• DOI:10.1103/physrevc.107.014001
• Corpus ID: 249712178

Bayesian estimation of the low-energy constants up to fourth order in the nucleon-nucleon sector of chiral effective field theory

@article{Svensson2022BayesianEO,
  title={Bayesian estimation of the low-energy constants up to fourth order in the nucleon-nucleon sector of chiral effective field theory},
  author={Isak Svensson and Andreas Ekstr{\"o}m and Christian Forss'en},
  journal={Physical Review C},
  year={2022}
}

• Isak Svensson, A. Ekström, C. Forss'en
• Published 16 June 2022
• Physics
• Physical Review C

We use Bayesian methods and Hamiltonian Monte Carlo (HMC) sampling to infer the posterior probability density (PDF) for the low-energy constants (LECs) up to next-to-next-to-next-to-leading order (N3LO) in a chiral effective field theory ( χ EFT) description of the nucleon-nucleon interaction. In a first step, we condition the inference on neutron-proton and proton-proton scattering data and account for uncorrelated χ EFT truncation errors. We demonstrate how to successfully sample the 31-dimensional space of LECs at N3LO using a revised HMC inference protocol. In a second step we extend the analysis by means of importance sampling and an empirical determination of the neutron-neutron scattering length to infer the posterior PDF for the leading charge-dependent contact LEC in the 1 S 0 neutron-neutron interaction channel. While doing so we account for the χ EFT truncation error via a conjugate prior. We use the resulting posterior PDF to sample the posterior predictive distributions for the effective range parameters in the 1 S 0 wave as well as the strengths of charge-symmetry breaking and charge-independence breaking. We conclude that empirical point-estimate results of isospin breaking in the 1 S 0 channel are consistent with the PDFs obtained in our Bayesian analysis and that, when accounting for χ EFT truncation errors, one must go to next-to-next-to-leading order to confidently detect isospin breaking effects.