Thermal field fluctuations in a chiral lagrangian with broken scale invariance

¹ Department of Applied Science and Technology, Politecnico di Torino, 10129, Torino, Italy
² INFN, Sezione di Torino, 10126, Torino, Italy
³ Department of Physics and Earth Science, University of Ferrara, 44122 Ferrara, Italy
⁴ INFN, Sezione di Ferrara, 44122 Ferrara, Italy

^* e-mail: luca_passarella@polito.it

Published online: 10 December 2024

Abstract

We study the finite temperature equation of state by using an effective lagrangian in which a dilaton field reproduces the breaking of scale symmetry in QCD. We start by extending a previous investigation in the pure gauge sector, where the dynamics of the gluon condensate, expressed in terms of a dilaton lagrangian, is dominated below the critical phase transition temperature, while at greater temperatures the condensate evaporates in the form of quasi-free gluons. In this context, we study the role of the inclusion of thermal fluctuations of the dilaton field and compare our results with the lattice QCD data. Moreover, we take into account of the meson sector at zero chemical potential by means of an effective lagrangian which incorporates broken scale in addition to spontaneously broken chiral symmetry. Beyond the mean-field approximation, the relevance of the thermal fluctuations of the scalar glueball, other than the contribution of the σ and π meson fields is considering by following a general technique. In this framework, we investigate the thermodynamic nature of the phase transition.