For my single particle Monte Carlo studies, I argued (here) that I needed to add a small amount of energy to each reconstructed photon to better match the data.  This small addition of energy brings the simulation mass distributions into better alignment with the mass distributions in the data.  I did not, however, subtract this small bit of energy from reconstructed (data) pions.  This affects A_LL in that pion counts will migrate to lower Pt bins and some will also exit the low end of the mass windown (or enter the high end.)  So I calculated A_LL after subtracting out the 'extra' energy from each photon.  The plot below shows the original A_LL measurement in black and the new measurement in red.

The values from both histograms are as follows:

Bin   black (orig)   red (new)

1      .0080           .0095

2      .0058           .0092

3      .0203           .0196

4      -.0084          -.0069

So things do not change too much.  I'm not sure which way to go with this one.  My gut tells me to leave the data alone (don't correct it) and assign a systematic to account for our lack of knowledge of the 'true' energy of the photons.  The error would be the difference between the two plots, that is:

Bin   Sys. Error (x10^-3)

1      1.5

2      3.4

3      0.7

4      1.5