After some discussion in the spin pwg meeting and on the spin list, it appears I have been vastly overestimating my eta systematic as I was not properly weighing my thrown single etas. I reanalyzed my single eta MC sample using weights and I found that the background contribution from etas underneath my pion peak is negligible. Thus I will not assign a systematic error eta background. The details of the analysis are as follows. First I needed to assign weights to the single etas in my simulation. I calculated these weights based on the published cross section of PP -> eta + X by the PHENIX collaboration (nucl-ex 06110066.) These points are plotted below. Of course, the PHENIX cross section on reaches to Pt = 11 GeV/c and my measurement reaches to 16 GeV/c. So I need to extrapolate from the PHENIX points out to higher points in Pt. To do this I fit the PHENIX data to a function of the form Y = A*(1 + (Pt)/(Po))^-n. The function, with the parameters A = 19.38, P0 = 1.832 and n = 10.63, well describes the available data.

I then caluclate the (properly weighted) two-photon invariant mass distribution and calculate the number of etas underneath the pion peak.  The eta mass distributions are normalized to the data along with the other simulations.  As expected, this background fraction falls to ~zero.  More specifically, there was less than ten counts in the signal reigon for all four Pt bins.  Even considering a large background asymmetry (~20%) this becomes a negligable addition to the total systematic error.  The plots below show the normalized eta mass peaks (in blue) along with the data (in black.)  As you can see, the blue peaks do not reach into the signal reigion.

Unfortunately, the statistics are not as good, as I have weighted-out many of the counts.  I think that the stats are good enough to show that Etas do not contribute to the background at any significant level.  For the final result I think I would want to spend more time studying both single particle etas and etas from full pythia. 

I should also note that for this study, I did not have to 'correct' the mass of these etas by adding a slight amount of energy to each photon.  At first I did do this correction and found that the mass peaks wound up not lining up with the data,  When I removed the correction, I found the peaks to better represent the data.

In summary: I will no longer be assigning a systematic from eta contamination, as the background fraction is of order 0.01% and any effect the would have on the asymmetry would be negligible.