Uncertainty Quantifications in Chiral Effective Field Theory

Sammanfattning: The nuclear force is a residual interaction between bound states of quarks and gluons. The most fundamentaldescription 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 unknowncoupling 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-protoninteractions 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 bindingenergies 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.