For the combinatoric 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 green and the signal (data) is in black and the background that falls in the signal reigon is filled-in with green.

The background fractions for the bins are

Bin 1:  6.1%

Bin 2:  6.1%

Bin 3:  5.7%

Bin 4:  6.2%

Then I consider how much this background fraction could affect my measured asymmetry.  So I need to meausre the asymmetry in the high-mass reigon.  I do this, taking the mass window to be 1.2 to 2.0 GeV/c².  I do not expect this asymmetry to be Pt-dependant, so I fit the asymmetry with a flat line and take this to be the asymmetry of the background, regardless of Pt.  The plot below shows this asymmetry and fit.

Finally, I calculate the systematic error Delta_A_LL = A_LL^True - A_LL^Measured where:

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

And C is the background fraction.  This yields in the end as a systematic error (x10^-3):

Bin 1:  1.0

Bin 2:  0.9

Bin 3:  1.6

Bin 4:  0.03