Bayesian and Frequentist Global Fits of Minimal 4D Composite Higgs Models

Abstract

Since the famous discovery of the Higgs boson at the Large Hadron Collider (LHC) in 2012, the field of elementary particle physics has been at an impasse. Ever more precise measurements of the particle's properties have served only to verify the predictions of the current prevalent theory - the Standard Model (SM) of particle physics - even though this theory is known to be incomplete. However, the SM is only able to properly describe the observed boson with an incredibly unnatural finetuning of its parameters, which has led many to propose alternative models that can more naturally accommodate the particle in the hope of establishing a more complete theory. We concern ourselves in this work with one class of such models, in which the Higgs boson is not an elementary particle as is assumed by the SM, but rather a bound state of some as-yet undiscovered strong dynamics. We give a pedagogical introduction to the theory of such composite Higgs models (CHMs), and provide a complete description of three different versions of the Two-Site Minimal 4D CHM - the simplest calculable extensions of the SM in which the Higgs boson is composite, based on the SO(5) ! SO(4) symmetry breaking pattern - that differ in their fermion sector embeddings. Convergent global fits are performed on these three models, under both frequentist and Bayesian frameworks, in order to end the regions of their parameter spaces that best fit a wide range of constraints, including recent Higgs measurements and exclusion bounds on heavy resonance production from Run II of the LHC. We use a novel technique to analyse the finetuning of the models, quantifying the tuning as the Kullback-Leibler divergence from the prior to the posterior probability on the parameter space. Each model is found to be able to satisfy all constraints at the 3 level simultaneously, but the model that has fermions embedded in the fundamental representation of SO(5), despite suffering from a \double tuning", is clearly favoured by a Bayesian model comparison. As a by-product of the fits, we analyse the collider phenomenology of our models in these viable regions. We find clear predictions of the minimally-tuned models that the gg ! H ! cross section is less than -90% that predicted by the SM, which is already in slight tension with experiment and could potentially be ruled out in the future high-luminosity run of the LHC. In addition, the lightest fermions F arising from the new strong dynamics in these models are seen in general to lie between -1:1 TeV and -3:0 TeV, with the F -> tW+ and F ->bW+ decays offering particularly promising channels for probing these models in future collider searches.