Collider constraints on tuning in composite Higgs models

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.