Sarah Wesolowski

Ohio State University

Bayesian truncation errors in chiral effective field theory

Properly constructed effective field theories hold the promise of model independence and order-by-order convergence of observable calculations. We have entered an era in low-energy nuclear physics where many-body methods are precise enough that we are sensitive to uncertainties in nuclear interactions. The predictable order-by-order improvement of EFT calculations means that systematic uncertainties from the interaction itself can in principle be estimated. Using Bayesian methods, we have developed a procedure to estimate truncation errors in EFT predictions as part of a larger program to fully quantify EFT uncertainties. The statistical model yields posterior probability distribution functions (pdfs) for these errors based on expectations of naturalness encoded in Bayesian priors and the observed order-by-order convergence pattern of the EFT. As a general example, we apply this method to the semi-local potentials of Epelbaum, Krebs, and Mei├čner (EKM) for a set of regulator parameters, energies, and NN observables. The Bayesian approach allows for statistical validations of the assumptions and enables the calculation of posterior pdfs for the EFT breakdown scale. The statistical model is validated when convergence behavior is not distorted by regulator artifacts.

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