Remarks on the U(1) axial symmetry and the chiral transition in QCD at finite temperature

Abstract

We discuss the role of the U(1) axial symmetry for the scalar and pseudoscalar meson mass spectrum of QCD at finite temperature, above the chiral transition at T_c, using a chiral effective Lagrangian model, which, in addition to the usual chiral condensate, also includes a (possible) genuine U(1)_A-breaking condensate that (possibly) survives across the chiral transition. The motivations for considering this Lagrangian (and a critical comparison with other effective Lagrangian models existing in the literature) are presented. A detailed comparison between the case N_f=3 (or N_f>3) and the (remarkably different) case N_f=2 is performed. The results obtained in the case N_f=2 are also critically compared with the available lattice results.

Revised version, published in PRD; 28 pages, 1 table, 1 figure

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• Relevance of the axial anomaly at the finite-temperature chiral transition in QCD
• The QCD chiral transition, $\ua$ symmetry and the Dirac spectrum using domain wall fermions
• Meson screening masses from lattice QCD with two light and the strange quark
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• Pion and $\eta$-meson mass splitting at the two-flavour chiral crossover
• Exploring axial $U(1)$ restoration in a modified 2+1 flavor Polyakov quark meson model
• Study of the interactions of the axion with mesons and photons using a chiral effective Lagrangian model
• How tetraquarks can generate a second chiral phase transition
• 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
• Light quarks at finite temperature: chiral restoration and the fate of the $U(1{)}_A$ symmetry
• The pion-kaon scattering amplitude and the $K^0(700)$ and $K^{\ast }(892)$ resonances at finite temperature
• The role of strangeness in chiral and $U(1{)}_A$ restoration
• Study of some local and global $U(1)$ axial condensates in QCD at finite temperature
• Theta dependence of the vacuum energy density in chiral effective Lagrangian models at finite temperature, above $T_c$