Deconfinement critical point of lattice QCD with $N_{\rm f}=2$ Wilson fermions

TL;DR

This study investigates the critical point of deconfinement in lattice QCD with two Wilson fermions, analyzing how the transition weakens with decreasing quark mass and estimating the pion mass at the critical point.

Contribution

The paper provides the first estimates of the critical hopping parameter and pion mass for Nf=2 Wilson fermions across multiple lattice spacings, highlighting significant cut-off effects.

Findings

Critical pion mass estimated at approximately 4 GeV.

The first-order transition region expands as lattice spacing decreases.

Quantitative assessment of systematic errors and fermion determinant approximations.

Abstract

The ${\rm SU}(3)$ pure gauge theory exhibits a first-order thermal deconfinement transition due to spontaneous breaking of its global $Z_3$ center symmetry. When heavy dynamical quarks are added, this symmetry is broken explicitly and the transition weakens with decreasing quark mass until it disappears at a critical point. We compute the critical hopping parameter and the associated pion mass for lattice QCD with $N_f=2$ degenerate standard Wilson fermions on $N_\tau\in\{6,8,10\}$ lattices, corresponding to lattice spacings $a=0.12\, {\rm fm}$, $a=0.09\, {\rm fm}$, $a=0.07\, {\rm fm}$, respectively. Significant cut-off effects are observed, with the first-order region growing as the lattice gets finer. While current lattices are still too coarse for a continuum extrapolation, we estimate $m_\pi^c\approx 4 {\rm GeV}$ with a remaining systematic error of $\sim 20\%$. Our results allow to assess the accuracy of the LO and NLO hopping expanded fermion determinant used in the literature for various purposes. We also provide a detailed investigation of the statistics required for this type of calculation, which is useful for similar investigations of the chiral transition.