Abstract
We investigate features of the deconfinement phase transition in an $SU({N}_{c})$ gauge theory as revealed by fluctuations of the order parameter. The tool of choice is an effective model built from one-loop expressions of the field determinants of gluon and ghost, in the presence of a Polyakov loop background field. We show that the curvature masses associated with the Cartan angles, which serve as a proxy to study the ${A}_{0}$-gluon screening mass, show a characteristic dip in the vicinity of the transition temperature. The strength of the observables, which reflects a competition between the confining and the deconfining forces, is sensitive to assumptions of dynamics, and thus provides an interesting link between the $Z({N}_{c})$ vacuum structure and the properties of gluon and ghost propagators.
Highlights
In this work we study the fluctuations of the order parameter in an SUðNcÞ gauge theory within an effective model
A common strategy to constructing an effective potential is via a polynomial of the order parameter field [12,13,14], i.e., the Ginzburg-Landau theory
We employ an effective potential built from one-loop expressions of the field determinants of gluon and ghost described in Ref. [15]. (See Ref. [16].) The model naturally describes both the confined and the deconfined phases, as related to the spontaneous breaking of ZðNcÞ symmetry
Summary
In this work we study the fluctuations of the order parameter in an SUðNcÞ gauge theory within an effective model. These observables are finite and temperature dependent even in the confined phase, providing important diagnostic information about the mechanism of deconfinement phase transition, and the properties of gluons (and ghosts) in relation to the structure of ZðNcÞ vacuum. Even when powerful numerical methods such as lattice QCD (LQCD) are available to perform ab initio calculations of the full theory [1,2,3], it is instructive, and sometimes essential, to work on an effective model description of a dynamical system First of all, it provides clear links between the observables and the underlying symmetry. We employ an effective potential built from one-loop expressions of the field determinants of gluon and ghost described in Ref. We present a possible relation between the glueball mass and Td suggested by the model
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