Anisotropic discretisations and practical all-to-all propagators for lattice QCD

Abstract

In this thesis, we concern ourselves primarily with improving the accuracy of the determination of correlation functions in lattice QCD. We detail two avenues of improvement and implement them both, separately and in combination. Firstly, we formulate an improved anisotropic action which is classically correct to O(a3s,a2t). The employment of an anisotropic lattice introduces the anisotropy ratio, ξ = as/at, which we tune non-perturbatively. In a quenched lattice simulation, we find that the mass dependence of the tuning of this parameter is weak, and a single tuning suffices for a range of quark masses from the strange quark mass to well above charm quark mass. The primary benefit of an anisotropic action is that it allows us an increased number of lattice sites in the temporal direction with which to study the exponential decay of correlation functions.