The 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 Nt =4 and 6. Calculations with improved staggered fermions have been performed for various light to strange quark mass ratios in the range, 0.05 <= ml/ms <= 0.5, and with a strange quark mass fixed close to its physical value. From a combined extrapolation to the chiral (ml -> 0) and continuum (aT = 1/Nt -> 0) limits we find for the transition temperature at the physical point Tc r0 = 0.457(7) where the scale is set by the Sommer-scale parameter r0 defined as the distance in the static quark potential at which the slope takes on the value, (dVqq(r)/dr)r=r0 = 1.65/r02. Using the currently best known value for r0 this translates to a transition temperature Tc = 192(7)(4)MeV. The transition temperature in the chiral limit is about 3% smaller. We discuss current ambiguities in the determination of Tc in physical units and also comment on the universal scaling behavior of thermodynamic quantities in the chiral limit.
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