Goldberger-Treiman relation and chiral-symmetry breaking

We review the dispersion-theory calculation of the Goldberger-Treiman discrepancy $\Delta \equiv 1-\frac{m{g}_A}{f_{\pi }g}$. Our estimate is still some way from the experimental value. The latter and its SU(3) counterparts can be used to determine the chiral-symmetry-breaking parameter $c$ appearing in the $(3, \overline{3})+(\overline{3}, 3)$ Hamiltonian $u_0+c{u}_8$. We find $c\approx -1\mathrm{}$ in agreement with its determination from phenomenological $\sigma$ terms.