Scalar susceptibilities and four-quark condensates in the meson gas within Chiral Perturbation Theory

Abstract

We analyze the properties of four-quark condensates and scalar susceptibilities in the meson gas, within finite temperature Chiral Perturbation Theory (ChPT). The breaking of the factorization hypothesis does not allow for a finite four-quark condensate and its use as an order parameter, except in the chiral limit. This is rigorously obtained within ChPT and is therefore a model-independent result. Factorization only holds formally in the large $N_c$ limit and breaks up at finite temperature even in the chiral limit. Nevertheless, the factorization breaking terms are precisely those needed to yield a finite scalar susceptibility, deeply connected to chiral symmetry restoration. Actually, we provide the full result for the SU(3) quark condensate to NNLO in ChPT, thus extending previous results to include kaon and eta interactions. This allows to check the effect of those corrections compared to previous approaches and the uncertainties due to low-energy constants. We provide a detailed analysis of scalar susceptibilities in the SU(3) meson gas, including a comparison between the pure ChPT approach and the virial expansion, where the unitarization of pion scattering is crucial to achieve a more reliable prediction. Through the analysis of the interactions within this approach, we have found that the role of the $\sigma$ resonance is largely canceled with the scalar isospin two channel interaction, leaving the $\rho (770)$ as the main contribution. Special attention is paid to the evolution towards chiral restoration, as well as to the comparison with recent lattice analysis.

22 pages and 5 figures

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Cited by in corpus (10)

• Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD
• Light- and strange-quark mass dependence of the $\rho (770)$ meson revisited
• Electromagnetic effects in the pion dispersion relation at finite temperature
• The role of chiral symmetry and the non-ordinary $\kappa /K_0^{\ast }(700)$ nature in ${\pi }^{\pm }{K}_S$ femtoscopic correlations
• Chiral Symmetry Restoration for the large-$N$ pion gas
• The pion-kaon scattering amplitude and the $K^0(700)$ and $K^{\ast }(892)$ resonances at finite temperature
• Light quarks at finite temperature: chiral restoration and the fate of the $U(1{)}_A$ symmetry
• Temperature dependence of Quark and Gluon condensate In The Dyson-Schwinger Equations At Finite Temperature
• The QCD scalar susceptibility and thermal scalar resonances in chiral symmetry restoration
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$