Inferring flavor mixtures in multijet events

Multijet events with heavy-flavors are of central importance at the LHC since many relevant processes -- such as $t\bar t$, $hh$, $t\bar t h$ and others -- have a preferred branching ratio for this final state. Current techniques for tackling these processes use hard-assignment selections through $b$-tagging working points, and suffer from systematic uncertainties because of the difficulties in Monte Carlo simulations. We develop a flexible Bayesian mixture model approach to simultaneously infer $b$-tagging score distributions and the flavor mixture composition in the dataset. We model multidimensional jet events, and to enhance estimation efficiency, we design structured priors that leverages the continuity and unimodality of the $b$-tagging score distributions. Remarkably, our method eliminates the need for a parametric assumption and is robust against model misspecification -- It works for arbitrarily flexible continuous curves and is better if they are unimodal. We have run a toy inferential process with signal $bbbb$ and backgrounds $bbcc$ and $cccc$, and we find that with a few hundred events we can recover the true mixture fractions of the signal and backgrounds, as well as the true $b$-tagging score distribution curves, despite their arbitrariness and nonparametric shapes. We discuss prospects for taking these findings into a realistic scenario in a physics analysis. The presented results could be a starting point for a different and novel kind of analysis in multijet events, with a scope competitive with current state-of-the-art analyses. We also discuss the possibility of using these results in general cases of signals and backgrounds with approximately known continuous distributions and/or expected unimodality.