Novel Phenomenology of Parton Distributions from the Drell-Yan Process

TL;DR

This paper surveys how Drell–Yan processes illuminate the partonic structure of hadrons beyond one-dimensional PDFs by leveraging factorization theorems for collinear and TMD frameworks. It highlights measurements of sea-quark flavor asymmetries, strange-quark content, and gluon distributions, and discusses the extraction of spin–momentum correlations through Sivers and Boer–Mulders functions, including their predicted sign change between SIDIS and Drell–Yan. The review also covers generalized DY channels with W/Z production to access flavor-separated polarized seas and nuclear PDFs, and addresses angular distributions and resummation effects via Lam–Tung and CSS formalisms. Collectively, it underscores Drell–Yan’s central role in testing QCD dynamics, validating factorization, and revealing the three-dimensional motion of quarks and gluons inside hadrons. It also sketches future facilities and measurements (fixed-target, RHIC/LHC, J-PARC, COMPASS) to advance the 3D mapping of hadron structure.

Abstract

The Drell-Yan massive lepton-pair production in hadronic collisions provides a unique tool complementary to the Deep-Inelastic Scattering for probing the partonic substructures in hadrons. We review key concepts, approximations, and progress for QCD factorization of the Drell-Yan process in terms of collinear or transverse momentum dependent (TMD) parton distribution functions. We present experimental results from recent fixed-target Drell-Yan as well as $W$ and $Z$ boson production at colliders, focussing on the topics of flavor structure of the nucleon sea as well as the extraction of novel Sivers and Boer-Mulders functions via single transverse spin asymmetries and azimuthal lepton angular distribution of the Drell-Yan process. Prospects for future Drell-Yan experiments are also presented.

Figures (23)

• Figure 1: Schematic view of a parton with longitudinal momentum fraction $x$, transverse momentum $k_T$, and transverse position $b_T$ in a hadron of momentum $p$ moving along z-direction.
• Figure 2: Sketch for scattering amplitude of Drell-Yan process (left) and scattering amplitude square in the cut diagram notation where the final-state is identified by a vertical line (right).
• Figure 3: Sample QCD modification to the scattering amplitudes of Drell-Yan mechanism: gluon radiation and interaction (left) and gluon interaction between spectators (right).
• Figure 4: Left (a): The Drell-Yan cross section ratios of $p+d$ over $2(p+p)$ versus $x_2$ (momentum fraction of the target partons) from FNAL E866. The curves are the calculated next-to-leading-order cross section ratios for the Drell-Yan using various PDFs including MRS MRS, GRV98 GRV98, MRST MRST, CTEQ4M CTEQ4M and CTEQ5M CTEQ5M. Right (b): $\bar{d}(x)/\bar{u}(x)$ versus $x$ extracted from FNAL E866. Parametrizations from various PDFs and the data point from NA51 are also shown (from e866e866-1e866-2).
• Figure 5: Left (a): $\bar{d} - \bar{u}$ as a function of $x$. The E866 results e866-2, scaled to fixed $Q^2 = 54$ GeV$^2$, are shown as the circles. Results from HERMES ($\langle Q^2\rangle = 2.3$ GeV$^2$) are shown as squares hermes98. Right (b): Comparison of the measured ${\bar{d}}(x)-{\bar{u}}(x)$ at $Q^2$ = 54 GeV$^2$ to predictions of several models of the nucleon sea e866-2. The curves correspond to pion-cloud model by Peng et al. e866-1 and Nikolaev et al. nikolaev, chiral-quark model by Szczurek et al. szczurek96, chiral-quark soliton model by Pobylitsa et al. pobylitsa, and instanton model by Dorokhov and Kochelev dorokhov.