$1/N_C$ Corrections to $g_A$ in the Light of PCAC$

Abstract

We comment on recently discovered $1/N_C$ corrections to the ` nucleon axial current in the framework of the Nambu--Jona-Lasinio soliton. This kind of corrections arises only for a special treatment of ordering ambiguities of collective coordinates and operators in the semiclassical quantization. In addition to the missing derivation of this special quantization scheme from first principles its na\"ıve application violates partial conservation of the axial current (PCAC). We show how within this scheme PCAC can be restored and determine the corresponding $1/N_C$ corrections to the equation of motion for the chiral soliton. The resulting self-consistent solution allows to evaluate the nucleon axial coupling constant $g_A$ directly as a matrix element of the axial current as well as indirectly from the pion profile function. Enhancement is found for those baryon properties which are sensitive to the long range behavior of the pion profile.