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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.

This dissertation investigates CsI(Tl) pulse shape discrimination (PSD) as a novel experimental technique to improve challenging areas of particle identification at high energy $e^+ e^-$ colliders using CsI(Tl) calorimeters. In this work CsI(Tl) PSD is implemented and studied at the Belle II experiment operating at the SuperKEKB $e^+ e^-$ collider, representing the first application of CsI(Tl) PSD at a $B$ factory experiment. Results are presented from Belle II as well as a testbeam completed at the TRIUMF proton and neutron irradiation facility. From the analysis of the testbeam data, energy deposits from highly ionizing particles are shown to produce a CsI(Tl) scintillation component with decay time of $630\pm10$ ns, referred to as the hadron scintillation component, and not present in energy deposits from electromagnetic showers or minimum ionizing particles. By measuring the fraction of hadron scintillation emission relative to the total scintillation emission, a new method for CsI(Tl) pulse shape characterization is developed and implemented at the Belle II experiment's electromagnetic calorimeter, constructed from 8736 CsI(Tl) crystals. A theoretical model is formulated to allow for simulations of the particle dependent CsI(Tl) scintillation response. This model is incorporated into GEANT4 simulations of the testbeam apparatus and the Belle II detector, allowing for accurate simulations of the observed particle dependent scintillation response of CsI(Tl). With $e^\pm$, $\mu^\pm$, $\pi^\pm$, $K^\pm$ and $p/\bar{p}$ control samples selected from Belle II collision data the performance of this new simulation technique is evaluated. In addition the performance of hadronic interaction modelling by GEANT4 particle interactions in matter simulation libraries is studied and using PSD potential sources of data vs. simulation disagreement are identified. A PSD-based multivariate classifier trained for $K_L^0$ vs. photon identification is also presented. With $K_L^0$ and photon control samples selected from Belle II collision data, pulse shape discrimination is shown to allow for high efficiency $K_L^0$ identification with low photon backgrounds as well as improved $\pi^0$ identification compared to shower-shape based methods. / Graduate