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 (effectively) 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 a U(1)-breaking condensate survives across the chiral transition. This scenario can be consistently reproduced using an effective Lagrangian model. The effects of the U(1) chiral condensate 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 pseudoscalar mesons in two photons: a comparison of our results with the experimental data is performed.

27 pages, LaTeX file. Completely revised version including new references and new comments on the results

References in corpus (14)

• Possibility of spontaneous parity violation in hot QCD
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Cited by in corpus (13)

• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Note on a sigma model connection with instanton dynamics
• Mesonic correlation lengths in high-temperature QCD
• Behaviour of the topological susceptibility in two colour QCD across the finite density transition
• Effects of the anomaly on the two-flavor QCD chiral phase transition
• Remarks on the U(1) axial symmetry and the chiral transition in QCD at finite temperature
• Study of the interactions of the axion with mesons and photons using a chiral effective Lagrangian model
• Study of the theta dependence of the vacuum energy density in chiral effective Lagrangian models at zero temperature
• QCD axion and topological susceptibility in chiral effective Lagrangian models at finite temperature
• The effects of an extra U(1) axial condensate on the radiative decay eta' --> gamma gamma at finite temperature
• Domain Wall in the Linear Sigma Model
• Theta dependence of the vacuum energy density in chiral effective Lagrangian models at finite temperature, above $T_c$
• The problem of the U(1) axial symmetry and the chiral transition in QCD