Quark-mass dependence of Tc in QCD:: Working up from m=0 or down from m = ∞? -: art. no. 074001

We analyze the dependence of the QCD transition temperature on the quark (or pion) mass. We find that a linear sigma model, which links the transition to chiral symmetry restoration, predicts a much stronger dependence of T-c on m(pi) than seen in present lattice data for m(pi)greater than or similar to0.4 GeV. On the other hand, working down from m(pi)=infinity, an effective Lagrangian for the Polyakov loop requires only small explicit symmetry breaking, b(1)similar toexp(-m(pi)), to describe T-c(m(pi)) in the above mass range. Physically, this is a consequence of the flat potential (large correlation length) for the Polyakov loop in the three-color pure gauge theory at T-c. We quantitatively estimate the end point of the line of first-order deconfining phase transitions: m(pi)similar or equal to4.2 rootsigma similar or equal to1.8 GeV and T(c)similar or equal to240 MeV for three flavors and three colors.