Extending the reach of uncertainty quantification in nuclear theory

Doctoral thesis, 2023

The theory of the strong interaction—quantum chromodynamics (QCD)—is unsuited to practical calculations of nuclear observables and approximate models for nuclear interaction potentials are required. In contrast to phenomenological models, chiral effective field theories (χEFTs) of QCD grant a handle on the theoretical uncertainty arising from the truncation of the chiral expansion. Uncertainties in χEFT are preferably quantified using Bayesian inference, but quantifying reliable posterior predictive distributions for nuclear observables presents several challenges. First, χEFT is parametrized by unknown low-energy constants (LECs) whose values must be inferred from low-energy data of nuclear structure and reaction observables. There are 31 LECs at fourth order in Weinberg power counting, leading to a high-dimensional inference problem which I approach by developing an advanced sampling protocol using Hamiltonian Monte Carlo (HMC). This allows me to quantify LEC posteriors up to and including fourth chiral order. Second, the χEFT truncation error is correlated across independent variables such as scattering energies and angles; I model correlations using a Gaussian process. Third, the computational cost of computing few- and many-nucleon observables typically precludes their direct use in Bayesian parameter estimation as each observable must be computed in excess of 100,000 times during HMC sampling. The one exception is nucleon-nucleon scattering observables, but even these incur a substantial computational cost in the present applications. I sidestep such issues using eigenvector-continuation emulators, which accurately mimic exact calculations while dramatically reducing the computational cost. Equipped with Bayesian posteriors for the LECs, and a model for the truncation error, I explore the predictive ability of χEFT, presenting the results as the probability distributions they always were.