Pion scattering poles and chiral symmetry restoration

Abstract

Using unitarized Chiral Perturbation Theory methods, we perform a detailed analysis of the $\pi \pi$ scattering poles $f_0(600)$ and $\rho (770)$ behaviour when medium effects such as temperature or density drive the system towards Chiral Symmetry Restoration. In the analysis of real poles below threshold, we show that it is crucial to extend properly the unitarized amplitudes so that they match the perturbative Adler zeros. Our results do not show threshold enhancement effects at finite temperature in the $f_0(600)$ channel, which remains as a pole of broad nature. We also implement T=0 finite density effects related to chiral symmetry restoration, by varying the pole position with the pion decay constant. Although this approach takes into account only a limited class of contributions, we reproduce the expected finite density restoration behaviour, which drives the poles towards the real axis, producing threshold enhancement and $\pi \pi$ bound states. We compare our results with several model approaches and discuss the experimental consequences, both in Relativistic Heavy Ion Collisions and in $\pi \to \pi \pi$ and $\gamma \to \pi \pi$ reactions in nuclei.

arXiv comment17 pages, 9 figures, final version to appear in Phys.Rev.D, added comments and references

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Cited by in corpus (17)

• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Hadron properties in the nuclear medium
• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• Transport coefficients and resonances for a meson gas in Chiral Perturbation Theory
• The Inverse Amplitude Method and Adler Zeros
• Chiral extrapolation of light resonances from one and two-loop unitarized Chiral Perturbation Theory versus lattice results
• Bulk viscosity and the conformal anomaly in the pion gas
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• A cross-channel study of pion scattering from lattice QCD
• Scalar susceptibilities and four-quark condensates in the meson gas within Chiral Perturbation Theory
• Chiral Symmetry Restoration and Scalar-Pseudoscalar partners in QCD
• Nature of the sigma meson as revealed by its softening process
• Thermal behaviors of light scalar resonances at low temperatures
• Chiral Symmetry and light resonances in hot and dense matter
• Chiral Extrapolation of light resonances from Unitarized Chiral Perturbation Theory
• Transport coefficients of a massive pion gas
• Review on recent progress in the study of the $N^{\ast }(920)$ subthreshold singularity and the $\sigma /f_0(500)$ meson