In this talk I discuss theories of dynamical electroweak symmetry breaking, with emphasis on the implications of a heavy top-quark on the weak-interaction $\rho$ parameter.

Since the pioneering work of Eichten and Lane it has been known that the scale of the interactions responsible for the generation of the strange-quark mass in extended technicolor theories must, absent any Glashow-Iliopoulos-Maiani mechanism for suppressing flavor-changing neutral currents, be greater than of order 1000 TeV. In this paper we point out that the constraint from the neutral D-meson system is now equally strong, implying that the charm quark mass must also arise from flavor dynamics at a scale this high. We then quantify the degree to which the technicolor condensate must be enhanced in order to yield the observed quark masses, if the extended technicolor scale is of order 1000 TeV. Our results are intended to provide a framework in which to interpret and apply the results of lattice studies of conformal strongly interacting gauge theories, and the corresponding numerical measurements of the anomalous dimension of the mass operator in candidate theories of walking technicolor. © 2010 The American Physical Society.

The triviality of the scalar sector of the standard one-doublet Higgs model implies that it is only an effective low-energy theory valid below some cut-off scale A. In this note we show that the experimental constraint on the amount of custodial symmetry violation, |Δρ*| = α|Τ| ≤ 0.4%, implies that the scale Λ must be greater than of order 7.5 TeV. For theories defined about the infrared-stable Gaussian fixed-point, we estimate that this lower bound on ΛA yields an upper bound of approximately 550 GeV on the Higgs boson's mass, independent of the regulator chosen to define the theory. We also show that some regulator schemes, such as higher-derivative regulators, used to define the theory about a different fixed-point are particularly dangerous because an infinite number of custodial-isospin-violating operators become relevant.

Technicolor and other theories of dynamical electroweak symmetry breaking invoke chiral symmetry breaking triggered by strong gauge-dynamics, analogous to that found in QCD, to explain the observed W, Z, and fermion masses. In this talk we describe why a realistic theory of dynamical electroweak symmetry breaking must, relative to QCD, produce an enhanced fermion condensate. We quantify the degree to which the technicolor condensate must be enhanced in order to yield the observed quark masses, and still be consistent with phenomenological constraints on flavor-changing neutral-currents. Lattice studies of technicolor and related theories provide the only way to demonstrate that such enhancements are possible and, hopefully, to discover viable candidate models. We comment briefly on the current status of non-perturbative investigations of dynamical electroweak symmetry breaking, and provide a "wish-list" of phenomenologically-relevant properties that are important to calculate in these theories

Motivated by models of holographic technicolor, we discuss a four-site deconstructed Higgsless model with nontrivial wave function mixing. We compute the spectrum of the model, the electroweak triple gauge-boson vertices, and, for brane-localized fermions, the electroweak parameters to O(MW2/Mρ2). We discuss the conditions under which αS vanishes (even for brane-localized fermions) and the (distinct but overlapping) conditions under which the phenomenologically interesting decay a1→Wγ is nonzero and suppressed by only one power of (MW/Mρ). © 2008 The American Physical Society.

LHC searches for the standard model Higgs Boson in γγ or ττ decay modes place strong constraints on the light technipion state predicted in technicolor models that include colored technifermions. Compared with the standard Higgs Boson, the technipions have an enhanced production rate (largely because the technipion decay constant is smaller than the weak scale) and also enhanced branching ratios into di-photon and di-tau final states (largely due to the suppression of WW decays of the technipions). These factors combine to make the technipions more visible in both channels than a standard model Higgs would be. Hence, the recent ATLAS and CMS searches for Higgs bosons exclude the presence of technipions with masses from 110GeV to nearly 2m t in technicolor models that (a)include colored technifermions (b)feature topcolor dynamics and (c)have technicolor groups with three or more technicolors (N TC3). For certain models, the limits also apply out to higher technipion masses or down to the minimum number of technicolors (N TC=2). The limits may be softened somewhat in models where extended technicolor plays a significant role in producing the top quark's mass. Additional LHC data on di-tau and di-photon final states will be extremely valuable in further exploring technicolor parameter space. © 2011 American Physical Society.

In this paper we discuss the global symmetries and the renormalizability of Lee-Wick (LW) scalar QED. In particular, in the "auxiliary-field" formalism we identify softly broken SO(1,1) global symmetries of the theory. We introduce SO(1,1) invariant gauge-fixing conditions that allow us to show in the auxiliary-field formalism directly that the number of superficially divergent amplitudes in a LW Abelian gauge theory is finite. To illustrate the renormalizability of the theory, we explicitly carry out the one-loop renormalization program in LW scalar QED and demonstrate how the counterterms required are constrained by the joint conditions of gauge and SO(1,1) invariance. We also compute the one-loop beta functions in LW scalar QED and contrast them with those of ordinary scalar QED. © 2010 The American Physical Society.

We discuss the phenomenology of models of dynamical electroweak symmetry breaking which attempt to generate the observed fermion mass spectrum. After briefly describing the variety of and constraints on proposed models, we concentrate on the signatures of colored pseudo-Nambu-Goldstone bosons and resonances at existing and proposed colliders. These particles provide a possibly unique signature: strongly produced resonances associated with electroweak symmetry breaking. (This is the subgroup report for the ``Electroweak Symmetry Breaking and Beyond the Standard Model" working group of the DPF Long Range Planning Study. This report will appear as a chapter in ``Electroweak Symmetry Breaking and Beyond the Standard Model", edited by T. Barklow, S. Dawson, H.E. Haber, and J. Siegrist, to be published by World Scientific.)

Experiments at the LHC may yet discover a dijet resonance indicative of Beyond the Standard Model (BSM) physics. In this case, the question becomes: what BSM theories are consistent with the unexpected resonance? One possibility would be a spin-2 object called the colorphilic graviton--a spin-2 color-singlet particle which couples exclusively to the quark and gluon stress-energy tensors. We assess the possibility of this state's discovery in the dijet channel as an s-channel resonance, and report the regions of parameter space where colorphilic gravitons have not yet been excluded by LHC-13 data but still may be discovered in the dijet channel at LHC-14 for integrated luminosities of 0.3, 1, and 3 ab$^{-1}$. We then delineate which of those regions remain accessible to future collider searches, once one accounts for applicability of the narrow-width approximation, detector mass resolution, and self-consistency according to tree-level partial-wave unitarity. We discover that--despite the strong constraints unitarity imposes on collider searches--the colorphilic graviton remains potentially discoverable in the LHC dijet channel. A means of investigation would be to apply the color discriminant variable (CDV), a dimensionless combination of quantities (cross-section, decay width, and invariant mass) that can be quickly measured after the discovery of a dijet resonance. Previous publications have demonstrated the CDV's utility when applied to theories containing Z', colorons, excited quarks, and diquarks. We extend this analysis to the colorphilic graviton by applying the CDV to the appropriate region of parameter space. We conclude that resolvable, discoverable dijet resonances consistent with colorphilic gravitons span a narrower range of masses than those consistent with leptophobic Z' models, and can be distinguished from those originating from coloron, excited quark, and diquark models.

It has recently been suggested that gauge invariance forbids the coupling of a massive color-octet vector meson to two gluons. While this is true for operators in an effective Lagrangian of dimension four or less, we demonstrate that dimension six interactions will lead to such couplings. In the case of technicolor, the result is a technirho-gluon-gluon coupling comparable to the naive vector meson dominance estimate, but with a substantial uncertainty. This has implications for several recent studies of technicolor phenomenology. © 2001 Published by Elsevier Science B.V.