After all the pion candidates have been found and all the cuts applied, we need to extract the number of pions in each bin (in each spin state for A_LL.)  To do this we simply count the number of pion candidates in a nominal mass window.  I chose the mass window to try to maximize the signal region and cut out as much background as possible. For the first three Pt bins, this window is from .08 - .25 GeV/c² and in the last bin the window is from .1 - .3 GeV/c².  The window for the last Pt bin is shifted mostly to cut out more of the low mass background and to capture more pions with higher than average reconstructed mass.  The windows can be seen below for bins 2 and 4.

These Pt bins are broken down by spin state, and the individual yields are reported below.