Intrinsic transverse momentum and the polarized Drell-Yan process

TL;DR

This paper analyzes polarized Drell–Yan scattering at leading order in $1/Q$ with measured lepton-pair transverse momentum $Q_T$, showing that each quark flavor is described by six transverse-momentum dependent distributions depending on $x$ and $k_T^2$. By employing the EFP diagrammatic framework and a careful Dirac-structure analysis, the authors derive a complete leading-twist set of TMDs ($f_1$, $g_{1L}$, $g_{1T}$, $h_{1T}$, $h_{1L}^ perp$, $h_{1T}^ perp$) and their antiquark counterparts, and express the DY cross sections in terms of convolutions of these distributions for various polarization configurations. They provide explicit results for the hadron tensor and cross sections, discuss $Q_T$-integrated and $Q_T=0$ limits, and explore Gaussian $k_T$-dependent models to illustrate the angular dependences and kinematic zeros. The work clarifies how intrinsic transverse momentum enters polarized DY and outlines the potential for accessing a rich set of spin and transverse-spin structures, while also highlighting unresolved issues about factorization and universality of TMDs in polarized processes.

Abstract

In this paper we study the cross section at leading order in $1/Q$ for polarized Drell-Yan scattering at measured lepton-pair transverse momentum $Q_T$. We find that for a hadron with spin $1/2$ the quark content at leading order is described by six distribution functions for each flavor, which depend on both the lightcone momentum fraction $x$, and the quark transverse momentum $\bbox{k}_T^2$. These functions are illustrated for a free-quark ensemble. The cross sections for both longitudinal and transverse polarizations are expressed in terms of convolution integrals over the distribution functions.

Figures (3)

• Figure 1: Quark and antiquark handbag diagrams for inclusive DIS.
• Figure 2: The quark and antiquark Born diagrams for the Drell-Yan process.
• Figure 3: The blob representing the quark correlation function.