One-Loop Matching for Parton Distributions: Non-Singlet Case

TL;DR

This work presents a concrete one-loop matching framework between time-independent quasi-distributions computed on the lattice and light-cone parton distributions for non-singlet quarks. By using a transverse-momentum cutoff regulator and axial gauge, it derives explicit one-loop corrections and a factorization kernel Z that maps lattice-accessible quasi-distributions to physical PDFs for unpolarized, helicity, and transversity channels. The results include explicit piecewise expressions for the quasi-distribution corrections, as well as matching factors across momentum-fraction regions, and they extend to antiquarks to cover full support. The study identifies regulator-induced linear divergences tied to the Wilson line and discusses principal-value prescriptions, establishing essential steps toward first-principles lattice extractions of PDFs and guiding future all-order factorization efforts.

Abstract

We derive one-loop matching condition for non-singlet quark distributions in transverse-momentum cut-off scheme, including unpolarized, helicity and transversity distributions. The matching is between the quasi-distribution defined by static correlation at finite nucleon momentum and the light-cone distribution measurable in experiments. The result is useful for extracting the latter from the former in a lattice QCD calculation.

Figures (1)

• Figure 1: One loop corrections to quasi quark distribution.