The non-perturbative QCD Debye mass from a Wilson line operator

TL;DR

This work establishes a gauge-invariant, non-perturbative determination of the $g^2T$ contribution to the QCD Debye mass by evaluating a Wilson line operator in the 3d SU(3) gauge theory, extending prior SU(2) results to the physical case. Using a lattice implementation with clover and smeared operators, the authors extract continuum coefficients $c_2=1.14(4)$ (SU(2)) and $c_3=1.65(6)$ (SU(3)), and show that at moderate temperatures the Debye mass is $m_D\sim 6T$ with a lightest gauge-invariant screening mass around $3T$ and a magnetic scale around $6T$, implying strong overlap between electric and magnetic sectors near $T_c$. The findings indicate that non-perturbative $g^2T$ effects dominate up to extremely high temperatures and that a dimensionally reduced theory including $A_0$ remains valid down to $T\sim 2T_c$, with $A_0$ playing a crucial dynamical role near the phase transition. These results coherently tie 3d Wilson-line measurements to 4d lattice results, supporting the reliability of the reduced-theory description for finite-temperature QCD.

Abstract

According to a proposal by Arnold and Yaffe, the non-perturbative g^2T-contribution to the Debye mass in the deconfined QCD plasma phase can be determined from a single Wilson line operator in the three-dimensional pure SU(3) gauge theory. We extend a previous SU(2) measurement of this quantity to the physical SU(3) case. We find a numerical coefficient which is more accurate and smaller than that obtained previously with another method, but still very large compared with the naive expectation: the correction is larger than the leading term up to T ~ 10^7 T_c, corresponding to g^2 ~ 0.4. At moderate temperatures T ~ 2 T_c, a consistent picture emerges where the Debye mass is m_D ~ 6T, the lightest gauge invariant screening mass in the system is ~ 3T, and the purely magnetic operators couple dominantly to a scale ~ 6T. Electric (~ gT) and magnetic (~ g^2T) scales are therefore strongly overlapping close to the phase transition, and the colour-electric fields play an essential role in the dynamics.

Figures (2)

• Figure 1: The local mass values, $m\,a =-\ln [G_F(n+1)/G_F(n)]$, from typical diagonalized operators at the different $\beta_G$'s. The masses have been converted to continuum units by multiplying the lattice values $m\, a$ with $\beta_G/6$.
• Figure 2: The results for SU(2) (left) and SU(3) (right). The continuum fits from Tables \ref{['table:su2']}, \ref{['table:su3']} have also been shown. The ranges of $1/\beta_G$ on the $x$-axes have been chosen such that in lattice units, the masses have comparable values for SU(2) and SU(3).