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 ${T}_{\mathrm{c}}$ of pure SU(3) gauge theory close to the continuum limit. The method allows us to estimate the critical coupling ${\beta}_{c}$ of the Wilson action for temporal extents up to ${N}_{\tau}\sim20$ with $\lesssim0.1$% uncertainties. Making use of the scale setting parameters ${r}_{0}$ and $\sqrt{{t}_{0}}$ in the same range of $\beta$-values, these results lead to the independent continuum extrapolations ${T}_{\mathrm{c}}{r}_{0}=0.7457(45)$ and ${T}_{\mathrm{c}}\sqrt{{t}_{0}}=0.2489(14)$, with the latter originating from a more convincing fit. Inserting a conversion of ${r}_{0}$ from literature (unfortunately with much larger errors) yields ${T}_{\mathrm{c}}/{\mathrm{\Lambda}}_{\overline{\mathrm{MS}}}=1.24(10)$