Baryons in the NJL model as solutions of the relativistic Faddeev equation

Abstract

Abstract The relativistic Faddeev equation for three quarks is solved in the SU(2) f × SU(3) c NJL model to get the nucleon and delta states. We truncate the interacting two-body channels to the scalar and axial vector diquark channels, which are expected to be dominant from the non-relativistic analogy. We find that both channels contribute attractively to the nucleon as well as the delta state, and that the principal mechanism for the mass spitting between the nucleon and the delta in this picture is the interaction in the scalar diquark channel, which is not present in the delta state. We show the dependences of the masses of the nucleon and the delta on the specific form of the interaction lagrangian, and derive restrictions on the possible forms of four-fermi interactions.