Person:

Georgi, Howard

We discuss an alternative to the topcolor seesaw mechanism. In our scheme, all the light quarks carry topcolor, and there are many composit e SU(2) doublets. This makes it possible to get the observed t quark mass and observed SU(2) × U(1) breaking in a way that is quite different from the classic seesaw mechanism. We discuss a model of this kind that arises naturally in the context of dynamically broken topcolor. There are many composite scalars in a theory of this kind. This has important effects on the Pagels-Stokar relation and the Higgs mass. We find mHiggs ∼< 330 GeV, lighter than in typical topcolor models. We also show that the electroweak singlet quarks in such a model can be lighter than the corresponding quarks in a seesaw model.

The top quark seesaw mechanism offers a method for constructing a composite Higgs field without the usual difficulties that accompany traditional technicolor or topcolor theories. The focus of this article is to study the phenomenology of the new physics required by this mechanism. After establishing a set of criteria for a plausible top quark seesaw theory, we develop two models, the first of which has a heavy weak singlet fermion with hypercharge 43 while the secon has, in addition, a heavy weak singlet hypercharge −23 fermion. At low energies, these theories contain one or two Higgs doublets respectively. We then derive the low energy effective Higgs potential in detail for the two-doublet theory as well as study the likely experimental signatures for both theories. A strong constraint on the one-doublet model is the measured value of the ρ parameter which permits the new heavy fermion to have a mass of about 5–7 TeV, when the Higgs has a mass greater than 300 GeV. In the two-doublet model, mixing of the new heavy Y = − 23 fermion and the b quark affects the prediction for R b. In order to agree with the current limits on R b, the mass of this fermion should be at least 12 TeV. The mass of the heavy Y = 43 fermion in the two-doublet model is not as sharply constrained by experiments and can be as light as 2 .5 TeV.

Motivated by recent works on “Higgsless theories,” I discuss an SU(2) 0 × SU(2) N × U(1) gauge theory with arbitrary bifundamental (or custodia l SU(2) preserving) symmetry breaking between the gauge subgroups and with ordinary matter transforming only under the U(1) and SU(2) 0. When the couplings, gj, of the other SU(2)s are very large, this reproduces the standard model at the tree level. I calculate the W and Z masses and other electroweak parameters in a perturbative expansion in 1/g 2j, and give physical interpretations of the results in a mechanical analog built out of masses and springs. In the mechanical analog, it is clear that even for arbitrary patterns of symmetry breaking, it is not possible (in the perturbative regime) to raise the Higgs mass by a large factor while keeping the S parameter small.

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 0-flavor 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.

We discuss exact results for the full nonperturbative effective superpotentials of four dimensional N = 1 supersymmetric U (N) gauge theories with additional chiral superfield in the adjoint representation and the free energies of the related zero dimensional bosonic matrix models with polynomial potentials in the planar limit using the Dijkgraaf-Vafa matrix model prescription and integrating in and out. The exact effective superpotentials are produced including the leading Veneziano-Yankielowicz term directly from the matrix models. We also discuss how to use integrating in and out as a tool to do random matrix integrals in the large N limit.

We summarize our findings on the quantum moduli constraints and superpotentials of an infinite family of moose extensions of n f = n c SUSY QCD. For n c = 2, we perform concrete calculations using traditional integrating out techniques as well as Intriligator’s “integrating in” technique. Checking the constraints and superpotentials in the limits of setting Λ’s to zero or integrating out mass terms, we find that the quantum moduli constraints are local in theory space and are equivalent to a consistent structure of “splitting relations” amongst the different theories. Extending the results to arbitrary nc, we show that the splitting relations, along with a set of rules for flowing from a high energy theory to a low energy theory, incorporate much of the physics of the moose chain. The relations can be used both to simplify perturbative calculations of symmetry breaking and to incorporate nonperturbative effects.

We present examples of four dimensional, non-supersymmetric field theories in which ultraviolet supersymmetry breaking effects, such as bose-fermi splittings and the vacuum energy, are suppressed by (α/4π) N , where α is a weak coupling factor and N can be made arbitrarily large. The particle content and interactions of these models are conveniently represented by a graph with sites and links, describing the gauge theory space structure. While the theories are supersymmetric “locally” in theory space, supersymmetry can be explicitly broken by topological obstructions.

We note that orbifold boundary conditions that produce chiral fermion zero modes in compactified higher dimensional theories may distort scalar field vacuum expectation values, giving rise to nontrivial dependence on the extra dimensions. We illustrate this in a simple five dimensional model which has chiral fermion zero-modes stuck to fat branes. The model could provide a simple and explicit realization of the separation of quarks and leptons in the fifth dimension. We discuss the KK expansion in some detail. We find that there are in general non-zero-mode states stuck to the brane, like the chiral zero modes. We see explicitly the transition from states dominated by the internal structure of the fat brane to those dominated by the compactification.

We study electroweak symmetry breaking involving the seesaw mechanism of quark condensation. These models produce a composite Higgs boson involving the left-handed top quark, yet the top mass arises naturally at the observed scale. We describe a schematic model which illustrates the general dynamical ideas. We also consider a generic low-energy effective theory which includes several composite scalars, and we use the effective potential formalism to compute their spectrum. We develop a more detailed model in which certain features of the schematic model are replaced by additional dynamics.