Critical point and scale setting in SU(3) plasma: An update

We explore a method developed in statistical physics which has been argued to have exponentially small finite-volume effects, in order to determine the critical temperature Tc of pure SU(3) gauge theory close to the continuum limit. The method allows us to estimate the critical coupling βc of the Wilson action for temporal extents up to Nτ∼20 with ≲0.1% uncertainties. Making use of the scale setting parameters r0 and t0−−√ in the same range of β-values, these results lead to the independent continuum extrapolations Tcr0=0.7457(45) and Tct0−−√=0.2489(14), with the latter originating from a more convincing fit. Inserting a conversion of r0 from literature (unfortunately with much larger errors) yields Tc/ΛMS¯¯¯¯¯=1.24(10).