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We perform the first convergent Bayesian global fits of 4D Composite HiggsModels with partially-composite third generation quarks and leptons based onthe minimal $SO(5) \rightarrow SO(4)$ symmetry breaking pattern. We considertwo models with the $\tau$ lepton and its associated neutrino in differentrepresentations of $SO(5)$. Fitting each model with a wide array ofexperimental constraints allows us to analyse the Bayesian evidence andcurrently-observed fine-tuning of each model by calculating theKullback-Leibler divergence between their respective priors and posteriors.Both models are found to be capable of satisfying all constraints at the$3\sigma$ level, although the model with leptons in the $\mathbf{14}$ and$\mathbf{10}$ representations is strongly preferred over those in the$\mathbf{5}$ representation from a Bayesian viewpoint. Finally, we consider theexperimental signatures for the preferred parameters in these models, includinglepton partner decay signatures and gluon-fusion produced Higgs signalstrengths, and discuss their potential phenomenology at future high-luminosityLHC runs.

Extending Global Fits of 4D Composite Higgs Models with Partially Composite Leptons