Chiral Lagrangian at finite temperature from the Polyakov-Chiral Quark Model

Details Chiral Lagrangian at finite temperature from the Polyakov-Chiral Quark Model Chiral Lagrangian at finite temperature from the Polyakov-Chiral Quark Model

2006-07-31

arxiv.org/abs/hep-ph/0607338v1

Phys.Rev.D74:114014,2006

Physics

High Energy Physics

High Energy Physics - Phenomenology

16 pages, no figures

Scientific paper

10.1103/PhysRevD.74.114014

We analyze the consequences of the inclusion of the gluonic Polyakov loop in chiral quark models at finite temperature. Specifically, the low-energy effective chiral Lagrangian from two such quark models is computed. The tree level vacuum energy density, quark condensate, pion decay constant and Gasser-Leutwyler coefficients are found to acquire a temperature dependence. This dependence is, however, exponentially small for temperatures below the mass gap in the full unquenched calculation. The introduction of the Polyakov loop and its quantum fluctuations is essential to achieve this result and also the correct large $N_c$ counting for the thermal corrections. We find that new coefficients are introduced at ${\cal O}(p^4)$ to account for the Lorentz breaking at finite temperature. As a byproduct, we obtain the effective Lagrangian which describes the coupling of the Polyakov loop to the Goldstone bosons.

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