Calculation of the K→πl+l- rare kaon decay amplitude using lattice quantum chromodynamics
Ó hÓgáin, Fionn
The K→πl+l- decay is a flavor changing neutral current process which is forbidden at tree level in the Standard Model and instead occurs as a second-order electroweak process. This suppression causes the decay to be sensitive to potential New Physics, however the decay channels are dominated by long-distance contributions which require non-perturbative methods of investigation. The details of a lattice calculation on a 483x96 zMöbius domain wall fermion action, with near-physical pion and kaon masses, Mπ ∼ 140 MeV and MK ∼ 500 MeV respectively, will be presented in this thesis. The challenges that occur when evaluating four-point correlation functions which include two effective operators, that are required to study second-order electroweak processes, will be discussed. These challenges include extracting unphysical intermediate states that grow exponentially in the Euclidean-space correlators, the ultra-violet divergence that occurs when the operators approach each other and the extrapolation to the physical charm quark mass needed to deal with this divergence. A comparison of different methods of creating quark propagators, the All-to-All method and using Coulomb gauge-fixed wall sources, will also be presented, showing that the All-to-All method is not suited for a study of this type of decay. The form factor V(z) for the K→πl+l- decay, where z = q2/MK2 and q is difference in the 4-momenta of the kaon and pion, is found to be V(z) = -0.8(5.9) for z = 0.0151(5). The large error on this result, that leads to our calculation of V(z) being consistent with zero, stems from a statistical decorrelational between the single-propagator traces of physical light- and charm-quarks. This statistical decorrelational will be presented along with a discussion on how it may be tackled in the future.