Single Transverse-Spin Asymmetry in Drell-Yan Production at Large and Moderate Transverse Momentum

TL;DR

The paper develops a unified description of the single-transverse spin asymmetry (SSA) in Drell-Yan production across large and moderate transverse momentum. It demonstrates that the twist-three quark-gluon correlation (ETQS) mechanism and the transverse-momentum-dependent (Sivers) framework describe the same physics in the overlapping regime, enabling perturbative generation of the Sivers function from twist-three inputs and providing a consistent link between two major SSA formalisms. The analysis covers soft and hard pole contributions in quark-antiquark and quark-gluon channels, derives the low-q_⊥ limit where TMD factorization applies, and confirms the matching between ETQS and TMD factorization with explicit expressions for cross sections and Sivers functions. This unification informs phenomenology and paves the way for resummation and SIDIS/DY process comparisons, including potential extensions to other twist-three correlators and Collins-type mechanisms.

Abstract

We study the single-transverse spin asymmetry for the Drell-Yan process. We consider production of the lepton pair at large transverse momentum, $q_\perp\sim Q$, where $Q$ is the pair's mass. The spin asymmetry is then of higher twist and may be generated by twist-three quark-gluon correlation functions. Expanding the result for $q_\perp\ll Q$, we make contact with the transverse-momentum-dependent QCD factorization involving the so-called Sivers functions. We find that the two mechanisms, quark-gluon correlations on one hand and the Sivers effect on the other, contain the same physics in this region. This ties the two together and imposes an important constraint on phenomenological studies of single transverse spin asymmetries.

Figures (10)

• Figure 1: A vertex diagram representing twist-three quark-gluon correlation function in a proton. When the proton is polarized, the gluon field has a definite polarization.
• Figure 2: Drell-Yan scattering amplitudes via (a) $q+\bar{q}\rightarrow \gamma^* + g$ and (b) $q+\bar{q} + g \rightarrow \gamma^* + g$; (c) A typical diagram, from the interference of the amplitudes in (a) and (b), that gives a contribution to the SSA.
• Figure 3: A typical Feynman diagram (a) and its complex conjugate (b) contributing to the single-spin asymmetry for the Drell-Yan process through the quark-antiquark scattering channel, containing both soft-pole "(S)" and hard-pole "(H)" contributions. The bars indicate the places where a pole arises and generates a strong interaction phase.
• Figure 4: Feynman diagrams for the soft-pole contributions to the single-transverse-spin asymmetry through the quark-antiquark scattering channel. The bars indicate the propagators yielding poles.
• Figure 5: Feynman diagrams for soft-pole contributions to the single-transverse-spin asymmetry through quark-gluon scattering.