Bayesian truncation errors in equations of state of nuclear matter with chiral nucleon-nucleon potentials

TL;DR

This paper applies Bayesian analysis to quantify and analyze truncation errors in equations of state of nuclear matter derived from chiral nucleon-nucleon potentials, demonstrating good convergence and consistency with previous error estimates.

Contribution

It introduces a Bayesian framework to evaluate truncation errors in nuclear matter EOSs from chiral potentials, providing a systematic uncertainty quantification method.

Findings

Truncation errors show good order-by-order convergence.

Bayesian credible intervals align with previous simple error estimates.

Breakdown scale values are validated through success rate analyses.

Abstract

The truncation errors in equations of state (EOSs) of nuclear matter derived from the chiral nucleon-nucleon ($NN$) potentials at different expansion orders are analyzed by a Bayesian model. These EOSs are expanded as functions of a dimensionless parameter, $Q$, which is determined by Fermi momentum, $k_F$ and breakdown scale, $\Lambda_b$. The degree-of-belief (DoB) intervals predicted by the chiral effective field theory are calculated within the corresponding expansion coefficients and the specific prior probability distribution functions in terms of Bayes theorem. The truncation errors of EOSs, generated by the DoB intervals, exhibit good order-by-order convergences with different chiral expansion order potentials. When DoB is considered as $1\sigma$ credibility, i.e., $68.27\%$ confidence interval, the truncation errors of binding energy per nucleon in symmetric nuclear matter and pure neutron matter are consistent with the results given by a simple error analysis method proposed by Epelbaum, {\it et al.} Finally, the reasonable values of the breakdown scale $\Lambda_b$ in nuclear matter are discussed through consistency checks of Bayesian method based on the calculations of success rate.