A New Look at Higgs Constraints on Stops

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.Comment: v2: references added, accepted by JHE

Electric Dipole Moments in Natural Supersymmetry

We discuss electric dipole moments (EDMs) in the framework of CP-violating natural supersymmetry (SUSY). Recent experimental results have significantly tightened constraints on the EDMs of electrons and of mercury, and substantial further progress is expected in the near future. We assess how these results constrain the parameter space of natural SUSY. In addition to our discussion of SUSY, we provide a set of general formulas for two-loop fermion EDMs, which can be applied to a wide range of models of new physics. In the SUSY context, the two-loop effects of stops and charginos respectively constrain the phases of $A_t \mu$ and $M_2 \mu$ to be small in the natural part of parameter space. If the Higgs mass is lifted to 125 GeV by a new tree-level superpotential interaction and soft term with CP-violating phases, significant EDMs can arise from the two-loop effects of $W$ bosons and tops. We compare the bounds arising from EDMs to those from other probes of new physics including colliders, $b \to s \gamma$, and dark matter searches. Importantly, improvements in reach not only constrain higher masses, but require the phases to be significantly smaller in the natural parameter space at low mass. The required smallness of phases sharpens the CP problem of natural SUSY model building.Comment: 37 pages plus appendices, 16 figures; v2: journal versio

Top Partners at the LHC: Spin and Mass Measurement

If one takes naturalness seriously and also assumes a weakly coupled extension of the Standard Model (SM) then there are predictions for phenomenology that can be inferred in a model independent framework. The first such prediction is that there must be some colored particle with mass O(TeV) that cancels the top loop contribution to the quadratic divergence of the Higgs mass. In this paper we begin a model independent analysis of the phenomenology of this "top partner," t'. We make one additional assumption that it is odd under a parity which is responsible for the stability of a WIMP dark matter candidate, N. We focus on three questions to be explored at the LHC: discovery opportunities, mass determination, and spin determination of this top partner. We find that within a certain region of masses for the t' and N, t'\bar{t'} is easily discovered in the t\bar{t}+2N decay with the tops decaying fully hadronically. We show that without having to rely on other channels for new physics that for a a given t' spin the masses of t' and N can be measured using kinematic information (e.g. average MET or H_T) and total cross section. A degeneracy due to the spin remains, but with several hundred inverse fb of luminosity we demonstrate potentially useful new methods for determining the t' spin over a wide range of masses. Our methods could be useful for distinguishing supersymmetric and non-supersymmetric models.Comment: 28 pages, 5 figure

The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff

We study ultraviolet cutoffs associated with the Weak Gravity Conjecture (WGC) and Sublattice Weak Gravity Conjecture (sLWGC). There is a magnetic WGC cutoff at the energy scale $e G_N^{-1/2}$ with an associated sLWGC tower of charged particles. A more fundamental cutoff is the scale at which gravity becomes strong and field theory breaks down entirely. By clarifying the nature of the sLWGC for nonabelian gauge groups we derive a parametric upper bound on this strong gravity scale for arbitrary gauge theories. Intriguingly, we show that in theories approximately saturating the sLWGC, the scales at which loop corrections from the tower of charged particles to the gauge boson and graviton propagators become important are parametrically identical. This suggests a picture in which gauge fields emerge from the quantum gravity scale by integrating out a tower of charged matter fields. We derive a converse statement: if a gauge theory becomes strongly coupled at or below the quantum gravity scale, the WGC follows. We sketch some phenomenological consequences of the UV cutoffs we derive.Comment: 50 pages, 5 figures. v2: references added, clarified remarks about Higgsin

Continuum-Mediated Dark Matter-Baryon Scattering

Many models of dark matter scattering with baryons may be treated either as a simple contact interaction or as the exchange of a light mediator particle. We study an alternative, in which a continuum of light mediator states may be exchanged. This could arise, for instance, from coupling to a sector which is approximately conformal at the relevant momentum transfer scale. In the non-relativistic effective theory of dark matter-baryon scattering, which is useful for parametrizing direct detection signals, the effect of such continuum mediators is to multiply the amplitude by a function of the momentum transfer q, which in the simplest case is just a power law. We develop the basic framework and study two examples: the case where the mediator is a scalar operator coupling to the Higgs portal (which turns out to be highly constrained) and the case of an antisymmetric tensor operator ${\cal O}_{\mu \nu}$ that mixes with the hypercharge field strength and couples to dark matter tensor currents, which has an interesting viable parameter space. We describe the effect of such mediators on the cross sections and recoil energy spectra that could be observed in direct detection.Comment: 30 pages, 6 figures. v2: minor changes, references adde