We explore naturalness constraints on the masses of the heavy Higgs bosons H 0 , H ± , and A 0 in supersymmetric theories. We show that, in any extension of MSSM which accommodates the 125 GeV Higgs at the tree level, one can derive an upper bound on the SUSY Higgs masses from naturalness considerations. As is well-known for the MSSM, these bounds become weak at large tan β. However, we show that measurements of b → sγ together with naturalness arguments lead to an upper bound on tan β, strengthening the naturalness case for heavy Higgs states near the TeV scale. The precise bound depends somewhat on the SUSY mediation scale: allowing a factor of 10 tuning in the stop sector, the measured rate of b → sγ implies tan β ∼ < 30 for running down from 10 TeV but tan β ∼ < 4 for mediation at or above 100 TeV, placing m A near the TeV scale for natural EWSB. Because the signatures of heavy Higgs bosons at colliders are less susceptible to being "hidden" than standard superpartner signatures, there is a strong motivation to make heavy Higgs searches a key part of the LHC's search for naturalness. In an appendix we comment on how the Goldstone boson equivalence theorem links the rates for H → hh and H → Z Z signatures. A H → hh, H → Z Z, and Goldstone equivalence: a comment on branching ratiosOne interesting search channel for a heavy Higgs is H → hh, which is particularly appealing since the Standard Model rate for events with two Higgs bosons is very small [98,[105][106][107][108][109][110][111][112].On the other hand, the dominant Higgs decay is to bb, a challenging signal to pull out of background. Given that the very clean h → Z Z * → 4 channel played a key role in the discovery of the 125 GeV Higgs boson, it is interesting to ask when, and to what extent, the H → hh decay mode dominates over H → Z Z. Answers to this question may be extracted from the literature,

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 O µν 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.

We study the classical color radiation from very high energy collisions that produce colored particles. In the extreme high energy limit, the classical color fields are confined to a light-shell expanding at c and are associated with a non-linear σ-model on the 2D light-shell with specific symmetry breaking terms. We argue that the quantum version of this picture exhibits asymptotic freedom and may be a useful starting point for an effective light-shell theory of the structure between the jets at a very high energy collider.

We discuss our work toward the construction of a light-shell effective theory (LSET), an effective field theory for describing the matter emerging from high-energy collisions and the accompanying radiation. We work in the highly simplified venue of 0flavor scalar quantum electrodynamics, with a gauge invariant product of scalar fields at the origin of space-time as the source of high-energy charged particles. Working in this simple gauge theory allows us to focus on the essential features of LSET. We describe how the effective theory is constructed and argue that it can reproduce the full theory tree-level amplitude. We study the 1-loop radiative corrections in the LSET and suggest how the leading double-logs in the full theory at 1-loop order can be reproduced by a purely angular integral in the LSET.

We derive the photon propagator in light-shell gauge (LSG), introduced in [1] in the context of light-shell effective theory.