Quark-mass dependence ofTcin QCD: Working up fromm=0or down fromm=∞?

Abstract

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 ${m}_{\ensuremath{\pi}}$ than seen in present lattice data for ${m}_{\ensuremath{\pi}}\ensuremath{\gtrsim}0.4\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V}$. On the other hand, working down from ${m}_{\ensuremath{\pi}}=\ensuremath{\infty}$, an effective Lagrangian for the Polyakov loop requires only small explicit symmetry breaking, ${b}_{1}\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}{m}_{\ensuremath{\pi}})$, to describe ${T}_{c}({m}_{\ensuremath{\pi}})$ 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: ${m}_{\ensuremath{\pi}}\ensuremath{\simeq}4.2\sqrt{\ensuremath{\sigma}}\ensuremath{\simeq}1.8\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V}$ and ${T}_{c}\ensuremath{\simeq}240\text{ }\text{ }\mathrm{M}\mathrm{e}\mathrm{V}$ for three flavors and three colors.