Simultaneous fit with background only control sample


I am trying to fit a background polynomial and some signal from a given histogram using RooChevychevPdf and RooHistPdf.
The idea is to simultaneously fit a control sample with the polynomial only, and a “physics” sample with the same polynomial +musignal_histogram, where mu is some “strength” parameter of interest.
I can’t find a way to make sure the fit for the physics sample is polynomial +mu
signal_histogram where the polynomial is exactly the same as the fitted control polynomial (up to scale), such that where the histogram is zero, both the control fit and the “physics” fit will give the same result for the same bin count.
Is there a way to do it?
I tried using RooAddPdf with f as the parameter, but then I have f*polynomial+(1-f)signal for the physics sample and just 1polynomial for the control sample, which gives different results where the signal is zero (assuming f isn’t 1).

I would really appreciate your help.

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