content_image/366438.jpg content_image/366439.jpg
The transition from a confined hadron-resonance phase to a deconfined phase, the quark gluon plasma (QGP), is expected at high temperatures and/or baryonic chemical potentials. For several decades, the bag model (BM) equation of state (EoS) has been used to describe the QGP (see, e.g., Ref. [1]). In the simplest form, i.e. for non-interacting massless constituents and zero values of all conserved charges, the BM EoS reads: 

<img src='content_image/366438.jpg'>

where the energy density ε and the pressure p have a simple dependence on temperature T modified by adding a positive constant B (“vacuum pressure”). The Stefan-Boltzmann (SB) constant σ$_{SB}$ in Eq. (1) equals to: 

<img src='content_image/366439.jpg'>

where d$_{B}$ and d$_{F}$ are the degeneracy factors for the bosons (gluons) and fermions (quarks and antiquarks), respectively. The zero value of the baryonic chemical potential in Eq. (1) is a valid approximation for the QGP created in nucleus-nucleus collisions at the BNL RHIC and even better for future experiments at the CERN LHC. Note that also most lattice QCD calculations for the QGP EoS correspond to zero or very small values of the baryonic chemical potential. Equation (1) is assumed to be valid at T > T$_{c}$ , where the critical temperature T$_{c}$ corresponds to a 1 st order phase transition in the pure SU(3) gluodynamics or to a smooth crossover in the full QCD. 

The main features of the QCD deconfined matter EoS can be illustrated by the Monte Carlo (MC) lattice results [2] for the SU(3) gluodynamics presented in Fig. 1. They can be qualitatively summarized as follows: 

1. The pressure p ( T ) rapidly increases at T ≳ T$_{c}$ , while at high T the system reaches the ideal massless gas behavior p ∼ = ε/ 3. 

2. However, the constant σ ∼ = ε/T 4 ∼ = 3 p/T 4 observed at high T is about 10 ÷ 20% smaller than the value of σ$_{SB}$ in Eq. (2). 

3. At high T , both ε/T 4 and 3 p/T 4 approach their limiting value σ from below. 

Note that these properties of the gluon plasma EoS are also valid in the full QCD. 

The phenomenological success of the BM EoS (1) is due to the fact that it satisfies the first property: it gives p ∼ = ε/ 3 at high T and shows an abrupt drop of p ( T ) near T$_{c}$ . However, the BM EoS is in a contradiction with the second and third features listed above (see Fig. 1). The 

