Extended linear sigma model in higher order mesonic interactions

The Gell-Mann and Levy model, as well as the Birse and Banerjee model, describe quark interactions via the exchange of σ and π-mesons. We extend these models to include higher order mesonic interactions. The field equations were solved in the mean-field approximation and good agreement with the data for nucleon properties was obtained. Our agreement is better than that obtained by the original model of Birse and Banerjee and by other models. This indicates the importance of including higher order meson correlations.