Quantifying the breakdown scale of pionless effective field theory

TL;DR

This paper uses Bayesian methods to estimate the energy scale at which pionless effective field theory ceases to be valid, confirming the pion mass as a key low-energy scale in nuclear physics.

Contribution

It provides a Bayesian inference of the pionless EFT breakdown scale using neutron-proton scattering data at NNLO, with a focus on standard power counting and renormalization schemes.

Findings

Median breakdown scale around 1.4 times the pion mass

68% credible interval for breakdown scale is [0.96, 1.69] times the pion mass

Results support the canonical role of the pion mass as a relevant low-energy scale

Abstract

We use Bayesian statistics to infer the breakdown scale of pionless effective field theory in its standard power counting and with renormalization of observables carried out using the power-divergence subtraction scheme and cutoff regularization. We condition our inference on predictions of the total neutron-proton scattering cross section up next-to-next-to leading order. We quantify a median breakdown scale of approximately 1.4$m_\pi$. The 68% degree of belief interval is $[0.96,1.69]m_\pi$. This result confirms the canonical expectation that the pion mass is a relevant scale in low-energy nuclear physics.