Relevance of the axial anomaly at the finite-temperature chiral transition in QCD

We investigate the nature of the finite-temperature chiral transition in QCD with two light flavors, in the case of an effective suppression of the U (1) ₀ symmetry breaking induced by the axial anomaly, which implies the symmetry breaking U (2) ₋ (2) ₑ (2) ₕ, instead of SU (2) ₋ (2) ₑ (2) ₕ. For this purpose, we perform a high-order field-theoretical perturbative study of the renormalization-group flow of the corresponding three-dimensional multiparameter Landau-Ginzburg-Wilson ^4 theory with the same symmetry-breaking pattern. We confirm the existence of a stable fixed point and determine its attraction domain in the space of the bare quartic parameters. Therefore, the chiral QCD transition might be continuous also if the U (1) ₀ symmetry is effectively restored at T₂. However, the corresponding universality class differs from the O (4) vector universality class which would describe a continuous transition in the presence of a substantial U (1) ₀ symmetry breaking at T₂. We estimate the critical exponents of the U (2) ₋ (2) ₑ (2) ₕ universality class by computing and analyzing the corresponding perturbative expansions. These results are important to discriminate among the different scenarios for the scaling behavior of QCD with two light flavors close to the chiral transition.