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

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.

arXiv comment12 pages, 4 figures, accepted to Phys. Lett. B

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• High-precision nuclear forces from chiral EFT: State-of-the-art, challenges and outlook
• Pairing properties of semilocal coordinate&momentum-space regularized chiral interactions
• Shell quenching in nuclear charge radii based on Monte Carlo dropout Bayesian neural network
• The one-pion-exchange potential with contact terms from lattice QCD simulations
• Properties of hyperons in nuclear matter from chiral hyperon-nucleon interactions at next-to-next-to-leading order