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

Journal article, 2025

We perform Bayesian model calibration of two-nucleon (NN) low-energy constants (LECs) appearing in an NN interaction based on pionless effective field theory (πEFT). 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(p2)] and next-to-next-to-next-to-leading order [N3LO,O(p4)]. We consider two classes of πEFT 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 Elab=5 MeV. Our analysis accounts for the correlated uncertainties that arise from the truncation of the πEFT. We simultaneously estimate both the EFT LECs and the parameters that quantify the truncation error. This permits quantitative estimates of the πEFT breakdown scale, Λb: the 95% intervals are Λb [50.11,63.03] MeV at NLO and Λb [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 πEFT. This exemplifies the possible use of Bayesian tools to identify inconsistencies in a proposed EFT power counting.