Reviewing the problem of the U ( 1 ) axial symmetry and the chiral transition in QCD

Reviewing the problem of the U (1) axial symmetry and the chiral transition in QCD Abstract We discuss the role of the U(1) axial symmetry for the phase structure of QCD at finite temperature. We expect that, above a certain critical temperature, also the U(1) axial symmetry will be restored. We will try to see if this transition has (or has not) anything to do with the usual chiral transition: various possible scenarios are discussed. In particular, supported by recent lattice results, we analyse a scenario in which the U(1) axial symmetry is still broken above the chiral transition. This scenario can be consistently reproduced using an effective Lagrangian model. A new order parameter is introduced for the U(1) axial symmetry and its effects on the slope of the topological susceptibility in the full theory with quarks are studied: we find that this quantity (in the chiral limit of zero quark masses) acts as an order parameter for the U(1) axial symmetry above the chiral transition. Further information on the new U(1) chiral order parameter is derived from the study (at zero temperature) of the radiative decays of the " light " pseudoscalar mesons in two photons: a comparison of our results with the experimental data is performed.