Scaling and the continuum limit of the finite temperature deconfinement transition in $\mathrm{SU}({N}_{c})$ pure gauge theory

Scaling and the continuum limit of the finite temperature deconfinement transition in $SU (N_{c})$ pure gauge theory

Saumen Datta and Sourendu Gupta

Phys. Rev. D 80, 114504 – Published 16 December 2009

Abstract

We investigated the finite temperature ( $T$ ) phase transition for $SU (N_{c})$ gauge theory with $N_{c} = 4$ , 6, 8 and 10 at lattice spacing, $a$ , of $1 / (6 T)$ or less. We checked that these theories have first-order transitions at such small $a$ . In many cases we were able to find the critical couplings with precision as good as a few parts in $10^{4}$ . We also investigated the use of two-loop renormalization group equations in extrapolating the lattice results to the continuum, thus fixing the temperature scale in units of the phase transition temperature, $T_{c}$ . We found that when $a \leq 1 / (8 T_{c})$ the two-loop extrapolation was accurate to about 1%–2%. However, we found that trading $T_{c}$ for the QCD scale, $Λ_{\bar{MS}}$ , increases uncertainties significantly, to the level of about 5%–10%.