Chiral phase transition for [formula presented] gauge theories via an effective Lagrangian approach

We study the chiral phase transition for vectorlike (Formula presented) gauge theories as a function of the number of quark flavors (Formula presented) by making use of an anomaly-induced effective potential. We modify an effective potential of a previous work, suggested for (Formula presented) and apply it to larger values of (Formula presented) where the phase transition is expected to occur. The new effective potential depends explicitly on the full (Formula presented) function and the anomalous dimension (Formula presented) of the quark mass operator. By using this potential we argue that chiral symmetry is restored for (Formula presented) A perturbative computation of (Formula presented) then leads to an estimate of the critical value (Formula presented) for the transition. © 1999 The American Physical Society.