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

We perform the first convergent Bayesian global fits of 4D Composite Higgs Models with partially-composite third generation quarks and leptons based on the minimal $SO(5) \rightarrow SO(4)$ symmetry breaking pattern. We consider two models with the $\tau$ lepton and its associated neutrino in different representations of $SO(5)$. Fitting each model with a wide array of experimental constraints allows us to analyse the Bayesian evidence and currently-observed fine-tuning of each model by calculating the Kullback-Leibler divergence between their respective priors and posteriors. Notably both models are found to be capable of satisfying all constraints simultaneously at the $3\sigma$ level at scales of $< 5$ TeV. From a Bayesian viewpoint of naturalness the model with leptons in the $\mathbf{14}$ and $\mathbf{10}$ representations is preferred over those in the $\mathbf{5}$ representation due to its lower fine-tuning. Finally, we consider the experimental signatures for the preferred parameters in these models, including lepton partner decay signatures and gluon-fusion produced Higgs signal strengths, and discuss their potential phenomenology at future high-luminosity LHC runs.