The Lattice Free Energy of QCD with Clover Fermions, up to Three-Loops

TL;DR

This paper computes the three-loop perturbative free energy in Lattice QCD with clover fermions, providing detailed results applicable to various gauge groups, fermion masses, and flavors, using automated Mathematica procedures.

Contribution

It presents the first three-loop calculation of the free energy in Lattice QCD with clover fermions, including automated diagram evaluation and results for arbitrary parameters.

Findings

Three-loop free energy results for Lattice QCD with clover fermions.

Numerical evaluation and extrapolation techniques for finite lattice calculations.

Results applicable to any SU(N_c) gauge group and fermion flavor number.

Abstract

We calculate the perturbative value of the free energy in Lattice QCD, up to three loops. Our calculation is performed using Wilson gluons and the Sheikholeslami - Wolhert (clover) improved action for fermions. The free energy is directly related to the average plaquette. To carry out the calculation, we compute all relevant Feynman diagrams up to 3 loops, using a set of automated procedures in Mathematica; numerical evaluation of the resulting loop integrals is performed on finite lattice, with subsequent extrapolation to infinite size. The results are presented as a function of the fermion mass m, for any SU(N_c) gauge group, and for an arbitrary number of fermion flavors. In order to enable independent comparisons, we also provide the results on a per diagram basis, for a specific mass value.