QCD factorization for chiral-odd parton quasi- and pseudo-distributions

TL;DR

This paper derives factorization formulas for chiral-odd nucleon distributions in lattice QCD, enabling the extraction of twist-three and twist-two distributions from quasi- and pseudo-distributions with one-loop accuracy.

Contribution

It provides the first derivation of factorization formulas for chiral-odd distributions in terms of twist-two and twist-three collinear distributions at one-loop order, applicable to lattice calculations.

Findings

Factorization formulas for chiral-odd distributions are derived.

Twist-two part of the $h_L$ distribution can be separated from twist-three.

Results are applicable in position and momentum space for lattice QCD.

Abstract

We study chiral-odd quark-antiquark correlation functions suitable for lattice calculations of twist-three nucleon parton distribution functions $h_L(x)$ and $e(x)$, and also the twist-two transversity distribution $\delta q(x)$. The corresponding factorized expressions are derived in terms of the twist-two and twist-three collinear distributions to one-loop accuracy. The results are presented both in position space, as the factorization theorem for Ioffe-time distributions, and in momentum space, for quasi- and pseudo-distributions. We demonstrate that the twist-two part of the $h_L$ quasi(pseudo)-distribution can be separated from the twist-three part by virtue of an exact Jaffe-Ji-like relation.