Applications of chiral perturbation theory to lattice quantum chromodynamics

Abstract

In this dissertation, we calculate hadronic observables through the application of chiral perturbation theory to lattice quantum chromodynamics. Quantum chromodynamics is the quantum field theory for the strong interaction which, in the low-energy regime, becomes non-perturbative. The lattice acts as a regulator for the theory and allows us to make predictions at low-energy even without a perturbative expansion. However, since these lattice calculations require non-zero lattice spacing and often assume light quark masses much greater than those provided by Nature, calculating observables requires us to extrapolate the results from multiple lattice ensembles to the physical, continuum limit. We perform these extrapolations using chiral perturbation theory, an effective field theory for quantum chromodynamics in which the degrees of freedom are the pseudo-Goldstone bosons emerging from the explicit, spontaneous breaking of chiral symmetry. We concentrate particularly on determining the gradient flow scales $w_0$ and $t_0$, which allow us to set the scale of our lattice; the ratio of the pseudoscalar decay constants $F_K/F_\pi$, from which we determine the ratio of the Cabibbo-Kobayashi-Maskawa matrix elements $|V_{us}|/|V_{ud}|$; the masses of the cascades, as a precursor to a lattice determination of the hyperon transition matrix elements; and finally the nucleon sigma term, which has implications for the cross section of the neutralino in the minimal supersymmetric Standard Model.Doctor of Philosoph