An Effective Action for Finite Temperature QCD with Fermions

TL;DR

This paper uses lattice perturbation theory to analyze finite temperature effects on fermionic corrections in QCD, revealing small corrections at low temperature and significant effects at intermediate temperatures, impacting phase transition properties.

Contribution

It provides the first detailed calculation of finite temperature fermionic corrections to plaquette couplings in lattice QCD with staggered fermions, highlighting their temperature dependence.

Findings

Finite temperature corrections are small at low temperatures.

Corrections become significant at intermediate temperatures.

Finite temperature effects can alter the order of the phase transition.

Abstract

Using lattice perturbation theory at finite temperature, we compute for staggered fermions the one-loop fermionic corrections to the spatial and temporal plaquette couplings as well as the leading $Z_N$ symmetry breaking coupling. Numerical and analytical considerations indicate that the finite temperature corrections to the zero-temperature calculation of A. Hasenfratz and T. DeGrand are small for small values of $\kappa = {1\over 2m_F}$, but become significant for intermediate values of $\kappa$. The effect of these finite temperature corrections is to ruin the agreement of the Hasenfratz-DeGrand calculation with Monte Carlo data. We conjecture that the finite temperature corrections are suppressed nonperturbatively at low temperatures, resolving this apparent disagreement. The $Z_N$ symmetry breaking coupling is small; we argue that it may change the order of the transition while having little effect on the critical value of $\beta$.