Soft parton radiation in polarized vector boson production: theoretical issues

TL;DR

This work develops a comprehensive theoretical framework for polarized vector-boson production at RHIC, focusing on small-$q_T$ resummation and fully differential lepton-level observables. Using the Collins-Soper-Sterman formalism in impact-parameter space, it combines one-loop finite-order cross sections with all-order Sudakov resummation, while carefully handling chiral $\\gamma_5$ in dimensional regularization/reduction and transforming results to the $\overline{MS}$ scheme for compatibility with polarized PDFs. It establishes the universality of the perturbative spin-dependent cross section, showing spin-independent Sudakov coefficients and a factorization structure that cleanly separates contributions from each beam. The paper provides explicit spin-dependent structure functions and C-functions, enabling precise predictions for polarized Drell-Yan and weak-boson production and informing measurements of sea-quark polarizations at RHIC (with further numerical results in a companion paper).

Abstract

Accurate measurement of spin-dependent parton distributions in production of electroweak bosons with polarized proton beams at the Relativistic Heavy Ion Collider depends on good understanding of QCD radiation at small transverse momenta $q_T$ of vector bosons. We present a theoretical formalism for small-$q_T$ resummation of the cross sections for production of virtual photons, W, and Z bosons, with the subsequent decay of these bosons into lepton pairs, for arbitrary longitudinal polarizations of the proton beams.

Figures (2)

• Figure 1: Notations for the momenta and helicities of the participating particles.
• Figure 2: Partonic subprocesses contributing to vector boson production.