The U(1) axial symmetry and the chiral transition in QCD

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, we analyse a scenario in which the U(1) axial symmetry is still broken above the chiral transitions. We will show that this scenario can be consistently reproduced using an effective Lagrangian model. A new order parameter is introduced for the U(1) axial symmetry.