Minimal Walking Technicolor: Set Up for Collider Physics

Different theoretical and phenomenological aspects of the Minimal and Nonminimal Walking Technicolor theories have recently been studied. The goal here is to make the models ready for collider phenomenology. We do this by constructing the low energy effective theory containing scalars, pseudoscalars, vector mesons and other fields predicted by the minimal walking theory. We construct their self-interactions and interactions with standard model fields. Using the Weinberg sum rules, opportunely modified to take into account the walking behavior of the underlying gauge theory, we find interesting relations for the spin-one spectrum. We derive the electroweak parameters using the newly constructed effective theory and compare the results with the underlying gauge theory. Our analysis is sufficiently general such that the resulting model can be used to represent a generic walking technicolor theory not at odds with precision data.Comment: 42 pages, 3 figures. RevTex forma

The Three Site Model at One-Loop

In this paper we compute the one-loop chiral logarithmic corrections to all O(p^4) counterterms in the three site Higgsless model. The calculation is performed using the background field method for both the chiral- and gauge-fields, and using Landau gauge for the quantum fluctuations of the gauge fields. The results agree with our previous calculations of the chiral-logarithmic corrections to the S and T parameters in 't Hooft-Feynman gauge. The work reported here includes a complete evaluation of all one-loop divergences in an SU(2) x U(1) nonlinear sigma model, corresponding to an electroweak effective Lagrangian in the absence of custodial symmetry.Comment: 40 pages, nine included eps figures. Minor corrections mad

The Status of Human Rights Protection in Europe: It’s complicated

The UK has voted to leave the European Union and Prime Minister Theresa May has expressed her aversion to the European Convention on Human Rights, but confusion abounds as to what the current architecture of Europe is, let alone what it might look like in the future. This article seeks to provide a comprehensive overview of the development of supranational human rights protections in Europe and the status of the current quest for greater integration. In particular, the stalled movement towards the accession of the EU to the ECHR is examined and likened to a riddle: to avoid subjecting Member States to conflicting obligations, the ECHR must be granted ultimate authority in the field of human rights, but without compromising the autonomy of EU law. The article concludes with a conversation with Dr Sonia Morano-Foadi, whose extensive research into the European human rights institutions enables her to shed some light on the likelihood of the accession riddle ever being solved and to provide a prognosis for European rights protections in the future

Top quark effects in composite vector pair production at the LHC

In the context of a strongly coupled Electroweak Symmetry Breaking, composite light scalar singlet and composite triplet of heavy vectors may arise from an unspecified strong dynamics and the interactions among themselves and with the Standard Model gauge bosons and fermions can be described by a $SU(2)_L\times SU(2)_R/SU(2)_{L+R}$ Effective Chiral Lagrangian. In this framework, the production of the $V^{+}V^{-}$ and $V^{0}V^{0}$ final states at the LHC by gluon fusion mechanism is studied in the region of parameter space consistent with the unitarity constraints in the elastic channel of longitudinal gauge boson scattering and in the inelastic scattering of two longitudinal Standard Model gauge bosons into Standard Model fermions pairs. The expected rates of same-sign di-lepton and tri-lepton events from the decay of the $V^{0}V^{0}$ final state are computed and their corresponding backgrounds are estimated. It is of remarkable relevance that the $V^{0}V^{0}$ final state can only be produced at the LHC via gluon fusion mechanism since this state is absent in the Drell-Yan process. It is also found that the $V^{+}V^{-}$ final state production cross section via gluon fusion mechanism is comparable with the $V^{+}V^{-}$ Drell-Yan production cross section. The comparison of the $V^{0}V^{0}$ and $V^{+}V^{-}$ total cross sections will be crucial for distinguishing the different models since the vector pair production is sensitive to many couplings. This will also be useful to determine if the heavy vectors are only composite vectors or are gauge vectors of a spontaneously broken gauge symmetry.Comment: 18 pages, 5 tables, 6 figures. Missing figures added. Matches published versio

Curing the Ills of Higgsless Models: the S Parameter and Unitarity

We consider various constraints on Higgsless models of electroweak symmetry breaking based on a bulk SU(2)_L x SU(2)_R x U(1)_{B-L} gauge group in warped space. First we show that the S parameter which is positive if fermions are localized on the Planck brane can be lowered (or made vanishing) by changing the localization of the light fermions. If the wave function of the light fermions is almost flat their coupling to the gauge boson KK modes will be close to vanishing, and therefore contributions to the S parameter will be suppressed. At the same time the experimental bounds on such Z' and W' gauge bosons become very weak, and their masses can be lowered to make sure that perturbative unitarity is not violated in this theory before reaching energies of several TeV. The biggest difficulty of these models is to incorporate a heavy top quark mass without violating any of the experimental bounds on bottom quark gauge couplings. In the simplest models of fermion masses a sufficiently heavy top quark also implies an unacceptably large correction to the Zb\bar{b} vertex and a large splitting between the KK modes of the top and bottom quarks, yielding large loop corrections to the T-parameter. We present possible directions for model building where perhaps these constraints could be obeyed as well.Comment: 21 pages, LaTeX, 5 figures. References and acknowledgements adde

Electroweak Corrections and Unitarity in Linear Moose Models

We calculate the form of the corrections to the electroweak interactions in the class of Higgsless models which can be "deconstructed'' to a chain of SU(2) gauge groups adjacent to a chain of U(1) gauge groups, and with the fermions coupled to any single SU(2) group and to any single U(1) group along the chain. The primary advantage of our technique is that the size of corrections to electroweak processes can be directly related to the spectrum of vector bosons ("KK modes"). In Higgsless models, this spectrum is constrained by unitarity. Our methods also allow for arbitrary background 5-D geometry, spatially dependent gauge-couplings, and brane kinetic energy terms. We find that, due to the size of corrections to electroweak processes in any unitary theory, Higgsless models with localized fermions are disfavored by precision electroweak data. Although we stress our results as they apply to continuum Higgsless 5-D models, they apply to any linear moose model including those with only a few extra vector bosons. Our calculations of electroweak corrections also apply directly to the electroweak gauge sector of 5-D theories with a bulk scalar Higgs boson; the constraints arising from unitarity do not apply in this case.Comment: 50 pages, 11 eps figures, typos correcte

The S-parameter in Holographic Technicolor Models

We study the S parameter, considering especially its sign, in models of electroweak symmetry breaking (EWSB) in extra dimensions, with fermions localized near the UV brane. Such models are conjectured to be dual to 4D strong dynamics triggering EWSB. The motivation for such a study is that a negative value of S can significantly ameliorate the constraints from electroweak precision data on these models, allowing lower mass scales (TeV or below) for the new particles and leading to easier discovery at the LHC. We first extend an earlier proof of S>0 for EWSB by boundary conditions in arbitrary metric to the case of general kinetic functions for the gauge fields or arbitrary kinetic mixing. We then consider EWSB in the bulk by a Higgs VEV showing that S is positive for arbitrary metric and Higgs profile, assuming that the effects from higher-dimensional operators in the 5D theory are sub-leading and can therefore be neglected. For the specific case of AdS_5 with a power law Higgs profile, we also show that S ~ + O(1), including effects of possible kinetic mixing from higher-dimensional operator (of NDA size) in the $5D$ theory. Therefore, our work strongly suggests that S is positive in calculable models in extra dimensions.Comment: 21 pages, 2 figures. v2: references adde

Invisible Higgs and Dark Matter

We investigate the possibility that a massive weakly interacting fermion simultaneously provides for a dominant component of the dark matter relic density and an invisible decay width of the Higgs boson at the LHC. As a concrete model realizing such dynamics we consider the minimal walking technicolor, although our results apply more generally. Taking into account the constraints from the electroweak precision measurements and current direct searches for dark matter particles, we find that such scenario is heavily constrained, and large portions of the parameter space are excluded.Comment: arXiv admin note: text overlap with arXiv:0912.229

Generalized Weinberg Sum Rules in Deconstructed QCD

Recently, Son and Stephanov have considered an "open moose" as a possible dual model of a QCD-like theory of chiral symmetry breaking. In this note we demonstrate that although the Weinberg sum rules are satisfied in any such model, the relevant sums converge very slowly and in a manner unlike QCD. Further, we show that such a model satisfies a set of generalized sum rules. These sum rules can be understood by looking at the operator product expansion for the correlation function of chiral currents, and correspond to the absence of low-dimension gauge-invariant chiral symmetry breaking condensates. These results imply that, regardless of the couplings and F-constants chosen, the open moose is not the dual of any QCD-like theory of chiral symmetry breaking. We also show that the generalized sum rules can be "solved", leading to a compact expression for the difference of vector- and axial-current correlation functions. This expression allows for a simple formula for the S parameter (L_10), which implies that S is always positive and of order one in any (unitary) open linear moose model. Therefore the S parameter is positive and order one in any "Higgsless model" based on the continuum limit of a linear moose regardless of the warping or position-dependent gauge-coupling chosen.Comment: 12 pages, 5 eps figures; reference to overlapping work adde