The Goldberger-Treiman Discrepancy in SU(3)

TL;DR

This paper analyzes the Goldberger-Treiman discrepancy in SU(3) using heavy baryon chiral perturbation theory, showing that leading order discrepancy is due to counterterms and subleading corrections are suppressed, with small one-loop contributions.

Contribution

It demonstrates that the discrepancy is dominated by counterterms at leading order and provides a detailed calculation of subleading corrections within HBChPT, aligning with recent experimental analyses.

Findings

Discrepancy at leading order is from order p^3 counterterms.

Subleading corrections are suppressed and include meson loops.

Calculated one-loop contributions are small and consistent with experimental data.

Abstract

The Goldberger-Treiman discrepancy in SU(3) is analyzed in the framework of heavy baryon chiral perturbation theory (HBChPT). It is shown that the discrepancy at leading order is entirely given by counterterms from the order p^3 Lagrangian, and that the first subleading corrections are suppressed by two powers in the HBChPT expansion. These subleading corrections include meson-loop contributions as well as counterterms from the order p^5 Lagrangian. Some one-loop contributions are calculated and found to be small. Using the three discrepancies (pi-N-N, K-N-Lambda and K-N-Sigma) which can be extracted from existing experimental data, we find that the HBChPT calculation favors the smaller g(pi-N-N) values obtained in recent partial wave analyses.