Initial-State Interactions in the Unpolarized Drell-Yan Process

TL;DR

This paper shows that initial- and final-state gluon exchanges can generate naive T-odd, chiral-odd transverse momentum dependent distributions such as h1^⊥, which in turn produce a cos(2φ) modulation in unpolarized Drell–Yan processes via h1^⊥ × ḣ1^⊥. Using a quark–scalar diquark model with gluon exchange, the authors compute h1^⊥ and demonstrate its equality to f1T^⊥ within the model, establishing a common mechanism behind both unpolarized and polarized spin asymmetries. They derive the cos(2φ) asymmetry ν in terms of TMD convolutions and provide illustrative numerical estimates (up to ~30% in p p̄ collisions in the explored kinematic window), highlighting the role of quark and gluon orbital angular momentum. The work connects the unpolarized cos(2φ) effect to SIDIS and Drell–Yan single-spin phenomena, offering a coherent picture of initial/final-state interactions and suggesting experimental tests at Tevatron/RHIC to probe orbital dynamics in hard QCD processes.

Abstract

We show that initial-state interactions contribute to the $\cos 2 φ$ distribution in unpolarized Drell-Yan lepton pair production $p p$ and $ p \bar p \to \ell^+ \ell^- X$, without suppression. The asymmetry is expressed as a product of chiral-odd distributions $h_1^\perp(x_1,\bm{p}_\perp^2)\times \bar h_1^\perp(x_2,\bm{k}_\perp^2) $, where the quark-transversity function $h_1^\perp(x,\bm{p}_\perp^2)$ is the transverse momentum dependent, light-cone momentum distribution of transversely polarized quarks in an {\it unpolarized} proton. We compute this (naive) $T$-odd and chiral-odd distribution function and the resulting $\cos 2 φ$ asymmetry explicitly in a quark-scalar diquark model for the proton with initial-state gluon interaction. In this model the function $h_1^\perp(x,\bm{p}_\perp^2)$ equals the $T$-odd (chiral-even) Sivers effect function $f^\perp_{1T}(x,\bm{p}_\perp^2)$. This suggests that the single-spin asymmetries in the SIDIS and the Drell-Yan process are closely related to the $\cos 2 φ$ asymmetry of the unpolarized Drell-Yan process, since all can arise from the same underlying mechanism. This provides new insight regarding the role of quark and gluon orbital angular momentum as well as that of initial- and final-state gluon exchange interactions in hard QCD processes.

Figures (5)

• Figure 1: Kinematics of the Drell-Yan process in the lepton center of mass frame.
• Figure 2: The leading order contribution to the Drell-Yan process
• Figure 4: Diagram which gives the lowest order $\Phi$ (called $\Phi_{L}^{\alpha\beta}$.
• Figure 5: Diagrams which yield $\Phi$ with final-state interaction ($\Phi_{F}^{\alpha\beta})$.
• Figure 6: Numerical result for $P \equiv B C \overline{C} F /(A \overline{A} G)$, using $M=0.94 \, \text{GeV}, m=0.3 \, \text{GeV}, \lambda = 0.8 \, \text{GeV}$ and $\Delta=\overline{\Delta} = 0.2$.