Quirks of QCD: Twist-2 Operators on the Lattice

To probe the structure of hadrons, we often use high energy electrons in scattering experiments, called Deep Inelastic Scattering or DIS. When doing theoretical calculations of the scattering cross section of a DIS process, we apply the operator product expansion to introduce the rotationally-invariant twist-2 operators, where twist is dimension minus spin. To move to numerical calculations, we break up space and time into discrete points on a lattice, rather than a continuum, which breaks rotational symmetry leading to the twist-2 operators having power-divergent mixing under renormalization. We propose that applying the gradient flow prescription to these operators on the lattice will remove the power-divergent mixing. The gradient flow is a regulator that smears the fields in a new parameter called the flow time. We give an example of two twist-2 operators that have a power-divergent mixing on the lattice, but where this power-divergence is removed under the gradient flow.