## Arts & Sciences Electronic Theses and Dissertations

Spring 5-15-2018

#### Author's School

Graduate School of Arts and Sciences

Physics

#### Degree Name

Doctor of Philosophy (PhD)

Dissertation

#### Abstract

The interactions of quarks and gluons form most of the visible matter around us. Yet, extracting precise predictions from the field theory describing them, Quantum Chromodynamics (QCD), is notoriously difficult. By simulating the QCD interaction on a Euclidean space time lattice, the field theory can be regularized non-perturbatively and familiar statistical techniques from classical statistical mechanics can be applied. Then, by systematically improving each component of the process, high precision results can be obtained. Some of the possible components to be improved include the discretization of the continuum action, the determination of the lattice scale(s), the generation of gauge field ensembles, and the interpolations to physical quark masses.

This work focuses on two primary analyses. Both start from the MILC collaboration's gauge field ensembles with $N_f=2+1+1$ flavors of highly improved staggered quarks (HISQ). The first analysis focuses on high precision scale setting. Gradient flow is used to smooth the gauge configurations and determine the relative lattice spacings for continuum extrapolations. The relative scale is set through two theoretically motivated observables, $\sqrt{t_0}$ and $w_0$. The continuum value and mass dependence for each of these scales is extracted to aid with future scale setting. With the lattice spacing set, the second analysis uses staggered chiral perturbation theory to fit lattice data for pseudoscalar meson masses and decay constants. This allows simultaneous interpolation of results to physical quark masses and control of discretization artifacts introduced by the staggered formalism. After extrapolation of the results to the continuum, preliminary results for the pion and kaon decay constants and light quark masses are obtained.

English (en)

Claude Bernard

#### Committee Members

Michael Ogilvie, Bhupal Dev, Renato Feres, Demetrios Sarantites,