| In order for Wilson fermions to be a competitive option to use in lattice QCD (LQCD) simulations, the large inherent discretization errors starting at O(a) (a being the lattice spacing) have to be removed. This can be accomplished through the Symanizk improvement program, where improvement terms have to be added to both the action and the operators of interest with coefficients appropriately chosen so that the rate of convergence to the continuum limit is quadratic in a. For this to be applicable to numerical simulations, improvement coefficients have to be determined non-perturbatively. A program for doing so has been pioneered by the Alpha collaboration. In this work, an extension of that program is made to improve all bilinear operators in QCD with two, three, and four flavours of non-degenerate quarks.; With even numbers of quark flavours, an alternative approach is afforded by twisted mass LQCD (tmLQCD), where O(a) improvement in physical quantities can be achieved automatically at maximal twist. In this work, the features and utilities of tmLQCD are studied in detail in the framework of chiral perturbation theory (chiPT). By matching onto an effective chiral theory, the phase structure of tmLQCD and the properties of the mesons (pions) in the theory has been investigated. Pionic quantities easy to calculate in numerical simulations and useful for probing the symmetry breaking effects of tmLQCD have been calculated, and conditions under which automatic O(a) improvement holds at maximal twist has been carefully studied.; The resulting twisted mass chiPT has also been extended to study the baryons in this work, which has not been done before. This allows one to probe tmLQCD with more quantities, and in particular, quantities that do not involve quark-disconnected diagrams and so are much easier to calculate in numerical simulations.; A major part of this dissertation has already appeared in published form. Chapters 3 through 5 are based on Refs. [1--5]. |
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