To study the pion peak section of the invariant mass distribution I looked at single pion simulations.  The pions were thrown with pt from 2 - 25 GeV/c flat and were reconstructed using the cuts and parameters described in the cuts, etc. page.  The mass of each reconstructed pion is corrected by adding a small amount of energy to each photon (as outlined here.)  After this correction the peak of the reconstructed mass distribution is aligned with the peak of the data.  The mass distributions from the four bins can be seen below.

Later, these peaks will be normalized, along with the other pieces, to the data.  However, the shape will not change.

If you are interested in seeing the errors on the above plots, I reproduce those below.