In the search for new physics beyond the Standard Model (SM) of particle physics,
one promising set of probes are rare decays, due to the possibility of large
contributions from new physics relative to their SM prediction. Two examples of
such processes are the long distance dominated
avour-changing neutral current
decays K⁺ → π⁺l⁺l⁻ and Σ⁺ → pl⁺l⁻, referred to as the rare kaon and rare
hyperon decays respectively. These processes contain the transition of a strange
quark into a down quark which can only occur at loop level within the SM, however
tree level contributions could exist from physics beyond the SM. Currently, the only
known method for making ab initio calculations of low energy hadronic quantities
such as these, is through the use of Lattice Quantum Chromodynamics (LQCD)
where correlation functions are computed numerically via Monte Carlo methods on
a discrete, nite and Euclidean space-time lattice.
Work from this PhD has contributed to a calculation of the rare kaon decay at
physical pion mass. We then investigate an alternative method utilising directly
integrated correlation functions in an attempt to reduce the large computational
cost of this and similar calculations.
In addition, we present work extending the existing theoretical framework for
computing the rare kaon decay using LQCD to the rare hyperon decay, including the
handling of exponentially growing intermediate states and the correction of power-like
fi nite volume effects. We also present the current status of the fi rst exploratory
calculation of the form factors of this decay with unphysically heavy pions and 2+1
flavours of domain wall fermions.
In order to perform this work, multiple developments have been made to the Grid
and Hadrons C++ libraries, which are open-source tools for performing large scale
lattice fi eld theory calculations on both CPU and GPU based machines
