some quasiparticle approaches aimed to
describe the confined and the deconfined phases of QCD. The thermodynamic of the confined
phase is addressed within a hadron resonance gas model. In particular, we investigate the glueballs
sector for arbitrary gauge groups. Next, a study of the Yang-Mills plasma is carried out in the
deconfined regime thanks to the Dashen, Ma and Bernstein (DMB) formulation of statistical
mechanics. A peculiarity of our approach is to explicitly take into account the two-body
interactions; This latter being computed within a T-matrix formalism. Finally, the thermodynamic of
the full QGP is also described thanks to the DMB formulation. All the produced equations of state
presented in this seminar will be compared to recent lattice QCD results.
