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

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 $251_{-50}^{+20}$ MeV and $211_{-30}^{+20}$ 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 $491_{-90}^{+60}$ MeV.