The gradient flow at higher orders in perturbation theory

The Gradient Flow formalism has proven to be a useful tool in both lattice gauge theory and perturbation theory since its introduction in its current form in 2010. Besides scale setting, which drove its prominence in lattice gauge theory, its smoothing properties and the connection to physical observables provided by the short flow-time expansion have made it a viable tool for lattice studies of various quantities, such as the energy-momentum tensor or four-quark operators describing B-meson mixing and lifetimes. In this thesis, we apply the Gradient Flow to the quark chromomagnetic dipole operator as a first step towards a determination of the neutron electric dipole moment. This requires input from both lattice gauge theory and perturbation theory, since the matching coefficients relating the physical unflowed operators to flowed ones can be calculated perturbatively, while the hadronic matrix elements of such flowed operators are calculated on the lattice. We determine the matching coefficients through next-to-next-to-leading order, up to terms vanishing at zero flow-time. As a second application, we study the flowed topological charge density and the flowed singlet axial current, which appear in the Adler–Bell–Jackiw anomaly. Finally, we extend the framework of flowed quantum chromodynamics to the unbroken phase of the Standard Model, excluding Yukawa interactions in this first approach. The flowed Standard Model offers an alternative method to infer the renormalization of Standard Model effective field theory operators to higher orders in perturbation theory. Such a calculation requires knowledge of the flowed field renormalization constants, which we determine, among other quantities, to next-to-next-to-leading order in the gauge couplings and the scalar coupling.