# Combining two constraints in a number counting experiment

Dear all,

I have a technical problem regarding the combination of the constraints on the number of background events from different auxiliary measurements.

Let me denote the background in the signal-like region by bkgd_3

Using a kind of ABCD method this background is constrained to be tau*bkgd_2 where bkgd_2 is the background of an auxiliary measurement (again number counting experiment). And I don’t want to move the tau to the auxiliary measurement

On the other hand I have two additional constraints for a part of bkgd_3 so bkgd_3 is a sum of three backgrounds (x1 + x2 + x3). x1 and x2 are constrained by auxiliary measurements

So given that this is a number counting experiment I would model my pdf by a poisson taking bkgd_3 + s as mean.

So if I had just one constraint I would either define bkgd_3 as RooProduct or as RooAddition (if I would move the tau to the auxiliar measurement of bkgd_2 it would also be trivial to do, but as said I would like to know how to do it without moving tau)

I imagine that it is a trivial problem to combine the two but I couldn’t figure out how to do it.
So please let me know if you have an idea.

Thanks!