Polyakov loop fluctuations in the presence of external fields

Abstract

We study the implications of the spontaneous and explicit Z(3) center symmetry breaking for the Polyakov loop susceptibilities. To this end, ratios of the susceptibilities of the real and imaginary parts, as well as of the modulus of the Polyakov loop are computed within an effective model using a color group integration scheme. We show that the essential features of the lattice QCD results of these ratios can be successfully captured by the effective approach. Furthermore we discuss a novel scaling relation in one of these ratios involving the explicit breaking field, volume, and temperature.

Deconfinement in the presence of a strong magnetic field

“…This suggests additional modifications of the Polyakov loop potential beyond the one-loop U Q are required to effectively enhance the Z(3) breaking. The same observation is made already for the B ¼ 0 case [39].…”

“…Unfortunately the linear breaking strength for Z(3) is not directly measured in most LQCD studies. A crude estimate [39] based on LQCD results on the ratios of Polyakov loop susceptibilities suggests a larger Z(3) breaking strength than the prediction from the PNJL model. Nevertheless, the issue is far from settled as the analysis is still marred by the unsolved problem of the proper renormalization of the Polyakov loop and its susceptibilities.…”

“…The fluctuation of the absolute value of the Polyakov loop, χ A , and the ratio R A ¼ χ A =χ L cannot be obtained simply within a mean-field approach. One way to compute the observable is by setting up a color group integration [39]. Here, we provide an approximate way to determine R A , based on the scaling relation discussed in Ref.…”

“…Here, we provide an approximate way to determine R A , based on the scaling relation discussed in Ref. [39].…”

“…Ratios of these fluctuations are excellent probes of deconfinement: In a pure gauge theory, they exhibit a jump at the transition temperature [36,37], with well-defined low temperature limits deducible from general theoretical constraints and the Z(3) symmetry. Even in full QCD, they provide a measure for the strength of explicit Z(3) symmetry breaking field induced by the light fermions, and show less renormalization scheme dependence than the Polyakov loop [38,39].…”