For the eta background systematic we first estimate the background contribution (or contamination factor) to the signal reigon.  That is we integrate our simulated background to discern the precentage of the signal yield that is due to background counts.  The plots below show, for each of the four bins, the background fraction underneath the singal peak.  The background (simulation) is in blue and the signal (data) is in black and the background that falls in the signal reigon is filled-in with.  Below that is the same four plots but blown up to show the contamination.

Here we blow up these plots

The background fractions for the bins are

Bin 1:  1.50%

Bin 2:  1.65%

Bin 3:  2.21%

Bin 4:  1.70%

Then I consider how much this background fraction could affect my measured asymmetry.  So I need to measure the asymmetry in the etas.  So instead of measuring the asymmetry in the etas I will use a theoretic prediction for A_LL.  From GRSV standard and GRSV min I approximate that the size of A_LL in my Pt range to be between 2 - 4%.

I stole this plot from C. Aidala's presentation at DNP in Fall 2007.  Since GRSV-Max is ruled out by the 2006 jet result I restrict myself only to min, standard and zero.  For a conservative estimate on the systematic, I should pick, for each Pt bin, the theory curve that maximizes the distance between the measured and theoretical asymmetries.  Unfortunately, at this time I do not have predictions for Pt above 8, so I must extrapolate from this plot to higher bins.  For the first two bins this maximum distance would correspond to GRSV standard (A_LL^bg ~ 0.02).  For the third bin, this would correspond to GRSV = 0 (A_LL^bg ~ 0.).  For the fourth bin (which has a negative measured asymmetry) I extrapolate GRSV standard to ~4% and use this as my background A_LL.

Systematic (x10^-3)

Bin 1:  0.18

Bin 2:  0.23

Bin 3:  0.43

Bin 4:  0.82