#### Spin Dependent Drell-Yan in QCD to Order Alpha-Strong Squared:
The Non-Singlet Sector

##### Sanghyeon Chang, Claudio Coriano, R. D. Field, and L. E. Gordon

##### Institute for Fundamental Theory, Department of Physics,
University of Florida, Gainesville, FL 32611

Submitted to
Nuclear Physics **B**.

#### Abstract

A study of the order alpha-strong squared corrections to the
Drell-Yan (*non-singlet*) differential cross section for incoming states of
arbitrary longitudinal helicities is presented. The transverse momentum
*distributions*, of the lepton pair are studied and the calculations of
Ellis, Martinelli, and Petronzio (EMP) are extended to include polarized initial states.
We use the MSbar scheme and the
t'Hooft-Veltman regularization for the helicity projectors.
From our results one can obtain the bulk of the totally inclusive
NNLO cross section for the production of a Drell-Yan pair in the
non-singlet sector by a simple integration over the virtual photon momentum.
We show that in the MSbar scheme helicity is not conserved along the quark lines, unless
a finite renormalization is done and one adapts the physical
MSbar_P scheme. This aspect of the calculation is similar to the order alpha-strong squared
polarized production of single and double photons. Our spin averaged *unpolarized*
differential cross sections agree with the EMP calculations.

This research was supported in part by a
grant from the U.S. Department of Energy
(DoE).

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