Uncertainty Quantifications in Chiral Effective Field Theory
Ladda ner
Typ
Examensarbete för kandidatexamen
Bachelor Thesis
Bachelor Thesis
Program
Engineering Physics (300 hp)
Publicerad
2014
Författare
Fahlin Strömberg, Dag
Lindby, Mattias
Lilja, Oskar
Mattsson, Björn
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
The nuclear force is a residual interaction between bound states of quarks and gluons. The most fundamental description of the underlying strong interaction is given by quantum chromodynamics (QCD)that becomes nonperturbative at low energies. A description of low-energy nuclear physics from QCD is currently not feasible. Instead, one can employ the inherent separation of scales between low- and high-energy phenomena, and construct a chiral effective field theory (EFT). The chiral EFT contains unknown coupling coefficients, that absorb unresolved short-distance physics, and that can be constrained by a non-linear least-square fitting of theoretical observables to data from scattering experiments. In this thesis the uncertainties of the coupling coefficients are calculated from the Hessian of the goodness-of-fit measure X2. The Hessian is computed by implementing automatic differentiation (AD)in an already existing computer model, with the help of the Rapsodia AD tool. Only neutron-proton interactions are investigated, and the chiral EFT is studied for leading-order (LO) and next-to-leadingorder (NLO). In addition, the correlations between the coupling coefficients are calculated, and the statistical uncertainties are propagated to the ground state energy of the deuteron. At LO, the relative uncertainties of the coupling coefficients are 0.01%, whereas most of the corresponding uncertainties at NLO are 1%. For the deuteron, the relative uncertainties in the binding energies are 0.2% and 0.5% for LO and NLO, respectively. Moreover, there seems to be no obvious obstacles that prevent the extension of this method to include the proton-proton interaction as well as higher chiral orders of the chiral EFT, e.g. NNLO. Finally, the propagation of uncertainties to heavier many-body systems is a possible further application.
Beskrivning
Ämne/nyckelord
Grundläggande vetenskaper , Fysik , Kärnfysik , Lågenergifysik , Basic Sciences , Physical Sciences , Nuclear physics , Low energy physics