Flowed gluon momentum fractions: A gradient flow-based renormalization approach

The parton momentum fractions carry important information about the nucleon mass and spin decompositions. Specifically, determining the gluon contribution to nucleon momentum is a key step in achieving a better understanding of the nucleon structure. In this talk I present recent work by the HadStruc collaboration on determining the gluon momentum fraction from lattice quantum chromodynamics using a novel renormalization procedure based on the gradient flow, a nonperturbative damping of ultraviolet fluctuations. The ratio of three- to two-point correlation functions, constructed from nucleon and gluon operators, are used to build linear combinations of different matrix elements to access the momentum fraction. The use of distillation and the variational method to improve the signal of the nucleon states will also be discussed. The nonperturbative renormalization and MS-bar scheme matching is implemented via a set of coefficients built from the short flow-time expansion. The application of these coefficients are detailed.