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The tricritical line of the first-order chiral phase transition isinvestigated in the U(Nf)xU(Nf) sigma model by means of the ring improvedone-loop finite temperature effective potential. To locate the tricritical linein the space of the coupling constants, we expand the effective potential up tothird order in the high temperature expansion, and up to sixth order in theorder parameter expansion. In this approximation, the tricritical line can beevaluated to the lowest order of the coupling constants and it follows ananalytic relation between the tree-level masses of the scalar bosons. Thevalidity of the high temperature expansion, the order parameter expansion, andthe ring improved perturbation is critically examined. This result does notalter if one includes the massless fermions with the small Yukawa couplings.

An analytic study of the tricritical line in the U(Nf)xU(Nf) sigma model