Bootstrapping Two-Nucleon Effective Field Theories

TL;DR

This paper compares two regularization methods in chiral effective field theory for two-nucleon interactions, using a toy model and bootstrap techniques to evaluate their consistency and validity range.

Contribution

It introduces a comparative analysis of renormalization approaches in chiral EFT using a toy model and bootstrap, highlighting the improved validity at NLO.

Findings

NLO potential extends the energy range of validity.

Bootstrap confirms statistical consistency of approaches.

Comparison with Granada phase-shift analysis supports findings.

Abstract

Chiral EFT yields singular potentials that require regularization and renormalization when implemented in a dynamical equation such as the Lippmann--Schwinger equation. We employ two different approaches, renormalization with contact terms -- as is most commonly done in chiral EFT -- and the exact N/D method with multiple subtractions. We start with a toy model in which we can control the finite-range expansion of the potential, treating the full potential as the `exact' theory. To assess the statistical consistency of the approaches with the full theory, we use the bootstrap technique. We apply the same framework to study the consistency of chiral EFT at LO and NLO with the Granada phase-shift analysis in the $^1S_0$ two-nucleon partial wave. Our results show that the NLO potential significantly extends the energy range over which the theory remains valid.