Full O(a) improvement in electrostatic QCD

Guy D Moore,Niels Schlusser

doi:10.1103/physrevd.100.034510

Guy D Moore, Niels Schlusser

Open Access

https://doi.org/10.1103/physrevd.100.034510

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Abstract

EQCD is a 3D bosonic theory containing SU(3) and an adjoint scalar, which efficiently describes the infrared, nonperturbative sector of hot QCD and which is highly amenable to lattice study. We improve the matching between lattice and continuum EQCD by determining the final unknown coefficient in the O(a) matching, an additive scalar mass renormalization. We do this numerically by using the symmetry-breaking phase transition point of the theory as a line of constant physics. This prepares the ground for a precision study of the transverse momentum diffusion coefficient C(qperp) within this theory. As a byproduct, we provide an updated version of the EQCD phase diagram.

Highlights

At low energy scales, and at low temperatures, the coupling of QCD becomes large and the theory’s behavior becomes nonperturbative
We should not be surprised if perturbation theory does not work for thermodynamical or dynamical properties as one approaches the QCD crossover temperature, T ∼ 150 MeV [1,2], from above
Thermodynamical properties such as the pressure have an expansion in g, the strong coupling which is known up to g6 lnðgÞ [3,4,5,6,7,8], and while the leading-order behavior is within 30% of the lattice result above 360 MeV [1,2], the series of corrections does not converge even for T 1⁄4 100 GeV, a scale where perturbation theory should work well [9]

Summary

Introduction

At low temperatures, the coupling of QCD becomes large and the theory’s behavior becomes nonperturbative. Thermodynamical properties such as the pressure have an expansion in g, the strong coupling which is known up to g6 lnðgÞ [3,4,5,6,7,8], and while the leading-order behavior is within 30% of the lattice result above 360 MeV [1,2], the series of corrections does not converge even for T 1⁄4 100 GeV, a scale where perturbation theory should work well [9] This problem was first understood broadly by Linde [10] and was diagnosed more completely starting in the mid-1990s with the work of Braaten and Nieto [11], who showed that the perturbative expansion could be understood as a two-step process. One can integrate out all but the n 1⁄4 0 modes of the spatial gauge field Ai and its temporal

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