Bayesian inference to study a signal with two or more decaying particles in a non-resonant background

We study the application of a Bayesian method to extract relevant information from data for the case of a signal consisting of two or more decaying particles and its background. The method takes advantage of the dependence that exists in the distributions of the decaying products at the event-by-event level and processes the information for the whole sample to infer the mixture fraction and the relevant parameters for signal and background distributions. The algorithm usually needs a numerical computation of the posterior, which we work out explicitly in a benchmark scenario of a simplified $pp\to hh \to b\bar b \gamma \gamma$ search. We perform a posterior predictive check on the results and we show how the signal fraction is correctly extracted from the sample, as well as many parameters in the signal and background distributions. The presented framework could be used for other searches such as $pp\to ZZ,\ WW,\ ZW$ and pair of Leptoquarks, among many others.