On R-duals and the duality principle in Gabor analysis

The concept of R-duals of a frame was introduced by Casazza, Kutyniok and Lammers in 2004, with the motivation to obtain a general version of the duality principle in Gabor analysis. For tight Gabor frames and Gabor Riesz bases the three authors were actually able to show that the duality principle is a special case of general results for R-duals. In this paper we introduce various alternative R-duals, with focus on what we call R-duals of type II and III. We show how they are related and provide characterizations of the R-duals of type II and III. In particular, we prove that for tight frames these classes coincide with the R-duals by Casazza et el., which is desirable in the sense that the motivating case of tight Gabor frames already is well covered by these R-duals. On the other hand, all the introduced types of R-duals generalize the duality principle for larger classes of Gabor frames than just the tight frames and the Riesz bases; in particular, the R-duals of type III cover the duality principle for all Gabor frames

Deconstructed Higgsless Models at LHC: The Top Triangle Moose

We describe a deconstructed Higgsless model in which electroweak symmetry breaking results largely from a Higgsless mechanism while the top quark mass is generated by a topcolor mechanism. The top quark mass arises from a Yukawa coupling to an effective top-Higgs which develops a small vacuum expectation value. Both the heavy partners of the electoweak gauge bosons and those for the SM fermions can be light enough to be visible at LHC.Comment: 5 pages, 3 figures; from the Proceedings of the 2010 Rencontres de Bloi

The Top Triangle Moose

We introduce a deconstructed model that incorporates both Higgsless and top-color mechanisms. The model alleviates the typical tension in Higgsless models between obtaining the correct top quark mass and keeping delta-rho small. It does so by singling out the top quark mass generation as arising from a Yukawa coupling to an effective top-Higgs which develops a small vacuum expectation value, while electroweak symmetry breaking results largely from a Higgsless mechanism. As a result, the heavy partners of the SM fermions can be light enough to be seen at the LHC.Comment: To appear in proceedings of SCGT09, Nagoya, Japan. 5 page

Electric Polarizability of Neutral Hadrons from Lattice QCD

By simulating a uniform electric field on a lattice and measuring the change in the rest mass, we calculate the electric polarizability of neutral mesons and baryons using the methods of quenched lattice QCD. Specifically, we measure the electric polarizability coefficient from the quadratic response to the electric field for 10 particles: the vector mesons $\rho^0$ and $K^{*0}$; the octet baryons n, $\Sigma^0$, $\Lambda_{o}^{0}$, $\Lambda_{s}^{0}$, and $\Xi^0$; and the decouplet baryons $\Delta^0$, $\Sigma^{*0}$, and $\Xi^{*0}$. Independent calculations using two fermion actions were done for consistency and comparison purposes. One calculation uses Wilson fermions with a lattice spacing of $a=0.10$fm. The other uses tadpole improved L\"usher-Weiss gauge fields and clover quark action with a lattice spacing $a=0.17$fm. Our results for neutron electric polarizability are compared to experiment.Comment: 25 pages, 20 figure

Low-Energy Effective Theory, Unitarity, and Non-Decoupling Behavior in a Model with Heavy Higgs-Triplet Fields

We discuss the properties of a model incorporating both a scalar electroweak Higgs doublet and an electroweak Higgs triplet. We construct the low-energy effective theory for the light Higgs-doublet in the limit of small (but nonzero) deviations in the rho parameter from one, a limit in which the triplet states become heavy. For small deviations in the rho parameter from one, perturbative unitarity of WW scattering breaks down at a scale inversely proportional to the renormalized vacuum expectation value of the triplet field (or, equivalently, inversely proportional to the square-root of the deviation of the rho parameter from one). This result imposes an upper limit on the mass-scale of the heavy triplet bosons in a perturbative theory; we show that this upper bound is consistent with dimensional analysis in the low-energy effective theory. Recent articles have shown that the triplet bosons do not decouple, in the sense that deviations in the rho parameter from one do not necessarily vanish at one-loop in the limit of large triplet mass. We clarify that, despite the non-decoupling behavior of the Higgs-triplet, this model does not violate the decoupling theorem since it incorporates a large dimensionful coupling. Nonetheless, we show that if the triplet-Higgs boson masses are of order the GUT scale, perturbative consistency of the theory requires the (properly renormalized) Higgs-triplet vacuum expectation value to be so small as to be irrelevant for electroweak phenomenology.Comment: Revtex, 11 pages, 7 eps figures included; references updated and three footnotes adde

Power filtration of CMB observational data

We propose a power filter Gp for linear reconstruction of the CMB signal from observational maps. This Gp filter preserves the power spectrum of the CMB signal in contrast to the Wiener filter which diminishes the power spectrum of the reconstructed CMB signal. We demonstrate how peak statistics and a cluster analysis can be used to estimate the probability of the presence of a CMB signal in observational records. The efficiency of the Gp filter is demonstrated on a toy model of an observational record consisting of a CMB signal and noise in the form of foreground point sources.Comment: 17 pages; 4 figures; submitted to International Journal of Modern Physic