Abstract
Two potential sources of tuning exist in composite Higgs models: one comes from keeping the Higgs VEV below the compositeness scale and one comes from keeping the Higgs light after constraints on the top partner masses are applied. We construct a measure that determines whether these tunings are independent or not and combines them appropriately. We perform a comprehensive scan of the parameter space for three explicit models and report the minimum tuning values compatible with existing collider constraints. Tuning values are given as functions of resonance masses and deviations to the Higgs couplings so the effect of future constraints can easily be quantified. The current minimum tuning in the minimal model is 2.5-5% and will be decreased to around 0.8-3.3% if no top partners are observed over the lifetime of the LHC
Highlights
A compositeness scale significantly higher than the electroweak scale, protection from physics at higher scales is not worth what it once was and most models reproducing the correct electroweak scale are expected to be tuned [6].1 The main aims of this paper are to find out just how tuned composite Higgs models are and how this will change after future collider experiments
Two potential sources of tuning exist in composite Higgs models: one comes from keeping the Higgs VEV below the compositeness scale and one comes from keeping the Higgs light after constraints on the top partner masses are applied
The machinations taking a parameter point to a Higgs VEV and mass are not invertible so we could be left with a costly scanning problem, especially if we want to be convinced that we have sufficient coverage of the parameter space for the tuning values we find to be representative
Summary
A compositeness scale significantly higher than the electroweak scale, protection from physics at higher scales is not worth what it once was and most models reproducing the correct electroweak scale are expected to be tuned [6].1 The main aims of this paper are to find out just how tuned composite Higgs models are and how this will change after future collider experiments. Our results comprise a set of overall tuning values as functions of phenomenologically interesting parameters: top partner masses, charged vector-boson resonance masses, deviations to the Higgs couplings, and the compositeness scale. We derive these for three explicit models. The 5-5 model is the simplest, the 14-14 model is a slightly more involved model but allows for lower tuning, and the 14-1 model accommodates a fully-composite right-handed top quark From this data we find minimal values for the tuning compatible with current collider constraints on the top partner masses and deviations to the Higgs couplings, and we project how the tuning will worsen if no new physics is seen in the imminent future. In all three models the double tuning associated with simultaneously getting a light enough Higgs and the correct VEV is the main contribution
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