Single-Spin Asymmetries in Semi-inclusive Deep Inelastic Scattering and Drell-Yan Processes

TL;DR

This paper analyzes the mechanisms behind the sign change of single transverse spin asymmetries between SIDIS and Drell-Yan processes, revealing that despite different cuts, the phases lead to a universal sign-flip in the Sivers functions.

Contribution

It demonstrates that the phases responsible for the asymmetries in SIDIS and Drell-Yan originate from different cuts but result in the same sign-flip, confirming a fundamental prediction in spin physics.

Findings

The phases in SIDIS and DY originate from different cuts in the amplitudes.

Despite different cuts, the contributions are identical in leading-twist kinematics.

The sign-flip relation between Sivers functions is confirmed in the model.

Abstract

We examine in detail the diagrammatic mechanisms which provide the change of sign between the single transverse spin asymmetries measured in semi-inclusive deep inelastic scattering (SIDIS) and in the Drell-Yan process (DY). This asymmetry is known to arise due to the transverse spin dependence of the target proton combined with a T-odd complex phase. Using the discrete symmetry properties of transverse spinors, we show that the required complex phase originates in the denominators of rescattering diagrams and their respective cuts. For simplicity, we work in a model where the proton consists of a valence quark and a scalar diquark. We then show that the phases generated in SIDIS and in DY originate from distinctly different cuts in the amplitudes, which at first appears to obscure the relationship between the single-spin asymmetries in the two processes. Nevertheless, further analysis demonstrates that the contributions of these cuts are identical in the leading-twist Bjorken kinematics considered, resulting in the standard sign-flip relation between the Sivers functions in SIDIS and DY. Physically, this fundamental, but yet untested, prediction occurs because the Sivers effect in the Drell-Yan reaction is modified by the initial-state "lensing" interactions of the annihilating antiquark, in contrast to the final-state lensing which produces the Sivers effect in deep inelastic scattering.