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authortlatorre <tlatorre@uchicago.edu>2019-09-24 12:40:50 -0500
committertlatorre <tlatorre@uchicago.edu>2019-09-24 12:40:50 -0500
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update shower position distribution parameters for muons
This commit updates the a and b parameters for the gamma distribution used to describe the position distribution of shower photons produced along the direction of the muon. Previously I had been assuming b was equal to the radiation length and using a formula from the PDG to calculate a from that. However, this formula doesn't seem to be valid for muons (the formula comes from a section describing the shower profile of electrons and gammas, so it's not surprising). Therefore, now we don't assume any relationship between a and b. Now, the value of a is approximated by a constant since I couldn't find any functional relationship as a function of energy to describe a very well (and it's approximately constant), and b is approximated by a single degree polynomial fit to the values I got from simulating muons in RAT-PAC as a function of energy. Note that looking at the simulation data it seems like the position distribution of shower photons from muons isn't even very well described by a gamma distribution, so in the future it might be a good idea to come up with a better parameterization. Even if I stick with the gamma distribution, it would be good to revisit this in the future and fit for a and b over a wider range of energies.
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