The spatial string tension and the nonperturbative Debye mass from the Field Correlator Method

TL;DR

This paper uses the Field Correlator Method to analyze the spatial string tension and Debye mass at high temperatures, showing good agreement with lattice data and supporting the method's validity in high-temperature QCD thermodynamics.

Contribution

The paper provides a numerical calculation of the coefficients relating spatial string tension and Debye mass to temperature within the FCM, confirming its consistency with lattice results.

Findings

Good agreement between FCM calculations and lattice data.

Validation of FCM for high-temperature space-like QCD phenomena.

Demonstration of FCM's parameter-free applicability in thermodynamics.

Abstract

The phenomenon of the almost linear growth of the square root of spatial string tension $\sqrt{\sigma_s(T)}= c_{\sigma} g^2 T$ and of the Debye mass $m_D(T)$ was found both in lattice and in theory, based on the Field Correlator Method (FCM). In the latter the string tension (both spatial and colorelectric) is expressed as an integral of the two gluon Green's function calculated with the same string tension: $\sigma= \int G^{(2g)}_{\sigma}$. This relation allows to check the selfconsistency of the theory and at high T it allows also to calculate $c_{\sigma}$ and hence $\sigma_s$. We calculate below in the paper the corresponding coefficients $c_{\sigma}$ and $c_D$ numerically in the FCM method and compare the results with lattice data finding a good agreement. This justifies the use of the FCM in the space-like region and in high T thermodynamics without extra parameters.