We explore the phase structure of a chiral model of constituent quarks and gluons implementing scale symmetry breaking at finite temperature and chemical potential. In this model the chiral dynamics is intimately linked to the trace anomaly saturated by a dilaton field. The thermodynamics is governed by two condensates, thermal expectation values of $\sigma$ and dilaton fields, which are the order parameters responsible for the phase transitions associated with the chiral and scale symmetries. Within the mean-field approximation, we find that with increasing temperature, a system experiences a chiral phase transition, and then a first-order phase transition of partial scale symmetry restoration characterized by a melting gluon condensate takes place at a higher temperature. There exists a region at finite chemical potential where the scale symmetry remains dynamically broken while the chiral symmetry is restored. We also give a brief discussion on the $\sigma$-meson mass constrained from lattice QCD.

• Received 16 October 2011

DOI:https://doi.org/10.1103/PhysRevC.85.025202