Bayesian Analysis of $\chi$EFT at Leading Order in a Modified Weinberg Power Counting Approach

Abstract

We present a Bayesian analysis of renormalization-group invariant nucleon-nucleon interactions at leading order in chiral effective field theory ($\chi$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 $\chi$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 $\chi$EFT interactions beyond leading order.

20 pages, 16 figures

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• A further study on the renormalization group aspect of perturbative corrections
• Low-energy theorems for neutron-proton scattering in $\chi$EFT using a perturbative power counting
• Reexamining the perturbative renormalizability of the coupled triplets
• Feasibility of perturbative generation of bound-states from resonances or virtual states
• Perturbative $\chi$EFT calculations of the deuteron and triton up to N${}^2$LO
• Meson-baryon scattering lengths without annihilation diagrams to order $p^4$ in heavy baryon chiral perturbation theory