Estimation of systematic uncertainty in the final result due to the uncertainty in the particle selection cuts.

Question

Let us consider a case where there is a polynomial background underneath a Gaussian signal. This is a typical case while selecting neutral pion from the invariant mass of two photons; the polynomial background appears due to uncorrelated combinatorial two photons. Typically the neutral pion is then selected by using about  \(Mean \pm 2.5\sigma\) of the Gaussian and the background is subtracted by various techniques. The question is: how to estimate the systematic uncertainty in the final result due to the aforementioned selection cuts? Here is what is commonly done, at least by the 300 members of my collaboration, which I think is wrong: Calculate the results with \(Mean \pm 2\sigma\) and \(Mean \pm 3\sigma\) and take the difference as the estimated systematic uncertainty in the final result due to the particle selection cuts. In my opinion this way of estimation does not measure the bias in the final result due to the particle selection cuts but measures the inherent statistical fluctuation in the final result due to the two particle selection cuts. Could you please suggest some other techniques with arguments.