  The gradient flow is a valuable tool for the lattice community, with
applications from scale-setting to implementing chiral fermions. Here I focus
on the gradient flow as a means to suppress power-divergent mixing.
Power-divergent mixing stems from the hypercubic symmetry of the lattice
regulator and is a particular difficulty for calculations of, for example, high
moments of parton distribution functions. The gradient flow removes
power-divergent mixing on the lattice, provided the flow time is kept fixed in
physical units, at the expense of introducing a new physical scale in the
continuum. One approach to dealing with this new scale is the smeared operator
product expansion, a formalism that systematically connects nonperturbative
calculations of flowed operators to continuum physics. I study the role of the
gradient flow in suppressing power-divergent mixing and present the first
nonperturbative study in scalar field theory.

High Energy Physics - Lattice