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

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