Quirks of QCD: Twist-2 Operators on the Lattice

In deep inelastic scattering (DIS) probes of hadronic structure, we approximate the matrix elements of the electromagnetic currents using the operator product expansion. The operators are ordered by their twist (dimension minus spin), with twist-2 being the leading order. We would like to perform such calculations on a discrete, Euclidean lattice, as this offers us access to the nonperturbative region on quantum chromodynamics; however, on the lattice, these operators experience power divergent mixing, diverging as we take the lattice spacing to zero. We aim to control this mixing by incorporating the gradient flow, a gauge-invariant Gaussian smearing of the gauge fields that removes ultraviolet fluctuations in those fields. We study an example in perturbation theory.