Bayesian analysis of nucleon-nucleon scattering data in pionless effective field theory

TL;DR

This paper uses Bayesian methods to calibrate low-energy constants in pionless EFT for nucleon-nucleon scattering, providing quantitative estimates of the EFT breakdown scale and highlighting inconsistencies in naive dimensional analysis.

Contribution

It introduces a Bayesian calibration framework for pionless EFT, estimating low-energy constants and EFT breakdown scale while accounting for truncation uncertainties.

Findings

Estimated EFT breakdown scale at NLO and N3LO

Identified inconsistencies in naive dimensional analysis

Provided Bayesian uncertainty quantification for LECs

Abstract

We perform Bayesian model calibration of two-nucleon ($NN$) low-energy constants (LECs) appearing in an $NN$ interaction based on pionless effective field theory (EFT). The calibration is carried out for potentials constructed using naive dimensional analysis in $NN$ relative momenta ($p$) up to next-to-leading order [NLO, $O(p^2)$] and next-to-next-to-next-to-leading order [N3LO, $O(p^4)$]. We consider two classes of pionless EFT potential: one that acts in all partial waves and another that is dominated by $s$-wave physics. The two classes produce broadly similar results for calibrations to $NN$ data up to $E_{\rm lab}=5$ MeV. Our analysis accounts for the correlated uncertainties that arise from the truncation of the pionless EFT. We simultaneously estimate both the EFT LECs and the parameters that quantify the truncation error. This permits the first quantitative estimates of the pionless EFT breakdown scale, $\Lambda_b$: the 95% intervals are $\Lambda_b \in [50.11,63.03]$ MeV at NLO and $\Lambda_b \in [72.27, 88.54]$ MeV at N3LO. Invoking naive dimensional analysis for the $NN$ potential, therefore, does not lead to consistent results across orders in pionless EFT. This exemplifies the possible use of Bayesian tools to identify inconsistencies in a proposed EFT power counting.