Bayesian History Matching of Chiral Effective Field Theory in the Two-Nucleon Sector
Examensarbete för masterexamen
The accurate calculation of nucleon-nucleon scattering observables from first principles is an ongoing challenge within nuclear physics. Working within the framework of chiral effective field theory provides a method for calculating such observables. This is achieved through the construction of an effective Lagrangian that maintains the symmetries of quantum chromodynamics (QCD). In this thesis, truncation of the Lagrangian is performed using a modified Weinberg power counting, introducing a set of unknown low-energy constants at each order in the chiral expansion. Bayesian history matching is used to explore the leading order description of the nucleon-nucleon system. This is achieved through the iterative reduction of the four-dimensional parameter space, taking a Bayes linear approach. The history matching implementation is validated on the nuclear liquid drop model. Several novel methods of sampling are introduced within the implementation with the purpose of capturing correlations between parameters; The generation of ellipsoidal distributed samples is shown to be the most successful. History matching is subsequently applied to the proton-neutron scattering problem. We identify the subset of parameter space containing all low-energy constants that produce model outputs consistent with experimental two-nucleon scattering data, accounting for relevant sources of uncertainty. Non-implausible parameter volumes are obtained across a range of momentum regulator cutoffs. A set of non-implausible samples are used to predict the deuteron binding energy. Results indicate that the inclusion of this observable within the history match could further constrain the volumes. The analysis performed in this thesis was successful in producing sets of nonimplausible samples. Such sets can be subsequently used as a starting point for a full Bayesian analysis, with the aim of producing posterior probability distributions of the parameters. For example, the samples can be used to initialise walkers within the Markov Chain Monte Carlo method.
global parameter search , computer models , history matching , nuclear physics , liquid drop model , nucleon-nucleon scattering , chiral effective field theory , modified Weinberg power counting , emulators