Structure of largeNccancellations in baryon chiral perturbation theory

Abstract

We show how to compute loop graphs in heavy baryon chiral perturbation theory including the full functional dependence on the ratio of the Delta-nucleon mass difference to the pion mass, while at the same time automatically incorporating the 1/N c cancellations that follow from the large-N c spin-flavor symmetry of baryons in QCD. The one-loop renormalization of the baryon axial vector current is studied to demonstrate the procedure. A new cancellation is identified in the one-loop contribution to the baryon axial vector current. We show that loop corrections to the axial vector currents are exceptionally sensitive to deviations of the ratios of baryon-pion axial couplings from SU (6) values.

Baryon vector current in the chiral and1/Ncexpansions

“…[31]; here that result is extended to the baryon vector current taking advantage of the fact that both currents transform as flavor octets so one can reach the very same conclusions in the discussion presented in Ref. [31].…”

“…Now, the correction arising from the Feynman diagram displayed in Fig. 1(b) is given in terms of the derivatives of the basic loop integral [31] …”

“…In the baryon rest frame, the combined HBChPT and 1/N c expansion effective Lagrangian at lowest order is given by [5,10,31]:…”

Effective theory of theΔ(1232)resonance in Compton scattering off the nucleon

“…At the same time (22) allows us to extend χPT to the Delta region. In developing our power counting below, we will often keep the dependence of amplitudes on m π and ∆ explicit, so that the behavior of the amplitudes in the (independent) chiral (m π → 0) or the large-N c (∆ → 0) limits is manifest [33]. Nevertheless, for the purposes of assigning an overall size to the amplitude arising from a particular graph or set of graphs we would like to have one expansion parameter:…”

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

“…In Ref. [16] the general structure of the various large-N c cancellations was analyzed. In particular, a new large-N c cancellation was identified.…”