High precision quark mass determinations and studies of meson properties using lattice QCD

Strongly interacting systems such as the internal dynamics of the myriad bound states seen in particle physics experiments are notoriously difficult to obtain a precise quantitative theoretical description of. Without systematically improvable methods of analysis of such system a vast region of particle physics phenomenology is left without proper confrontation with theory and systematic uncertainties arising from knowledge of fundamental particle physics parameters in the strong sector are difficult to control. Lattice quantum chromodynamics (QCD) has arisen as a methodological solution to the calculational difficulties raised by the theory of the strong interaction. The main testing ground for high precision calculations utilised here is the properties of the two lowest lying states of the chamronium spectrum, the $\eta_c$ and the $J/\psi$. Certain properties of these mesons are experimentally determined to high precision which makes them good targets for high precision lattice QCD calculations. At this level of precision it becomes necessary to include at least leading order electromagnetic corrections. This is addressed in this thesis with the inclusion of quenched QED in the study of charmonium properties. In various calculations renormalisation factors need to be computed to high precision. The technique of nonperturbatively computing renormalisation factors in a momentum subtraction scheme on the lattice provides a computationally cheap method for the determination of these factors and is examined using the Highly Improved Staggered Quark (HISQ) action. The charmonium calculations are then extended to higher masses leading up to the $b$ quark mass allowing for comparisons with experimental results. It is demonstrated that this method offers a way to improve on the precision of previous lattice calculations that used nonrelativistic quark actions. Finally, sub-percent determinations of the strange and charm quark masses are presented, making use of nonperturbatively determined mass renormalisation factors. These are shown to agree, at this high level of precision, with other lattice calculations that use different methodologies, indicating that the systematic uncertainties are appropriately controlled