Baryon axial vector current in large-$N_c$ chiral perturbation theory: Complete analysis for $N_c=3$

TL;DR

This paper calculates the baryon axial vector current in large-$N_c$ chiral perturbation theory, including one-loop corrections, and compares it with traditional methods, achieving a good match and providing numerical predictions based on experimental data.

Contribution

It provides a comprehensive analysis of the baryon axial vector current in the large-$N_c$ limit, including all relevant one-loop corrections and a detailed comparison with conventional approaches for $N_c=3$.

Findings

Perfect agreement between large-$N_c$ and conventional chiral perturbation theory.

Successful numerical fit to experimental data.

Remarkable predictive power of the formalism.

Abstract

The baryon axial vector current is computed in heavy baryon chiral perturbation theory in the large-$N_c$ limit, where $N_c$ is the number of color charges. One-loop nonanalytic corrections of order $m_q \ln m_q$ are comprised in the analysis, with contributions of both intermediate octet and decuplet baryon states, to all orders in the $1/N_c$ expansion of the axial vector current relevant for $N_c=3$. Theoretical expressions are obtained in the limit of vanishing decuplet-octet mass difference only, which allows one to carry out a full comparison with conventional heavy baryon chiral perturbation theory results for three flavors of light quarks and at the physical value $N_c=3$. Both approaches perfectly agree to all orders considered. Furthermore, a numerical analysis via a least-squares fit is performed in order to extract the values of the free parameters of the theory, using the experimental data available. The predictions of formalism are remarkable.