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.
Highlights
For physical quark mass values, the thermal QCD transition is known to be an analytic crossover [1]
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
In this work we focused our attention on the Nf 1⁄4 2 deconfinement critical point and studied its location on progressively finer lattices simulating at Nτ ∈ f6; 8; 10g
Summary
For physical quark mass values, the thermal QCD transition is known to be an analytic crossover [1]. It is interesting to observe that the direction of the cutoff effect in the bare parameter space is the same for the critical deconfinement boundary in the heavy quark mass regime as for the critical chiral boundary in the light quark mass regime with both Wilson [16,17,18] and staggered [19,20,21,22,23] discretizations (in some other studies employing improved staggered fermion discretizations [24,25], no chiral critical line is seen, bounding a potential chiral first-order region). The shift of the chiral Z2 boundary implies an increase in the simulation cost while the continuum is approached, which is drastic in the chiral transition region This further motivates us to attempt a continuum limit in the heavy quark mass regime first, where it should be more feasible.
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