Twist-3 Gluon Fragmentation Contribution to Polarized Hyperon Production in Unpolarized Proton-Proton Collision

TL;DR

This paper derives the leading-order twist-3 gluon fragmentation function contribution to hyperon polarization in unpolarized proton-proton collisions, completing the theoretical framework for understanding this phenomenon.

Contribution

It introduces the first derivation of the twist-3 gluon fragmentation contribution at leading order, ensuring gauge invariance and frame independence in the collinear factorization approach.

Findings

Derived the LO twist-3 gluon FF contribution

Established model-independent relations among twist-3 gluon FFs

Confirmed gauge invariance and frame independence of the cross section

Abstract

Understanding the origin and mechanism of the transverse polarization of hyperons produced in unpolarized proton-proton collision, $pp\to \Lambda^\uparrow X$, has been one of the long-standing issues in high-energy spin physics. In the framework of the collinear factorization applicable to large-$p_T$ hadron productions, this phenomenon is a twist-3 observable which is caused by multi-parton correlations either in the initial protons or in the process of fragmentation into the hyperon. We derive the twist-3 gluon fragmentation function (FF) contribution to this process in the leading order (LO) with respect to the QCD coupling constant. Combined with the known results for the contribution from the twist-3 distribution function and the twist-3 quark FF, this completes the LO twist-3 cross section. We also found that the model independent relations among the twist-3 gluon FFs based on the QCD equation of motion and the Lorentz invariance property of the correlation functions guarantee the color gauge invariance and the frame-independence of the cross section.