Speaker
Description
We investigate the finite-temperature equation of state (EOS) within an effective Lagrangian framework, where a dilaton field accounts for the breaking of scale symmetry in QCD. We start by extending a previous investigation in the pure gauge $SU (3)_c$ sector [1], describing the dynamics of the gluon condensate in terms of a dilaton Lagrangian. Below the critical temperature, the condensate is dominated by the dilaton field, whereas at higher temperatures, it evaporates in the form of quasi-free gluons. Additionally, for the first time, we incorporate into the calculations the lightest glueballs, i.e. J = 2, 4, 6, assuming that their masses lie on a linear Regge trajectory, as suggested in Ref. [2]. The masses of the exciteted glueballs are affected by the presence of a string tension term [3]. In this context, we explore the role of thermal fluctuations of the dilaton field using the technique proposed in Refs. [4, 5], which successfully reproduces lattice QCD results for thermodynamic quantities such as pressure and energy density [6]. Furthermore, we extend our study to an EOS that includes additional degrees of freedom, namely the $\sigma, \pi, \omega$ and $\rho$ mesons, along with nucleons, at finite chemical potential. This is achieved through an effective Lagrangian incorporating both broken scale symmetry and explicitly broken chiral symmetry [7, 8]. Beyond the mean-field approximation, we consider the effects of thermal fluctuations of the scalar glueball, other than the contributions of the $\sigma, \pi, \omega$ and $\rho$ meson fields, to gain insights of the thermodynamic properties of the phase transition.
References
[1] A. Drago, M. Gibilisco, and C. Ratti, “Evaporation of the gluon condensate: a model for pure gauge $SU(3)_c$ phase transition,” Nuclear Physics A, vol. 742, no. 1, pp. 165–181, 2004.
[2] H. B. Meyer and M. J. Teper, “Glueball regge trajectories and the pomeron: a lattice study, ”Physics Letters B, vol. 605, no. 3, pp. 344–354, 2005.
[3] N. Cardoso and P. Bicudo, “Lattice qcd computation of the su(3) string tension critical curve,”Phys. Rev. D, vol. 85, p. 077501, Apr 2012.
[4] G. W. Carter, O. Scavenius, I. N. Mishustin, and P. J. Ellis, “Effective model for hot gluodynamics,”Phys. Rev. C, vol. 61, p. 045206, Mar 2000.
[5] A. Mocsy, I. N. Mishustin, and P. J. Ellis, “Role of fluctuations in the linear σ model with quarks,”Phys. Rev. C, vol. 70, p. 015204, Jul 2004.
[6] S. Borsanyi, G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Szabo, “Precision $SU(3)$ lattice thermodynamics for a large temperature range,” Journal of High Energy Physics, vol. 2012, July 2012.
[7] G. Carter, P. Ellis, and S. Rudaz, “An effective lagrangian with broken scale and chiral symmetry iii. mesons at finite temperature,” Nuclear Physics A, vol. 618, no. 3, pp. 317–329, 1997.
[8] L. Bonanno and A. Drago, “Chiral lagrangian with broken scale: Testing the restoration of symmetries in astrophysics and in the laboratory,” Phys. Rev. C, vol. 79, p. 045801, Apr 2009.
