Ok, now we're cooking.  Most of the ingredients are in place.  We have our background subtracted raw yields.  We have our generalized correction factor to account for inefficiencies in trigger, reconstruction, etc.  Now, it's time to take a first look at a cross section.  At a high level, we'll be starting with the raw yields, and applying a number of corrections for geometrical acceptance, efficiencies, etc. to recreate the true distribution.  The formula for the invariant differential cross section:

Where:

Pt = Average Pt in a bin (as an aside, all points are plotted at this value)

N_raw = background subtracted raw yields

delta_pt = bin width in pt

delta_eta = 1.4 (= size of pseudorapidity range -.7 to .7)

C_trig+reco = Trigger + Reconstruction Efficiency (Generalized) Correcton Factor

Gamma/Gamma = branching fraction for Pi⁰ -> gamma gamma (=98.8%)

L = Luminosity

After applying all of these corrections, we arrive at the cross-section below.

The a) panel shows the invariant cross section along with 2 NLO pQCD predictions (based on DSS and KKP FFs.)  The b) panel shows the relative statistical errors on the cross section.  Panel c) shows the (data-NLO)/NLO for both pQCD predictions as well as for predictions from DSS at two different factorization scales.  The points are placed at the average Pt for a bin.  As you can see on in panel c) the measured cross section agrees well with theory for both DSS and KKP FFs.