The last piece of the invariant mass distribution is the combinatoric background. This is the result of combining two non-daughter photons into a pion candidate. Since each photon in an event is mixed with each other photon in an attempt to find true pions, we will find many of these combinatoric candidates. Below is a slide from a recent presentation describing the source of this background and how it is modeled.

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As it says above we take photons from different events, rotate them so as to line up the jet axes from the two events, and then combine them to pion candidates. We can then run the regular pion finder over the events and plot out the mass distribution from these candidates. The result can be seen below.

These distributions will be later combined with the other pieces and normalized to the data. For those who are interested in the errors on these plots please see below.