I am trying to make a PDF of a narrow resonance convoluted by a quite broad resolution. The resolution is (roughly) a sum of two Gaussians, one with ~6MeV and one with ~14MeV. The narrow one makes up about 80% and the wide one makes up 20%. I convolute a RooBreitWigner with this function (made using RooAddPdf) and then generate data from it.
Given that the BreitWigner has a very small width, I expect that the convoluted PDF looks very similar to the resolution function. What I find is that the convoluted PDF has a much larger fraction of the wide Gaussian compared to the Resolution function, and disagrees completely. This behaviour surprised me as the physics PDF can be considered as a delta function compared to the resolution.
Attached is a very simple script which reproduces the problem, could anyone tell me if I am configuring the PDF incorrectly or if this behaviour is somehow expected?