One suggested contributor to the simulation-data disagreement I see with the pi0's is the width of the BEMC gain distribution, with the gains possibly distributed too narrowly in simulation.  To test this, I calculated a gain adjustment for each BEMC tower by sampling a gaussian based around 1, using widths from 0 to 1 in steps of .01.  Figure 1 shows an example for a width of .2.  Here the RMS of the gain distribution increases by roughly 25%.  The width of the gaussian fit, also shown, increases from .0023 to .0041, but since the original gain distribution is not particularly gaussian, it's not clear how trustworthy this measurement is.

Figure 1: At left, the original distribution of BEMC tower gains; at right, the distribution after being widened by a gaussian with width of .2.  Both distributions are fit to a gaussian.

The gain adjustment was applied to the gain for each tower to determine the invariant mass of pi0 candidates in simulation.  A simulated pion peak was then extracted from this adjusted invariant mass distribution and the data was fit, as usual, to this plus the two backgrounds.  By repeating this 100 times for each width and plotting the chi-square of the fit vs. the width used, it's possible to get some idea of whether the fit improves as the gain distribution widens.  As can be seen in Figure 1, the chisquare values clearly show a minimum somewhere around .2 or .3, though it's not the same in each pT bin and the improvement isn't great.

Figure 1: Chi-square vs. width in pT bins.

Figures 2 and 3 show the results of using a gain adjustment width of .2.  There is some improvement in the fit, and it is also more regular in each pT bin, but there are still clearly problems.

Figure 2: Fit to data, simulation gain width expanded by .2.

Figure 3: (Data-Fit)/Data

As the actual value of the width that produces the minimum chi-square is somewhat ambiguous, I also tried with a gain adjustment width of .3, but the results here are clearly worse.

Figure 4: Fit to data, simulation gain width expanded by .3

Figure 5: (Data-Fit)/data

While incorrect BEMC gain width may explain some of the issues with the fit, it doesn't seem to be able to explain all of it.