Gauge fixed gluonic observables and neutral kaon mixing on the lattice
This thesis presents gauge fixed gluonic observable and neutral Kaon mixing matrix element measurements using nf=2+1 Domain Wall Fermion (DWF) configurations. These were generated with the Iwasaki gauge action by the RBC and UKQCD collaborations. Results from the first measurement of the QCD strong coupling with these ensembles using the triple gluon vertex are shown. We find that while a very accurate measurement of the coupling is possible using this technique, the systematic error from the perturbative matching at current lattice scales is large. We also discuss the utilisation of this method as a probe for possible Technicolor theories. The calculation of the QCD strong coupling constant from the triple gluon vertex required an implementation of a fast code to fix lattice gauge configurations. I provide details on my implementation of a parallel and optimised Fourier-accelerated algorithm for both Landau and Coulomb gauge fixing. I include the first calculation of the highly accurate W0-scale using these ensembles, allowing for percent-level scale setting. I show results from a wide variety of smearing methods and present the first gluonic measurement of different smearing radii. This thesis also details the first nf=2+1 measurement of the BSM neutral Kaon mixing renormalised matrix elements from lattice simulations with almost exact chiral symmetry in the valence sector and the sea.