Polarized and unpolarized Drell-Yan angular distribution in the helicity formalism

TL;DR

This paper develops a helicity formalism for analyzing polarized and unpolarized Drell-Yan processes, deriving angular distributions and Sivers effects within a QCD factorization framework considering parton transverse momentum.

Contribution

It introduces a helicity tensor decomposition for the Drell-Yan process and provides analytical expressions for angular distributions including the Sivers effect, applicable in a specific kinematic regime.

Findings

Derived angular distribution formulas for unpolarized Drell-Yan.

Provided analytical expressions for Sivers asymmetry with Gaussian transverse momentum dependence.

Simplified results in the limit of small transverse momentum relative to dilepton mass.

Abstract

We present a decomposition of the hadronic tensor for a general polarized Drell-Yan process AB --> l^+ l^- X in terms of helicity structure functions using the helicity axes of the dilepton rest frame as a basis. Next, we consider a QCD parton model and in the framework of a generalized QCD factorization scheme, which applies when the dilepton invariant mass M is much larger than the transverse component of the photon momentum, q_T, in the hadronic center of mass frame. In this approximation we compute the angular distribution of the unpolarized Drell Yan cross section and of the Sivers effect, in single polarized Drell-Yan scattering, by taking into account the transverse motion of partons inside the initial hadrons, k_\perp. Interesting and simple results are found in the kinematical region of k_\perp similar to q_T << M, to first order in a q_T / M expansion. Finally, explicit analytical expressions, convenient for phenomenological studies, are obtained assuming a factorized Gaussian dependence on intrinsic momenta for the unpolarized and Sivers distribution functions, in analogy to those obtained for semi-inclusive deep inelastic scattering.