Study Of η- η′ Mixing Within The Framework Of U(3) Chiral Effective Field Theory

Chiral Perturbation Theory(XPT) is a reliable tool to study the low energy dynamics of QCD and it is based on the global symmetry of QCD. As a consequence, the results from xPT are automatically consistent with the symmetries dictated by QCD, such as C, P and chiral symmetries. The degrees of freedom of xPT are not quarks and gluons, but relevant hadrons observed in experiments.In this thesis, we focus on the η-η’ mixing in the framework of U(3) xPT. A general treatment to address the η-η’ mixing, including the higher-derivative, mass and kinematic mixing terms is provided in detail. The connections between the four mixing parameters (F0, F8,θ0,θ8) in the two-mixing-angle scheme and the low energy constants in the U(3) chiral effective theory are provided both in the singlet-octet and the quark-flavor bases. In addition, we also fit other physical quantities, which include the masses of η and η’, the decay constants of K and π mesons, the masses of K meson and the ratio of quark mass ms/m. We consider in the fits the lattice simulation and experimental data and the phenomenological inputs. The quark-mass dependences of mη, mη’ and mk are found to be well described at next-to-leading order. Nevertheless, in order to simultaneously describe the lattice and experimental data and phenomenological determinations for the light pseudoscalars π, K, ηand η’, we find that the contribution of next-to-next-to-leading order is important. Our determinations of the chiral low energy constants are found to be compatible with the previous works within the uncertainty. Thus we conclude that our theoretical formulas can provide a reasonable and reliable chiral extrapolation form for lattice simulations.