The Drell-Yan (DY) process[17], 
(or 
), has been studied for over twenty years,
largely by measuring muon pairs in fixed target experiments at Fermilab and
CERN[18]. With the advent of QCD descriptions, including next-to-leading-order
corrections, it can be characterized as well understood theoretically[18].
Phenomenological evaluations of parton structure functions now routinely use DY as well
as DIS data. The parton-model expression for the DY cross section,
is often multiplied by a factor, 
, which accounts for next-to-leading order
QCD effects.
We first consider the measurement of 
in the DY process, since its close relation
to 
of DIS experiments allows a reasonably quantitative analysis.
The expression for the
longitudinal spin asymmetry in the DY process has the simple form[8,14],
with 
. The superscripts refer to parton spin projections parallel (+) or
antiparallel (-) to the parent hadron's spin projection. For
the denominator of Eq. 2 is dominated by the term,
, allowing a substantial
simplification,
where the notation 
has been introduced.
Neglecting small sea-quark effects, one can use approximate expressions for the structure
functions of DIS,
to achieve an important further simplification.
The measured values of
in DIS are shown in Figs 4 and 5. For 
one sees that
, and with the above relations Eq. 3 becomes,
The second step follows if 
. Equation 5 has
the familiar form of an experimentally measured asymmetry being determined by the product of a beam
polarization and the asymmetry of a physical process. Thus for the DY process with 
, a longitudinally polarized proton can be thought of as a beam of polarized u quarks with
. It is apparent from the large measured values of
that longitudinal spin asymmetry in the DY process
will be a sensitive measure of the polarization of the 
quark distribution of
the proton.
Figure 4: Longitudinal asymmetry and 
structure function for
deep-inelastic lepton scattering from the proton from
CERN[1,4] and SLAC[2]
Figure 5: Longitudinal asymmetry and 
structure function for
deep-inelastic lepton scattering from the neutron (
) from
SLAC[6]
Equation 5 permits estimates to be made for actual experimental conditions,
given some assumptions about the antiquark polarization. Until recently little guidance
could be found on the subject of antiquark polarization beyond the strong indication that
the strange quark sea makes a significant integral contribution to the proton's
spin[3,4,5]. Bourrely and Soffer[19] adopt an approach to
quark and antiquark polarization inspired by a possible connection between light-flavor
asymmetries and spin asymmetries. Two recent experiments[20,21]
strongly suggest
in the proton. Bourrely and Soffer propose,
where the relation is fixed at 
by a recent measurement of the 
asymmetry of the proton using the DY process[21].
Equations 1 (including a K-factor of 2) and 5 can be used with the model of
Ref.[19] to make sensitivity estimates for realistic running conditions. Monte Carlo DY
events are thrown in to the full acceptance of the enhanced PHENIX muon spectrometer, with
100% detection efficiency assumed for single muons above 2 GeV in the end caps, and above 1.3 GeV
in the central arms. The luminosity of RHIC is assumed[16] to be
. Results at 
for
an integrated luminosity
are shown in Fig. 6; beam polarizations were taken to be
0.7[16]. A total of 10.8 K muon pairs, 
, are detected (Table 1). The errors
on 
would be twice as large if measured at 
with an integrated
luminosity 
(see Appendix B). With the proposed PHENIX muon upgrade
a sensitive measurement of the antiquark helicity distribution of the proton is clearly feasible.
Figure 6: 
using Eq. 5 and the model of Bourrely
and Soffer[19]. Two extrapolations consistent with
the experimental results from CERN NA51[21] yield the
two curves. Error bars (shown on the lower curve) are based on an
integrated luminosity of 
at 
, yielding
10.8K muon pairs; beam polarizations are taken to be 0.7.
Table 1: Number of Drell-Yan dimuons detected by the upgraded
PHENIX muon spectrometer at
with an integrated luminosity 
.
Based on extensive experience with dimuon production in fixed-target experiments, the most
serious source of background competing with the DY process is semileptonic charm decay. Drell-Yan
production experiments at Fermilab[23,24] (
) provide strong
evidence that the charm contribution is negligible for 
. However extensive
simulations performed for the PHENIX CDR[25] indicate competition from charm
decay for
at
where the production cross section is considerably larger. Thus relatively low energies
for DY physics are also indicated from the standpoint of background minimization.
