The breakdown scale of pionless effective field theory in the three-nucleon sector

TL;DR

This paper predicts neutron-deuteron cross sections using pionless effective field theory and employs Bayesian analysis to estimate the theory's breakdown scale, finding it near the pion mass, consistent with theoretical expectations.

Contribution

It provides the first Bayesian inference of the breakdown scale of pionless EFT in the three-nucleon sector using order-by-order predictions.

Findings

Breakdown scale near 100 MeV

Bayesian posterior peaks near pion mass

Consistent with pionless EFT expectations

Abstract

We make order-by-order predictions of neutron-deuteron total cross sections up to next-to-next-to-leading order in pionless effective field theory. Using Bayesian methods, we infer a posterior distribution for the breakdown scale. The result shows a mode near 100 MeV, and a combined analysis with neutron-proton scattering further sharpens the inference, placing the mode close to the pion mass scale, consistent with the expected range of pionless effective field theory.