Higgs-precision constraints on colored naturalness

The presence of weak-scale colored top partners is among the simplest solutions to the Higgs hierarchy problem and allows for a natural electroweak scale. We examine the constraints on generic colored top partners coming solely from their effect on the production and decay rates of the observed Higgs with a mass of 125 GeV. We use the latest Higgs precision data from the Tevatron and the LHC as of EPS 2017 to derive the current limits on spin-0, spin-1/2, and spin-1 colored top partners. We also investigate the expected sensitivity from the Run 3 and Run 4 of the LHC, as well from possible future electron-positron and proton-proton colliders, including the ILC, CEPC, FCC-ee, and FCC-hh. We discuss constraints on top partners in the Minimal Supersymmetric Standard Model and Little Higgs theories. We also consider various model-building aspects - multiple top partners, modified couplings between the Higgs and Standard-Model particles, and non-Standard-Model Higgs sectors - and evaluate how these weaken the current limits and expected sensitivities. By modifying other Standard-Model Higgs couplings, we find that the best way to hide low-mass top partners from current data is through modifications of the top-Yukawa coupling, although future measurements of top-quark-pair production in association with a Higgs will extensively probe this possibility. We also demonstrate that models with multiple top partners can generically avoid current and future Higgs precision measurements. Nevertheless, some of the model parameter space can be probed with precision measurements at future electron-positron colliders of, for example, the e(+) e(-) -> Zh cross section.