Probing the Gluon Sivers Function with an Unpolarized Target: GTMD Distributions and the Odderons.

Renaud Boussarie,Lech Szymanowski,Yoshitaka Hatta,Samuel Wallon

doi:10.1103/physrevlett.124.172501

Abstract

It is commonly believed that the Sivers function has uniquely to do with processes involving a transversely polarized nucleon. In this Letter we show that this is not necessarily the case. We demonstrate that exclusive pion production in unpolarized electron-proton scattering in the forward region is a direct probe of the gluon Sivers function due to its connection to the QCD odderon.

Highlights

Introduction.—Recently, there has been renewed interest in the interplay between spin physics and small-x physics, largely motivated by the necessity to understand the small-x behavior of the helicity distributions inside a longitudinally polarized proton
Recent activities include calculations of various higher order corrections [2] and the generalization to the orbital angular momentum sector [3], as well as alternative approaches to resummation [4,5,6]. Another very interesting, and rather unexpected interplay between spin and small-x physics has been elucidated by Zhou [7] in the transverse polarization sector
In this Letter, we dig into this correspondence to a deeper level and establish relations between the odderon and the so-called generalized transverse momentum dependent (TMD) (GTMDs) [17]

Summary

Published by the American Physical Society

UP; ð1Þ where the trace is in the fundamental representation and we defined the staple gauge links where Uv 1⁄4 1⁄2∞; −∞v. The dependence on x on the l.h.s. is hidden in the regularization of the lightlike Wilson line operators in the small-x effective formalism [22,23,24]. In the eikonal approximation eixPþv− ≈ 1, this term vanishes due to its PT symmetry [25]. Note that this expression is finite despite the denominator, due to the remarkable simplicity of dipole-type GTMDs, which are all proportional to this denominator. The notation 1⁄2x; yz denotes a straight Wilson line from y to x at fixed z. Boldface letters denote transverse vectors and i, j 1⁄4 1, 2 are their indices. The following symmetry properties are known [17]

PðvÞ þ

Þγ ψ