Meson loop effects in the NJL model at zero and non-zero temperature

Abstract

We compare two different possibilities to include meson-loop corrections in the Nambu-Jona-Lasinio model: a strict 1/N_c-expansion in next-to-leading order and a non-perturbative scheme corresponding to a one-meson-loop approximation to the effective action. Both schemes are consistent with chiral symmetry, in particular with the Goldstone theorem and the Gell-Mann-Oakes-Renner relation. The numerical part at zero temperature focuses on the pion and the rho-meson sector. For the latter the meson-loop-corrections are crucial in order to include the dominant rho -> pipi-decay channel, while the standard Hartree + RPA approximation only contains unphysical qqbar-decay channels. We find that m_π, f_π, and quantities related to the rho-meson self-energy can be described reasonably with one parameter set in the 1/N_c-expansion scheme, whereas we did not succeed to obtain such a fit in the non-perturbative scheme. We also investigate the temperature dependence of the quark condensate. Here we find consistency with chiral perturbation theory to lowest order. Similarities and differences of both schemes are discussed.