QCD factorization for twist-three axial-vector parton quasidistributions

Abstract

The transverse component of the axial-vector correlation function of quark fields is a natural starting object for lattice calculations of twist-3 nucleon parton distribution functions. In this work we derive the corresponding factorization expression in terms of twist-2 and twist-3 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 the axial-vector quasi- and pseudodistributions.

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

“…The similarly defined (regularized) invariant functions for the light-like separations z 2 = 0 give rise to the chiral-odd parton distributions in position space (see below) are called Ioffe-time distributions (ITDs) [35,37,38]. The terminology for the corresponding off-light cone position-space matrix elements is not well established: they are referred to as quasi-ITDs in [16,36] and pseudo-ITDs in [39][40][41]. In this work, we use the abbreviation qITD for the functions…”

“…Our method of calculation is based on the light-ray operator product expansion (OPE) [42,43] in combination with the background field technique [44,45]. We used the same approach for chiral-even distributions in our previous publication [16], where it is JHEP10(2021)087 described in details. The present case only differs from ref.…”

“…In ref. [16] we have formulated the factorization theorem for the axial-vector qPDF (and pPDF) to twist-three accuracy, which is more involved compared to the twist-two case [17] and calculated the corresponding coefficient functions to one-loop accuracy. In this paper, we repeat the same analysis for the chiral-odd case and formulate the factorization theorem for the quasi(pseudo) distributions related to the twist-three PDFs h L (x) and e(x).…”

“…In ref. [16] we have pointed out that the extraction of the chiral-even twist-three PDF g T (x) from lattice calculations is complicated by the breakdown of the Wandzura-Wilczek relation at the qPDF (pPDF) level. Thus, the separation of twist-three contributions of interest from the dominant twist-two terms at the level of lattice data appears to be highly nontrivial.…”

“…This work follows ref. [16] both conceptually and methodologically, so we present only the necessary definitions and the final expressions for the factorization theorems and NLO coefficient functions and omit technical details. Section 2 is introductory, and it contains JHEP10(2021)087 general definitions and notation.…”