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

Abstract

The temperature behaviour of meson condensates $<{\sigma }_0>$ and $<{\sigma }_8>$ is calculated in the $SU(3)\times SU(3)$-linear sigma model. The couplings of the Lagrangian are fitted to the physical $\pi ,K,\eta ,{\eta }^{\prime }$ masses, the pion decay constant and a $O^{+}(I=0)$ scalar mass of $m_{\sigma }=1.5$ 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 $T\ge T_c$.

Comments: 17 pages, HD--TVP--93--15. (3 figures - available on request)