Alternate Calculation of Eta Systematic

At the moment I am calculating the systematic error on A_LL from the presence of Etas in the signal reigon using theoretical predictions to estimate A_LL^eta.  The study below is an attempt to see how things would change if I instead calculated this systematic from the measured A_LL^eta.  Perhaps, also, this would be a good place to flesh out some of my original motivation for using theory predictions.

First order of buisness is getting A_LL^eta.  Since this was done in a quick and dirty fashion, I have simply taken all of my pion candidates from my pion analysis and moved my mass window from the nominal pion cuts to a new window for etas.  For the first three bins this window is .45 GeV/c² < mass < .65 GeV/c² and for the fourth bin this is .5 GeV/c² < mass < .7 GeV/c².  Here is a plot of A_LL^eta, I apologize for the poor labeling.

 

 I guess my first reason for not wanting to use this method is that, unlike the other forms of background, the Etas A_LL ought to be Pt dependent.  So I would need to calculate the systematic on a bin-by-bin basis, and now I start to get confused because the errors on these points are so large.  Should I use the nominal values?  Nominal values plus one sigma?  I'm not sure.

For this study I made the decison to use A_LL^true as the values, where A_LL^true is calculated from the above A_LL using the following formula:

A_LL^M = (A_LL^T + C*A_LL^Bkgd)/(1 + C)

Remembering that a large portion the counts in the Eta mass window are from the combinatoric background.  I then calculate the background fraction or comtamination factor for this background (sorry I don't have a good plot for this) and get the following values

Bin   Bkg fraction

1      77.2%

2      60.9%

3      44.6%

4      32.6%

Plugging and chugging, I get the following values for A_LL^true:

Bin   A_LL^T

1      .0298

2      .0289

3      -.0081

4      .175

Using these values of ALL to calculate the systematic on A_LL^pion I get the following values:

Bin   Delta_A_LL^pion (x10^-3)

1      .33

2      .38

3      .63

4      3.1

Carl was right that these values would not be too significant compared to the quad. sum of the other systematics, except for final bin which becomes the dominant systematic.  In the end, I would not be opposed to using these values for my systematic *if* the people think that they tell a more consistent story or are easier to justify/explain than using the theory curves.  (i.e. if they represent a more accurate description of the systematic.)