Production of 
and 
bosons at 
at RHIC offers an important
opportunity in polarized quark structure function physics, complementary to continuum DY production.
As was emphasized in the RSC proposal[15], polarized-beam experiments present an opportunity
for new physics discovery in the domain where the weak interaction predominates.
The cross section for
production is given by,
where 
is the Fermi coupling constant. The structure functions are
evaluated at the mass scale of the vector bosons. Because 
production occurs via a purely left-handed current (in the Standard Electroweak Model) the
helicity asymmetries are more complex than for the DY process. Bourrely and Soffer[19]
define three parity violating asymmetries and one parity conserving asymmetry. They further show,
with the reasonable
approximation, 
, that the parity violating single and double
spin asymmetries contain the same information. For 
production the parity violating
single-spin (measurable with a single polarized beam) and parity-conserving double spin
asymmetries are given respectively by,
and,
Using the model for antiquark polarization described in Sect. 2.1
has been calculated[19] for 
collisions at 
; the
calculations are shown in Fig 8.
Figure 8: Parity violating asymmetries for 
production at
. The solid lines use the antiquark
polarization as described in Ref. [19]; the
dashed lines correspond to 
.
Polarization effects in 
production are measured by detection of single high-
muons, an inclusive process that integrates over a range of 
and 
. The PHENIX
end caps have very short (
) decay distances which effectively discriminate
against muons from pion and kaon decay and are hence ideal for high-momentum
single muon detection. The principal background to the 
signal is from muon decay of heavy
quarks. Based on experience at 
colliders[28,29], the most effective method of
discriminating against heavy-quark decays is to use only the highest 
part of the
spectrum.
Figure 9, an ISAJET calculation for the
PHENIX end caps at 
, shows that the region 
is dominated by
decays. This threshold results in a combined acceptance in the two end caps of 10%,
yielding production of 
24K (9K) 
(
) events with
.
Figure 9: Production of single muons from charm, beauty, and vector boson
decay into the PHENIX end caps at 
using
ISAJET.
The lines show two possible extrapolations of the beauty decays
to higher transverse momenta where the calculation has insufficient
statistical precision.
The high 
cut also limits the acceptance to the large 
kinematic range, 
, where simplifications in the spin asymmetries similar to those discussed in Sect. 2.1
apply. Under these conditions Eq. 9 yields,
while Eq. 10 reduces to,
The second step for 
production shows the similarity to the DY process, Eq.
5. Thus both the parity violating and parity conserving asymmetries provide a
measure of the ratio of the polarized to unpolarized antiquark structure functions at
(range roughly 
). Based on the number of 
events estimated
above, the errors on 
from the use of Eq. 11 would be
comparable to those obtainable via the DY process in the same 
range.
