Automated perturbation theory for x-dependent hadron structure*

Lattice quantum chromodynamics (QCD) provides a nonperturbative approach to the determination of hadron structure from first principles. Parton distribution

functions (PDFs) can be extracted from lattice QCD calculations of matrix elements of space-like separated fields via the large momentum effective theory and short distance

factorization frameworks. We present a calculation of the matrix element of the unpolarized gluon operator at one loop in perturbation theory and decomposed into tensor projection form factors. This decomposition allows the determination of arbitrary renormalizable operator combinations without recalculation and paves the way for future calculations at higher order in perturbation theory, the inclusion of gradient-flow smeared fields, and the perturbative determination of a more complete suite of gluon

matrix elements relevant to collinear hadron structure at leading twist and beyond.