Deconfinement critical point of lattice QCD with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math> Wilson fermions
Francesca Cuteri, Owe Philipsen, Alena Schön, Alessandro Sciarra
Abstract
The $\mathrm{SU}(3)$ 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 ${N}_{\mathrm{f}}=2$ degenerate standard Wilson fermions on ${N}_{\ensuremath{\tau}}\ensuremath{\in}{6,8,10}$ lattices, corresponding to lattice spacings $a=0.12\text{ }\text{ }\mathrm{fm}$, $a=0.09\text{ }\text{ }\mathrm{fm}$, $a=0.07\text{ }\text{ }\mathrm{fm}$, respectively. Significant cutoff 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 ${m}_{\ensuremath{\pi}}^{c}\ensuremath{\approx}4\text{ }\text{ }\mathrm{GeV}$ with a remaining systematic error of $\ensuremath{\sim}20%$. Our results allow us to assess the accuracy of the leading-order and next-to-leading-order 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.