Large-$N$ pion scattering at finite temperature: the $f_0(500)$ and chiral restoration

Abstract

We consider the $O(N+1)/O(N)$ Non-Linear Sigma Model for large $N$ as an effective theory for low-energy QCD at finite temperature $T$, in the chiral limit. At $T=0$ this formulation provides a good description of scattering data in the scalar channel and generates dynamically the $f_0(500)$ pole, the pole position lying within experimental determinations. Previous $T=0$ results with this model are updated using newer analysis of pion scattering data. We calculate the pion scattering amplitude at finite $T$ and show that it satisfies exactly thermal unitarity, which had been assumed but not formally proven in previous works. We discuss the main differences with the $T=0$ result and we show that one can define a proper renormalization scheme with $T=0$ counterterms such that the renormalized amplitude can be chosen to depend only on a few parameters. Next, we analyze the behaviour of the $f_0(500)$ pole at finite $T$, which is consistent with chiral symmetry restoration when the scalar susceptibility is saturated by the $f_0(500)$ state, in a second-order transition scenario and in accordance with lattice and theoretical analysis.

24 pages, 12 figures. Funding agency added in the Acknowledgments

References in corpus (33)

• Critical Phenomena and Renormalization-Group Theory
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• NJL-model analysis of dense quark matter
• The chiral and deconfinement aspects of the QCD transition
• Is there still any Tc mystery in lattice QCD? Results with physical masses in the continuum limit III
• The QCD transition temperature: results with physical masses in the continuum limit II.
• QCD Equation of State and Hadron Resonance Gas
• Thermal hadron production in relativistic nuclear collisions: the hadron mass spectrum, the horn, and the QCD phase transition
• The QCD phase transition with physical-mass, chiral quarks
• Non-perturbative Approach to effective chiral Lagrangians and Meson Interactions
• Hadronic Production of Thermal Photons
• The inverse amplitude method in Chiral Perturbation Theory
• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• Elastic $\pi \pi$ scattering to two loops
• Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis
• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• On the magnetic equation of state in (2+1)-flavor QCD
• The QCD chiral transition, $\ua$ symmetry and the Dirac spectrum using domain wall fermions
• Transport coefficients and resonances for a meson gas in Chiral Perturbation Theory
• Chiral symmetry at finite temperature: linear vs nonlinear $\sigma$-models
• A new global fit of the $L_i^r$ at next-to-next-to-leading order in Chiral Perturbation Theory
• Thermal rho and sigma mesons from chiral symmetry and unitarity
• Role of the tetraquark in the chiral phase transition
• Finite Temperature Pion Scattering to one-loop in Chiral Perturbation Theory
• Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory
• Chiral Symmetry Restoration and Scalar-Pseudoscalar partners in QCD
• Thermodynamics of O(N) sigma models: 1/N corrections
• Pion Mass Effects in the Large $N$ Limit of $\chiPT$
• Study of the gluon propagator in the large-N_f limit at finite temperature and chemical potential for weak and strong couplings
• The Gross-Neveu model at finite temperature at next to leading order in the 1/N expansion
• Pion Decay Constant at Finite Temperature in the Nonlinear Sigma Model
• Electromagnetic effects in the pion dispersion relation at finite temperature
• Thermal Meson properties within Chiral Perturbation Theory

Cited by in corpus (6)

• Thermal behaviors of light scalar resonances at low temperatures
• The role of the thermal $f_0(500)$ in chiral symmetry restoration
• Chiral Symmetry Restoration for the large-$N$ pion gas
• Revisiting $O(N)$ $\sigma$ model at unphysical pion masses and high temperatures
• Light Meson Masses using AdS/QCD modified Soft Wall Model
• Chiral Symmetry restoration from the hadronic regime