On the deconfinement phase transition in the resonance gas

Abstract

We obtain the constraints on the ruling parameters of the dense hadronic gas model at the critical temperature and propose the quasiuniversal ratios of the thermodynamic quantities. The possible appearence of thermodynamical instability is discussed.

Quantum and stringy corrections to the equation of state of holographic QCD matter and the nature of the chiral transition

“…At small T the effect, of course, is striking. One observes further that the minimum mass obtained from thermodynamics is now almost equal to the one from direct computation in (19) and that T c is only 10% above the temperature at which p = 0. Due to this closeness the derivatives are also larger and the peak in interaction measure even sharper.…”

“…where ρ 0 is a dimensionless number. The degeneracy factor N 2 f of the m = 0 Goldstone bosons and the massive flavor nonsinglet states was factored out from (19). For the massive states with m > m 0 , we assume an exponential Hagedorn spectrum together with a power of m. Using this spectrum we get for the scaled hadron gas pressurê…”

“…Some examples are as follows: Ref. [16] computes ρ(m) in the bag model, [17] writes "confining phase is consistent with effective string theory in which conformal symmetry and modular invariance play a significant role", [18] for the first time discusses a separate density for mesons and baryons, but believes that they should be equal to exponential accuracy, [19] tries to connect hadronic and plasma phases like here, [20]- [22] believes that the mesonic and baryonic densities should be different and fits both of them, [24] doubts the empirical validity of the exponential mass spectrum and [25] updates mass spectrum fits and includes the chemical potential in the hadron gas discussion. From all the work on ρ(m) it is obvious that there is no unique parametrisation for it.…”

“…As a second step, the right panel of Fig. 5 shows numerical results for the 2nd log T derivative of the scaled pressure solution ( 35) of ( 28) at T 0 = 0.5 but now integrated over the exponential mass spectrum (19) ρ(m, b, a, m 0 ). A large negative value of a is needed, here a = −10.…”

“…The hadronic pressure will then vanish at T = 0. To see what this implies quantitatively, take the hadron mass spectrum in (19), use the toy model parameters in (26) and replace δ(m) → δ(m − m gb ) with m gb = 0.5 ≈ T c . The argument here is that for physical QCD T c is close to m π .…”