Quasi parton distributions and the gradient flow

TL;DR

The paper presents a gradient-flow-based approach to compute light-front PDFs from lattice QCD by introducing smeared quasi PDFs that are finite in the continuum when the flow time $\tau$ is fixed in physical units. In the regime $\Lambda_{\mathrm{QCD}}, M_N \ll P_z \ll \tau^{-1/2}$, a short-distance expansion connects smeared quasi-PDF moments to renormalized light-front moments, enabling a convolution relation with a universal kernel. A DGLAP-like evolution equation for the matching kernel is derived, describing the scale dependence of the kernel and its relation to the light-front PDFs through continuum perturbation theory. The framework decouples lattice specifics from the continuum matching, offering a regulator-independent path to first-principles PDFs and guiding nonperturbative implementations. Overall, it provides a theoretically solid route to extract light-front PDFs from lattice computations using gradient-flow smearing to circumvent renormalization complications.

Abstract

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.