Investigation of meson loop effects in the Nambu-Jona-Lasinio model

TL;DR

This paper studies meson loop effects in the Nambu-Jona-Lasinio model, demonstrating their impact on meson properties, quark condensate, and phase transition behavior, using different approximation schemes.

Contribution

It compares 1/N_c expansion and meson-loop approximation schemes, establishing their validity and implications for meson and quark condensate properties.

Findings

Goldstone theorem and Gell-Mann-Oakes-Renner relation hold in both schemes

Parameter sets can describe pion and rho-meson properties in 1/N_c expansion

A first order chiral phase transition occurs at high temperature in meson-loop scheme

Abstract

The influence of mesonic fluctuations on quantities in the Nambu-Jona-Lasinio model is examined in different approximation schemes: an expansion in powers of 1/N_c and an expansion up to one-meson loop in the effective action formalism. It is explicitely proved that the Goldstone theorem as well as the Gell-Mann-Oakes-Renner relation hold within those schemes. The influence of meson-loop effects on the quark condensate, the pion mass, the pion decay constant and properties of rho- and sigma-meson are investigated. First we focus on the determination of a consistent set of parameters. In the 1/N_c expansion scheme it is possible to find a set of parameters which allows to simultaneously describe the quantities in the pion sector and those related to the rho-meson, whereas this turns out to be not possible within the expansion of the effective action. Besides, the relation of our model to hadronic models is discussed. In the last part of this thesis the behavior of the quark condensate at nonzero temperature is studied. In the low-temperature region agreement with the model independent chiral perturbation theory result in lowest order can be obtained. The perturbative 1/N_c expansion scheme does not allow for an examination of the chiral phase transition at higher temperatures, whereas this is possible within the meson-loop approximation scheme. A first order phase transition is found.