Renormalization of the baryon axial vector current in large-$N_c$ chiral perturbation theory: Effects of the decuplet-octet mass difference and flavor symmetry breaking

The baryon axial vector current is computed at one-loop order in large-$N_c$ baryon chiral perturbation theory, where $N_c$ is the number of colors. Loop graphs with octet and decuplet intermediate states are systematically incorporated into the analysis and the effects of the decuplet-octet mass difference and SU(3) flavor symmetry breaking are accounted for. As expected, large-$N_c$ cancellations between different one-loop graphs are observed as a consequence of the large-$N_c$ spin-flavor symmetry of QCD baryons. Fitting our analytical formulas against experimental data on baryon semileptonic decays and the strong decays of decuplet baryons, a detailed numerical analysis regarding the determination of the basic parameters of large-$N_c$ baryon chiral perturbation theory as well as the extraction of the baryon axial vector couplings is performed. The large-$N_c$ baryon chiral perturbation theory predictions are in very good agreement both with the expectations from the $1/N_c$ expansion and with the experimental data.

Figure 1

One-loop corrections to the baryon axial vector current.