Pion dispersion relation at finite density and temperature

Abstract

We study the behavior of the pion dispersion relation in a pion medium at finite density and temperature. We introduce a pion chemical potential to describe the finite pion number density and argue that such description is valid during the hadronic phase of a relativistic heavy-ion collision between chemical and thermal freeze-out. We make use of an effective Lagrangian that explicitly respects chiral symmetry through the enforcement of the chiral Ward identities. The pion dispersion relation is computed through the computation of the pion self-energy in a non-perturbative fashion by giving an approximate solution to the Schwinger-Dyson equation for this self-energy. The dispersion relation is described in terms of a density and temperature dependent mass and an index of refraction which is also temperature, density as well as momentum dependent. The index of refraction is larger than unity for all values of the momentum for finite $\mu$ and $T$. We conclude by exploring some of the possible consequences for the propagation of pions through the boundary between the medium and vacuum.

7 pages, 5 figures, 3 new references, published version

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• Thermal and Hadrochemical Equilibration in Nucleus-Nucleus Collisions at the SPS
• Equation of State, Radial Flow and Freeze-out in High Energy Heavy Ion Collisions
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• The Chiral Fermion Meson Model at Finite Temperature
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• Chemical Freezeout in Heavy Ion Collisions
• Pion propagation in the linear sigma model at finite temperature
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Cited by in corpus (13)

• Thermal Pions at Finite Isospin Chemical Potential
• Properties of neutral mesons in a hot and magnetized quark matter
• Weak decay constant of neutral pions in a hot and magnetized quark matter
• Effect of anomalous magnetic moment of quarks on the phase structure and mesonic properties in the NJL model
• Thermal pion masses in the second phase: $|{\mu }_I|>m_{\pi }$
• Superluminal pions in a hadronic fluid
• Bose-Einstein condensation and chiral phase transition in linear sigma model
• Chemical nonequilibrium for interacting bosons: applications to the pion gas
• rho propagation and dilepton production at finite pion density and temperature
• The mass and spectral function of scalar and pseudoscalar mesons in a hot and chirally imbalanced medium using the two-flavor NJL model
• Mass Spectra and Decay of Mesons under Strong External Magnetic Field
• Thermodynamical consistent CJT calculation in studying nuclear matter
• Shear Viscosity of hadronic matter at finite temperature and magnetic field