Abstract
We present a simple new way to visualize the constraints of Higgs coupling measurements on light stops in natural SUSY scenarios beyond the MSSM, which works directly in the plane of stop mass eigenvalues (with no need to make assumptions about mixing angles). For given stop mass eigenvalues, the smallest value of $X_t$ that can bring the correction to the $h \to gg$ and $h\to \gamma\gamma$ couplings into agreement with data is computed. Requiring that this $X_t$ is consistent--i.e. that the chosen mass eigenvalues can be the outcome of diagonalizing a matrix with a given off-diagonal term--rules out the possibility that both stops have a mass below $\approx$ 400 GeV. Requiring that $X_t$ is not fine-tuned for agreement with the data shows that neither stop can be lighter than $\approx$ 100 GeV. These constraints are interesting because, unlike direct searches, they apply no matter how stops decay, and suggest a minimum electroweak fine-tuning of between a factor of 5 and 10. We show that a multi-parameter fit can slightly weaken this conclusion by allowing a large Higgs coupling to $b$-quarks, but only if a second Higgs boson is within reach of experiment. Certain models, like $R$-symmetric models with Dirac gauginos, are much more strongly constrained because they predict negligible $X_t$. We illustrate how the constraints will evolve given precise measurements at future colliders (HL-LHC, ILC, and TLEP), and comment on the more difficult case of Folded Supersymmetry.
Highlights
Our main innovation, relative to earlier studies of Higgs constraints on stops, is to provide a two-dimensional plot that clearly shows how the measured Higgs properties constrain the amount of fine-tuning arising in the stop sector
We present a simple new way to visualize the constraints of Higgs coupling measurements on light stops in natural SUSY scenarios beyond the MSSM, which works directly in the plane of stop mass eigenvalues
This is a further important motivation for searching for heavy Higgs bosons: tighter constraints on their masses turn into tighter constraints on stops from the Higgs fit. (Further naturalness arguments for searching for the heavy Higgs bosons may be found in ref. [39].) We conclude our look at stop constraints in section 3.4 by showing that the ILC or TLEP would significantly extend the excluded region of stop masses by performing accurate measurements of Higgs couplings
Summary
We comment on notation: we define the modifications to the Higgs couplings to SM particles as ri. The low-energy theorem asserts that the loop correction from a particle with mass M (v) is ∝ ∂ log M 2(v)/∂ log v; the mixing contributes negatively because a larger Higgs vev would mean a larger off-diagonal term and would decrease the lightest stop mass. These have received a great deal of recent attention because Dirac gluinos ameliorate the “second-order naturalness problem” of the gluino mass lifting the stop mass through RGEs [43,44,45,46] (though see [4, 47] for a less sanguine take) In such models, the experimental constraint from Higgs data on stop masses will be much stronger, because we no longer have the freedom to cancel a positive contribution against a negative one from mixing. We will illustrate this stronger constraint on R-symmetric models below
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