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Theories of physics beyond the Standard Model that address the hierarchyproblem generally involve top partners, new particles that cancel the quadraticdivergences associated with the Yukawa coupling of the Higgs to the top quark.With extensions of the Standard Model that involve new colored particles comingunder strain from collider searches, scenarios in which the top partners carryno charge under the strong interactions have become increasingly compelling.Although elusive for direct searches, these theories predict modified couplingsof the Higgs boson to the Standard Model particles. This results in correctionsto the Higgs production and decay rates that can be detected at the LargeHadron Collider (LHC) provided the top partners are sufficiently light, and thetheory correspondingly natural. In this paper we consider three theories thataddress the little hierarchy problem and involve colorless top partners,specifically the Mirror Twin Higgs, Folded Supersymmetry, and the Quirky LittleHiggs. For each model we investigate the current and future bounds on the toppartners, and the corresponding limits on naturalness, that can be obtainedfrom the Higgs program at the LHC. We conclude that the LHC will not be able tostrongly disfavor naturalness, with mild tuning at the level of about one partin ten remaining allowed even with 3000 fb$^{-1}$ of data at 14 TeV.

Colorless Top Partners, a 125 GeV Higgs, and the Limits on Naturalness