Five-loop epsilon expansion forU(n) U(m) models: finite-temperature phase transition in light QCD

We consider the U(n)xU(m) symmetric Phi^4 Lagrangian to describe thefinite-temperature phase transition in QCD in the limit of vanishing quarkmasses with n=m=N_f flavors and unbroken anomaly at T_c. We compute theRenormalization Group functions to five-loop order in Minimal Subtractionscheme. Such higher order functions allow to describe accurately thethree-dimensional fixed-point structure in the plane (n,m), and to reconstructthe line n^+(m,d) which limits the region of second-order phase transitions byan expansion in epsilon=4-d. We always find n^+(m,3)>m, thus nothree-dimensional stable fixed point exists for $n=m$ and the finitetemperature transition in light QCD should be first-order. This result isconfirmed by the pseudo-epsilon analysis of massive six-loop three dimensionalseries.Comment: 12 pages, no figur