Title: Precision Light Flavor Physics from Lattice QCD
Description: In this thesis we present three distinct contributions to the study of light flavor physics using the techniques of lattice QCD. These results are arranged into four self-contained papers. The first two papers concern global fits of the quark mass, lattice spacing, and finite volume dependence of the pseudoscalar meson masses and decay constants, computed in a series of lattice QCD simulations, to partially quenched SU(2) and SU(3) chiral perturbation theory (χPT). These fits determine a subset of the low energy constants of chiral perturbation theory — in some cases with increased precision, and in other cases for the first time — which, once determined, can be used to compute other observables and amplitudes in χPT. We also use our formalism to self-consistently probe the behavior of the (asymptotic) chiral expansion as a function of the quark masses by repeating the fits with different subsets of the data. The third paper concerns the first lattice QCD calculation of the semileptonic K0 → π −` +ν` (K`3) form factor at vanishing momentum transfer, f Kπ + (0), with physical mass domain wall quarks.

The value of this form factor can be combined with a Standard Model analysis of the experimentally measured K0 → π −` +ν` decay rate to extract a precise value of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vus, and to test unitarity of the CKM matrix. We also discuss lattice calculations of the pion and kaon decay constants, which can be used to extract Vud through an analogous Standard Model analysis of experimental constraints on leptonic pion and kaon decays. The final paper explores the recently proposed exact one flavor algorithm (EOFA). This algorithm has been shown to drastically reduce the memory footprint required to simulate single quark flavors on the lattice relative to the widely used rational hybrid Monte Carlo (RHMC) algorithm, while also offering modest O(20%) speed-ups. We independently derive the exact one flavor action, explore its equivalence to the RHMC action, and demonstrate that additional preconditioning techniques can be used to significantly accelerate EOFA simulations.

We apply EOFA to the ongoing RBC/UKQCD calculation of the ∆I = 1/2 K → ππ decay amplitude, and demonstrate that, in this context, gauge field configurations can be generated a factor of 4.2 times faster using an EOFAbased simulation rather than the previous RHMC-based simulations. We expect that EOFA will help to significantly reduce the statistical error in the first-principles determination of the Standard Model CP-violation parameters ε and ε′ offered by the K → ππ calculation.