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

The baryon axial vector current is computed at one-loop order in heavy baryon chiral perturbation theory in the large-$N_c$ limit, where $N_c$ is the number of colors. Loop graphs with octet and decuplet intermediate states cancel to various orders in $N_c$ as a consequence of the large-$N_c$ spin-flavor symmetry of QCD baryons. These cancellations are explicitly shown for the general case of $N_f$ flavors of light quarks. In particular, a new generic cancellation is identified in the renormalization of the baryon axial vector current at one-loop order. A comparison with conventional heavy baryon chiral perturbation theory is performed at the physical values $N_c=3$, $N_f=3$.

Figure 1

One-loop corrections to the baryon axial vector current.

Figure 2

One-loop wave function renormalization graph.