I am working on an LHCb experiment, in particular the $B^0 \rightarrow K^{*0} \gamma$ decay.
The $K^{*0}$ decays into $K^+$ and $\pi^-$. So the decay products of the decay are $\gamma, K^+ $and $ \pi^-$ (and their antiparticles in case of an $\overline{B^0}$ decay).
The mass is reconstructed in the following way: the 4-momenta of the decay products are summed together to get the total 4-momentum $p^{\mu}_{B^0} $ : $p^{\mu}p_{\mu}$ then gives the invariant mass squared, $(mc^2)^2$.
From the uncertainties of the detectors, I can propagate the uncertainty on the reconstructed mass of every single event (i.e. every single collection of $\gamma, K^{+} $ and $\pi^-$).
When we make a histogram of all the events (5,000,000+), I get this:
And I want to estimate, beforehand, what the spread in the signal peak should be. How can I do this?