Quark-Quark Correlations in the Nucleon in a Generalized Nambu-Jona-Lasinio Model

Abstract

We present a relativistic model of the nucleon based upon a quark-diquark structure that emerges from a study of the Nambu-Jona-Lasinio model. Similar calculations, made by other authors, have been carried out after a Wick rotation is performed. These previous calculations have neglected confinement; therefore, the masses of the quarks and diquarks had to be adjusted so that the diquarks and the nucleon were stable, in which case the Wick rotation may be made. In our work, we include a momentum-space model of confinement developed earlier and we are therefore able to carry out the calculation in Minkowski space, after making a number of approximations. We determine the relative admixture of a scalar-isoscalar diquark and an axialvector-isovector diquark dynamically and find that an approximately equal admixture provides a reasonable fit to the nucleon magnetic moments. While the original problem (without approximation) requires the specification of eight scalar functions of two variables, our various approximations allow us to calculate several functions of a single variable. We find that only two of these functions are important. Therefore, we can exhibit a relatively simple relativistic wave function of the nucleon expressed in terms of two wave functions describing the relative motion of the quarks and diquarks.