Universality of the baryon axial vector current operator in large-$N_c$ chiral perturbation theory

Abstract: The baryon axial vector current is computed in a combined formalism in $1/N_c$ and chiral corrections. Flavor $SU(3)$ symmetry breaking is accounted for in two ways: Implicitly through the integrals occurring in the one-loop graphs and explicitly through perturbative symmetry breaking. Loop integrals can be expanded in a power series in the ratio of the decuplet-octet baryon mass difference to the pseudoscalar meson mass and the first three terms in the series are retained and evaluated. The universal baryon axial vector current so constructed is neither diagonal nor off-diagonal in the sense that it can connect baryon states of either different or equal spins to obtain appropriate axial vector couplings. Processes of interest are found in octet-baryon and decuplet-baryon semileptonic decays and strong decays of decuplet baryons. A fit to the available experimental information is performed to determine the free parameters in the formalism, which allows one to estimate, for instance, the leading axial vector coupling in the semileptonic decay $\Omega^- \to{\Xi^*}^0\ell^-\overline{\nu}_\ell$.