An Observation Concerning the Process Dependence of the Sivers Functions

TL;DR

This paper investigates the process dependence of the Sivers functions and finds a sign mismatch between the Sivers function and the twist-three correlation function, raising questions about their role in single-spin asymmetries.

Contribution

It provides a consistent comparison of the Sivers function and the twist-three correlation function, revealing a sign mismatch that challenges current theoretical understanding.

Findings

Sign mismatch between Sivers function and twist-three correlation function.

Magnitude of functions roughly consistent despite sign discrepancy.

Implication that current data may not fully constrain the Sivers functions.

Abstract

The $k_\perp$-moment of a quark's Sivers function is known to be related to the corresponding twist-three quark-gluon correlation function $T_{q,F}(x, x)$. The two functions have been extracted from data for single-spin asymmetries in semi-inclusive deep inelastic scattering and in single-inclusive hadron production in $pp$ collisions, respectively. Performing a consistent comparison of the extracted functions, we find that they show a "sign mismatch": while the magnitude of the functions is roughly consistent, the $k_\perp$-moment of the Sivers function has opposite sign from that of $T_{q,F}(x, x)$, both for up and for down quarks. Barring any inconsistencies in our theoretical understanding of the Sivers functions and their process dependence, the implication of this mismatch is that either, the Sivers effect is not dominantly responsible for the observed single-spin asymmetries in $pp$ collisions or, the current semi-inclusive lepton scattering data do not sufficiently constrain the $k_\perp$-moment of the quark Sivers functions. Both possibilities strengthen the case for further experimental investigations of single-spin asymmetries in high-energy $pp$ and $ep$ scattering.