Inferring the breakdown scales of the chiral expansions for $g_A$ and $m_N$

TL;DR

This paper uses Bayesian inference to determine the energy scales at which chiral perturbation theory ceases to be valid for predicting the nucleon mass and axial-vector coupling, revealing different breakdown points for each observable.

Contribution

The study introduces a Bayesian method to infer the breakdown scales of chiral expansions for $g_A$ and $m_N$, providing quantitative estimates with uncertainty ranges.

Findings

Breakdown scale for $g_A$ is approximately 251 MeV.

Breakdown scale for $m_N$ is approximately 491 MeV.

Different observables have distinct chiral expansion validity ranges.

Abstract

We apply Bayesian inference to the order-by-order chiral perturbation theory ($\chi$PT) expansions for the axial-vector coupling constant $g_A$ and the nucleon mass m_N, and thereby infer the scales at which $\chi$PT breaks down for these two observables. Using a pointwise Bayesian analysis, we find that the inferred breakdown scales are notably different for the two observables. For the chiral expansion of $g_A$, we obtain $251^{+20}_{-50}$ MeV and $211^{+20}_{-30}$ MeV using two distinct sets of low-energy constants, while for the chiral expansion of $m_N$ we infer a significantly larger breakdown scale of $491^{+60}_{-90}$ MeV.