Developing an Analysis Framework in Julia for Bayesian Uncertainty Quantification for the Mu2e Experiment

The Mu2e experiment at Fermilab aims to observe the extremely rare process of muon-to-electron conversion in the presence of a nucleus, without the emission of neutrinos, a signal of physics beyond the Standard Model. With a predicted probability lower than 10^-16, detecting such an event is a major challenge, requiring precise statistical tools to differentiate true signals from large background noise sources.
We develop a Bayesian analysis framework in Julia using BAT.jl (Bayesian Analysis Toolkit), which employs Markov Chain Monte Carlo (MCMC) methods to perform parameter estimation in the Mu2e dataset(s). Our model incorporates the key signal and background components of the energy spectra of electrons. We specifically focus on the role of the nuisance parameters in evaluating the discovery sensitivity or upper limits on the muon-to-electron conversion rate.