Thermodynamics of the glueball resonance gas

Abstract

We study the thermodynamic properties – pressure, entropy and trace anomaly – of a gas of glueballs that includes the glueball states obtained by various lattice simulations. We show that this model, called glueball resonance gas (GRG) approach, describes well the thermal properties of the Yang–Mills sector of QCD below the critical temperature $$T_c$$ T c , provided that $$T_c$$ T c is properly matched to the corresponding determination of the glueball masses, obtaining $$T_c \sim 320 \pm 20$$ T c ∼ 320 ± 20 MeV. The inclusion into the GRG of heavier glueballs not yet seen on the lattice, assuming that glueballs follow Regge trajectories as quark-antiquark states do, leads only to a small correction. We consider the contribution to the pressure of the interactions between scalar-scalar and tensor-tensor glueballs, which turn out to be also negligible.

Introductory Visual Lecture on QCD at Large \(N_{c}\): Bound States, Chiral Models, and Phase Diagram

“…As shown in [35], when N c is large, gluons dominate: a first-order phase transition between the deconfined and confined phases at T dec ≃ 300 ∝ N 0 c MeV (see [79] for a compilation of results) is expected for any value of the chemical potential. This is utterly different from the QCD phase diagram for N c = 3 [3], which is cross-over along the T direction and first order along the µ one.…”

“…[44,78] (for a recent compilation and comparison of lattice results, see Ref. [79]). The glueball wave function must be colorless.…”

“…For an explicit study of the scattering of tensor glueballs using the Lagrangian above, see Ref. [79].…”

The θ-dependence of the Yang-Mills spectrum from analytic continuation

“…Indeed, these corrections can not be all independent from each other, since they are indirectly related to the θ-dependence of the free energy in the confined phase. This can be easily understood by using hadron resonance gas models like, e.g., those discussed in [103,104], where it was shown that a determination of the glueball masses is sufficient to obtain quantitatively accurate estimates of thermodynamical quantities. Finally, it would be very interesting to study models in which s 2 and m 2 or, more generally, the θ-dependence of the spectrum, can be investigated analytically (and is non-trivial).…”