USING LATTICE QUANTUM CHROMODYNAMICS FOR NON-PERTURBATIVE RENORMALIZATION OF THE GLUON MOMENTUM FRACTION OF THE NUCLEON

Lattice quantum chromodynamics, often abbreviated as lattice QCD or LQCD, presents a non-perturbative method for calculating phenomenological quantities in quantum field theory (QFT). However, scale-dependent quantities such as the gluon momentum fraction $\expval{x}_g$ must be renormalized in order to compare lattice calculations to other theory and even other lattice calculations. The gluon momentum fraction is useful for understanding hadron structure and calculating the parton distribution function (PDF). I obtain the energy spectrum and ground state matrix elements of the gluon energy-momentum tensor (EMT) from the 2pt and 3pt correlators calculated from LQCD. Then, I calculate of the NPR renormalization constants using the regularization-independent momentum subtraction scheme (RI/MOM) for various lattice spacings with a pion mass $M_\pi\approx310\mathrm{MeV}$. This calculation required various steps in \texttt{Chroma} and \texttt{Mathematica}, and the workflow for this process is comprehensively detailed.