Bayesian analysis of chiral effective field theory at leading order in a modified Weinberg power counting approach
Oliver Thim, Eleanor May, A. Ekström, C. Forssén
Abstract
We present a Bayesian analysis of renormalization-group invariant nucleon-nucleon interactions at leading order in chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$) with momentum cutoffs in the range 400--4000 MeV. We use history matching to identify relevant regions in the parameter space of low-energy constants (LECs) and subsequently infer the posterior probability density of their values using Markov chain Monte Carlo. All posteriors are conditioned on experimental data for neutron-proton scattering observables and we estimate the $\ensuremath{\chi}\mathrm{EFT}$ truncation error in an uncorrelated limit. We do not detect any significant cutoff dependence in the posterior predictive distributions for two-nucleon observables. For all cutoff values we find a multimodal LEC posterior with an insignificant mode harboring a bound $^{1}S_{0}$ state. The $^{3}P_{0}$ and $^{3}P_{2}$ phase shifts emerging from the Bayesian analysis are less constrained and typically more repulsive compared to the results of a phase shift optimization. We expect that our inference will impact predictions for nuclei. This work demonstrates how to perform inference in the presence of limit-cycle-like behavior and spurious bound states, and lays the foundation for a Bayesian analysis of renormalization-group invariant $\ensuremath{\chi}\mathrm{EFT}$ interactions beyond leading order.