Transition temperature in QCD

Abstract

We present a detailed calculation of the transition temperature in QCD with two light and one heavier (strange) quark mass on lattices with temporal extent ${N}_{\ensuremath{\tau}}=4$ and 6. Calculations with improved staggered fermions have been performed for various light to strange quark mass ratios in the range, $0.05\ensuremath{\le}{\stackrel{^}{m}}_{l}/{\stackrel{^}{m}}_{s}\ensuremath{\le}0.5$, and with a strange quark mass fixed close to its physical value. From a combined extrapolation to the chiral (${\stackrel{^}{m}}_{l}\ensuremath{\rightarrow}0$) and continuum ($aT\ensuremath{\equiv}1/{N}_{\ensuremath{\tau}}\ensuremath{\rightarrow}0$) limits we find for the transition temperature at the physical point ${T}_{c}{r}_{0}=0.457(7)$ where the scale is set by the Sommer-scale parameter ${r}_{0}$ defined as the distance in the static quark potential at which the slope takes on the value, $(\mathrm{d}{V}_{\overline{q}q}(r)/\mathrm{d}r{)}_{r={r}_{0}}=1.65/{r}_{0}^{2}$. Using the currently best known value for ${r}_{0}$ this translates to a transition temperature ${T}_{c}=192(7)(4)\text{ }\text{ }\mathrm{MeV}$. The transition temperature in the chiral limit is about 3% smaller. We discuss current ambiguities in the determination of ${T}_{c}$ in physical units and also comment on the universal scaling behavior of thermodynamic quantities in the chiral limit.