Renormalization of the baryon axial vector current in large-Ncchiral perturbation theory

Abstract

The baryon axial vector current is computed at one-loop order in heavy baryon chiral perturbation theory in the large-Nc limit, where Nc is the number of colors. Loop graphs with octet and decuplet intermediate states cancel to various orders in Nc as a consequence of the large-Nc 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 Nc = 3, N f = 3.

Baryon vector current in the chiral and1/Ncexpansions

“…Among the most relevant QCD operators studied in the 1/N c expansion are the Hamiltonian (baryon masses) [25,27], axial [6,7,10,23,28] and vector [29] currents and magnetic moments [8,9,28].…”

“…The low energy constants m 0,1 2 ,g A , C HF , and c 1 are O (N 0 c ). As defined here, and at lowest order, the leading order axial couplingg A (to be later denotation by a 1 ) is related to the one of the nucleon at N c = 3 byg A = 6 5 g A , where g A = 1.27 is the well known nucleon axial coupling.…”

“…(5) and (6). In the rest frame of the decaying baryon, the dominant contribution to the matrix elements of the vector current is the corresponding charge term given by f 1 , which is O (p 0 × N 0 c ).…”

“…[6,7] within these two scenarios was limited to determining only g 1 and g, because the f 1 's were given at their SU(3) symmetric values, f SU (3) 1 , in view of the AG theorem. The present analysis, however, is uniquely positioned in the sense that, on the same footing as g 1 , the one-loop corrections to f 1 within large-N c chiral perturbation theory have been computed, including the effects of a non-zero baryon decuplet-octet mass splitting.…”

“…At a more detailed level, the q 2 −dependence of the leading form factors can be parametrized in a dipole form whereas the q 2 −dependence of f 2 and g 2 can be neglected due to the q factor already present in the matrix elements (5) and (6).…”