On a possible node in the Sivers and Qiu-Sterman functions

TL;DR

This paper explores the theoretical possibility of a node in the x dependence of the Sivers and Qiu-Sterman functions, which has implications for experimental tests of the Sivers effect sign change and proton structure modeling.

Contribution

It introduces an x-dependent relation linking the Qiu-Sterman function to a twist-3 part of g_2, suggesting a natural node in the Qiu-Sterman function and its experimental verification.

Findings

Proposes a relation indicating a potential node in the Qiu-Sterman function.

Highlights the importance of including the full Wilson line in Sivers function modeling.

Discusses the role of a node in satisfying the Burkardt sum rule.

Abstract

The possibility of a node in the x dependence of the Sivers and Qiu-Sterman functions is discussed in light of its importance for the experimental check of the overall sign change of the Sivers effect between semi-inclusive DIS and the Drell-Yan process. An x-dependent version of the Ehrnsperger-Schaefer-Greiner-Mankiewicz relation between the Qiu-Sterman function and a twist-3 part of g_2 is presented, which naturally suggests a node in the Qiu-Sterman function. This relation could be checked experimentally as well and could provide qualitative information on the gluonic field strength inside the proton. Satisfying the Burkardt sum rule by means of a node is briefly discussed and the importance of modelling the Sivers function including its full Wilson line is pointed out.