Carragher, E.Goh, K.Su, W.White, M.Williams, A.G.2025-02-122025-02-122024The Journal of High Energy Physics, 2024; 2024(8):185-0-185-471029-84791029-8479https://hdl.handle.net/2440/143693We 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) → SO(4) symmetry breaking pattern. We consider two models with the τ 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 3σ level at scales of < 5TeV. From a Bayesian viewpoint of naturalness the model with leptons in the 14 and 10 representations is preferred over those in the 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.enOpen Access, © The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.Compositeness; Hierarchy Problem; Specific BSM PhenomenologyJournal article10.1007/jhep08(2024)185704846Goh, K. [0000-0002-5991-2704]White, M. [0000-0001-5474-4580]Williams, A.G. [0000-0002-1472-1592]