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

Abstract

We compare two different possibilities of including meson-loop corrections in the Nambu-Jona-Lasinio model: a strict 1/N c expansion in the next-to-leading order and a nonperturbative 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 ρ-meson sector. For the latter, meson-loop corrections are crucial in order to include the dominant ρ → ππ-decay channel, while the standard Hartree + RPA approximation only contains unphysical $$m_\pi ,f_\pi ,\left\langle {\bar \psi \psi } \right\rangle $$ -decay channels. We find that $$q\bar q$$ , and quantities related to the ρ-meson self-energy can be described reasonably with one parameter set in the 1/N c-expansion scheme, whereas we did not succeed in obtaining such a fit in the nonperturbative scheme. We also investigate the temperature dependence of the quark condensate. Here, we find consistency with the chiral perturbation theory to the lowest order. Similarities and differences of both schemes are discussed.