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

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-le ading order and a nonperturbative scheme corresponding to a one-meson-loop approximation to the effective action. Both schemes are consistent with chi ral symmetry, in particular, with the Goldstone theorem and the Gell-Mann-O akes-Renner relation. The numerical part at zero temperature focuses on the pion and the rho -meson sector. For the latter, meson-loop corrections are crucial in order to include the dominant rho --> pi pi -decay channel, whi le the standard Hartree + RPA approximation only contains unphysical q(q) o ver bar -decay channels. We find that m(pi), f(pi) (<(<psi>)over bar>psi), and quantities related to the p-meson self-energy can be described reasonab ly 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 inv estigate the temperature dependence of the quark condensate. Here, we find consistency with the chiral perturbation theory to the lowest order. Simila rities and differences of both schemes are discussed. (C) 2001 MAIK "Nauka/ Interperiodica".