I have incorporated run by run polarization corrections.

Review of the systematic uncertainties for the cross section and longitudinal spin asymmetries.

The background asymmetry estimate has been 0.000 +/- 0.100 was used.  This was chosen as an very conservative number based on the studies in this blog and this blog last December, which most likely did not use all the available runs.  Due to the limited statistics, a fair amount of the observed fluctation seems due to statistics, and keeping with 0 +/- 0.1 would lead to the dominant systematic uncertainty.  Also, as some aspects of the analysis may have been updated since then, it is worth revisiting.  Since it was already decided a single value for all pT is sufficiently accurate, given the statistical fluctations, it is fair to consider the value of A_LL integrated over all pT.  The following show A_LL vs pT for each of three mass bins (0-0.1 GeV, 0.1-0.2 GeV, and 0.2-0.3 GeV) and the results for each mass bin are fit to a constant.