Goldberger–Treiman relation and gπNN from the three quark BS/Faddeev approach in the NJL model Original Research Article

A systematic evaluation method of matrix elements of quantum one-body operators between nucleon states in the three-quark Bethe–Salpeter(3qBS)/Faddeev approach in the NJL model is reviewed. We do not confine ourselves to a particular truncation scheme of the 3qBS kernel. One of our main aims is to derive a general condition to be imposed on a given BS kernel in order that the PCAC relation is satisfied correctly. We apply this condition to some particular 3qBS kernels. We numerically calculate View the MathML source in the 3qBS/Faddeev approach to estimate the violation of the Goldberger–Treiman/PCAC relation due to the UV-regularization scheme. We finally consider the nonvanishing current quark mass effects on the Goldberger–Treiman relation.