Quasi parton distributions and the gradient flow

We propose a new approach to determining quasi parton distribution functions (PDFs) from lattice quantum chromodynamics. By incorporating the gradient flow, this method guarantees that the lattice quasi PDFs are finite in the continuum limit and evades the thorny, and as yet unresolved, issue of the renormalization of quasi PDFs on the lattice. In the limit that the flow time is much smaller than the length scale set by the nucleon momentum, the moments of the smeared quasi PDF are proportional to those of the light-front PDF. We use this relation to derive evolution equations for the matching kernel that relates the smeared quasi PDF and the light-front PDF. As part of this discussion, we elucidate the relationship between the quasi and light-front PDFs.