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Chiral Symmetry Restoration at Finite Temperature in the Linear Sigma--Model

D. Metzger·H. Meyer--Ortmanns·H. --J. Pirner
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Abstract

The temperature behaviour of meson condensates $<σ_0>$ and $<σ_8>$ is calculated in the $SU(3)\times SU(3)$-linear sigma model. The couplings of the Lagrangian are fitted to the physical $π,K,η,η'$ masses, the pion decay constant and a $O^+(I=0)$ scalar mass of $m_σ=1.5$ GeV. The quartic terms of the mesonic interaction are converted to a quadratic term with the help of a Hubbard-Stratonovich transformation. Effective mass terms are generated this way, which are treated self-consistently to leading order of a $1/N$-expansion. We calculate the light $<\bar q q>$ and strange $<\bar s s>$-quark condensates using PCAC relations between the meson masses and condensates. For a cut-off value of 1.5 GeV we find a first-order chiral transition at a critical temperature $T_c\sim 161$ MeV. At this temperature the spontaneously broken subgroup $SU(2)\times SU(2)$ is restored. Entropy density, energy density and pressure are calculated for temperatures up to and slightly above the critical temperature. To our surprise we find some indications for a reduced contribution from strange mesons for $T\geq T_c$.

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D. Metzger, H. Meyer--Ortmanns, H. --J. Pirner. 1993-12-10. Chiral Symmetry Restoration at Finite Temperature in the Linear Sigma--Model. https://doi.org/10.1016/0370-2693(94)90328-x

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