Colorless top partners, a 125 GeV Higgs boson, and the limits on naturalness

Theories of physics beyond the standard model that address the hierarchy problem generally involve top partners, new particles that cancel the quadratic divergences associated with the Yukawa coupling of the Higgs boson to the top quark. With extensions of the standard model that involve new colored particles coming under strain from collider searches, scenarios in which the top partners carry no charge under the strong interactions have become increasingly compelling. Although elusive for direct searches, these theories predict modified couplings of the Higgs boson to the standard model particles. This results in corrections to the Higgs production and decay rates that can be detected at the LHC provided the top partners are sufficiently light, and the theory correspondingly natural. In this paper we consider three theories that address the little hierarchy problem and involve colorless top partners, specifically the mirror twin Higgs, folded supersymmetry, and the quirky little Higgs. For each model we investigate the current and future bounds on the top partners, and the corresponding limits on naturalness, that can be obtained from the Higgs program at the LHC. We conclude that the LHC will not be able to strongly disfavor naturalness, with mild tuning at the level of about one part in ten remaining allowed even with $3000\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data at 14 TeV.