Hyperon polarization from the twist-3 distribution in the unpolarized proton-proton collision

TL;DR

This paper explores the origin of hyperon polarization in unpolarized proton collisions using twist-3 distribution formalism, revealing that only the derivative of the soft-gluon-pole distribution contributes to the polarization.

Contribution

It provides the first calculation showing the vanishing of the soft-fermion-pole contribution and clarifies why only the derivative term of the twist-3 distribution affects hyperon polarization.

Findings

Soft-fermion-pole cross section vanishes.

Derivative of the soft-gluon-pole distribution is the sole contributor.

Clarifies the mechanism behind hyperon polarization in unpolarized collisions.

Abstract

We investigate the transverse polarization of a hyperon produced in the high-energy unpolarized proton-proton collision, $pp\to\Lambda^\uparrow X$, based on the collinear twist-3 factorization formalism. We focus on the contribution from the twist-3 distribution in one of the unpolarized proton and the transversity fragmentation function for the final hyperon. Utilizing the "master formula" for the soft-gluon-pole cross section, we clarify the reason for why it receives only the derivative term of the twist-3 distribution. We also present the first computation of the soft-fermion-pole cross section and found that it vanishes. This means that the derivative of the soft-gluon-pole function is the only source for the twist-3 cross section from the unpolarized twist-3 distribution, which provides a useful basis for a phenomenological analysis.