Higher baryon and winding numbers in the Nambu-Jona-Lasinio model

Abstract

A bosonized version of the SU(2) Nambu-Jona-Lasinio model is solved self-consistently for hedgehog fields on the chiral circle in the solitonic sector with baryon number B=2. The authors consider explicitly the case in which the baryon number is raised by occupying B-bound valence quark states for different winding numbers omega of the chiral angle. It is found that only the cases B>or= omega allow the existence of self-consistent solutions. Fractional windings are also excluded in practice by the self-consistency condition. For the description of nucleon properties the constituent mass has to be chosen around 400 MeV. There no solitons with higher winding numbers are found in contrast to the results of the Skyrme model. On the other hand, in this region the binding energy of the deuteron and the alpha -particle can be roughly reproduced with winding number one.