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

We consider the U(n) x U(m) symmetric Phi(4) lagrangian to describe the finite-temperature phase transition in QCD in the limit of vanishing quark masses with n=M=N(f) flavors and unbroken anomaly at T(c). We compute the Renormalization Group functions to five-loop order in Minimal Subtraction scheme. Such higher order functions allow to describe accurately the three-dimensional fixed-point structure in the plane (n, m), and to reconstruct the line n(+) (m, d) which limits the region of second-order phase transitions by an expansion in epsilon=4-d. We always find n(+) (m, 3)>m, thus no three-dimensional stable fixed point exists for n=m and the finite temperature transition in light QCD should be first-order. This result is confirmed by the pseudo-epsilon analysis of massive six-loop three dimensional series.