As we move forward with the unfolding, we'd like to use a power law as a prior.  So here are 4 spectra from Pythia fitted with power laws (that way we have a reasonable estimate of what the default parameters should be in the prior).

Here are the parameters organized into a table:

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To get a better fit, here're the same spectra fit over a smaller range: the pi0 spectra are fit over 'pTjet = 2 - 20' GeV/c and the gamma-direct spectra are fit over 'pTjet = 2' GeV/c to the upper limit of the trigger eT.

And in a table:

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To get an even better fit, I restricted the fit range further.  Below I fit each spectrum with a power law over 'pTjet = 2' GeV/c to either the upper limit on the trigger 'pT' (for the pi0 case) or the lower limit on the trigger 'pT' (for the gamma-direct case).

And in a table: