Twist-3 effect from the longitudinally polarized proton for $A_{LT}$ in hadron production from $pp$ collisions

TL;DR

This paper calculates the twist-3 contribution to the double-spin asymmetry $A_{LT}$ in inclusive hadron production from proton-proton collisions, revealing how the longitudinally polarized proton's effects can be expressed through simpler distributions.

Contribution

It introduces a method to express the twist-3 quark-gluon correlator in terms of twist-3 quark distributions and transversity, completing the leading-order cross section calculation.

Findings

Derived the relation eliminating the twist-3 quark-gluon correlator.

Provided the complete leading-order cross section for $A_{LT}$.

Enhanced understanding of spin asymmetries in proton-proton collisions.

Abstract

We compute the contribution from the longitudinally polarized proton to the twist-3 double-spin asymmetry $A_{LT}$ in inclusive (light) hadron production from proton-proton collisions,i.e., $p^\uparrow \vec{p}\to h\,X$. We show that using the relevant QCD equation-of-motion relation and Lorentz invariance relation allows one to eliminate the twist-3 quark-gluon correlator (associated with the longitudinally polarized proton) in favor of one-variable twist-3 quark distributions and the (twist-2) transversity parton density. Including this result with the twist-3 pieces associated with the transversely polarized proton and unpolarized final-state hadron (which have already been calculated in the literature), we now have the complete leading-order cross section for this process.