Duality violations and spectral sum rules

We study the issue of duality violations in the VV-AA vacuum polarization function in the chiral limit. This is done with the help of a model with an expansion in inverse powers of the number of colors, Nc, allowing us to consider resonances with a finite width. Due to these duality violations, the Operator Product Expansion (OPE) and the moments of the spectral function (e.g. the Weinberg sum rules) do not match at finite momentum, and we analyze this difference in detail. We also perform a comparative study of many of the different methods proposed in the literature for the extraction of the OPE parameters and find that, when applied to our model, they all fare quite similarly. In fact, the model strongly suggests that a significant improvement in precision can only be expected after duality violations are included. To this end, we propose a method to parameterize these duality violations. The method works quite well for the model, and we hope that it may also be useful in future determinations of OPE parameters in QCD.Comment: 29 pages, 9 figures, LateX file. Small changes to match journal versio

Charged Particles in a 2+1 Curved Background

The coupling to a 2+1 background geometry of a quantized charged test particle in a strong magnetic field is analyzed. Canonical operators adapting to the fast and slow freedoms produce a natural expansion in the inverse square root of the magnetic field strength. The fast freedom is solved to the second order. At any given time, space is parameterized by a couple of conjugate operators and effectively behaves as the `phase space' of the slow freedom. The slow Hamiltonian depends on the magnetic field norm, its covariant derivatives, the scalar curvature and presents a peculiar coupling with the spin-connection.Comment: 22 page

Orbital order out of spin disorder: How to measure the orbital gap

The interplay between spin and orbital degrees of freedom in the Mott-Hubbard insulator is studied by considering an orbitally degenerate superexchange model. We argue that orbital order and the orbital excitation gap in this model are generated through the order-from-disorder mechanism known previously from frustrated spin models. We propose that the orbital gap should show up indirectly in the dynamical spin structure factor; it can therefore be measured using the conventional inelastic neutron scattering method

Langevin dynamics of the Lebowitz-Percus model

We revisit the hard-spheres lattice gas model in the spherical approximation proposed by Lebowitz and Percus (J. L. Lebowitz, J. K. Percus, Phys. Rev.{\ 144} (1966) 251). Although no disorder is present in the model, we find that the short-range dynamical restrictions in the model induce glassy behavior. We examine the off-equilibrium Langevin dynamics of this model and study the relaxation of the density as well as the correlation, response and overlap two-time functions. We find that the relaxation proceeds in two steps as well as absence of anomaly in the response function. By studying the violation of the fluctuation-dissipation ratio we conclude that the glassy scenario of this model corresponds to the dynamics of domain growth in phase ordering kinetics.Comment: 21 pages, RevTeX, 14 PS figure

Neutralino, axion and axino cold dark matter in minimal, hypercharged and gaugino AMSB

Supersymmetric models based on anomaly-mediated SUSY breaking (AMSB) generally give rise to a neutral wino as a WIMP cold dark matter (CDM) candidate, whose thermal abundance is well below measured values. Here, we investigate four scenarios to reconcile AMSB dark matter with the measured abundance: 1. non-thermal wino production due to decays of scalar fields ({\it e.g} moduli), 2. non-thermal wino production due to decays of gravitinos, 3. non-thermal wino production due to heavy axino decays, and 4. the case of an axino LSP, where the bulk of CDM is made up of axions and thermally produced axinos. In cases 1 and 2, we expect wino CDM to constitute the entire measured DM abundance, and we investigate wino-like WIMP direct and indirect detection rates. Wino direct detection rates can be large, and more importantly, are bounded from below, so that ton-scale noble liquid detectors should access all of parameter space for m_{\tz_1}\alt 500 GeV. Indirect wino detection rates via neutrino telescopes and space-based cosmic ray detectors can also be large. In case 3, the DM would consist of an axion plus wino admixture, whose exact proportions are very model dependent. In this case, it is possible that both an axion and a wino-like WIMP could be detected experimentally. In case 4., we calculate the re-heat temperature of the universe after inflation. In this case, no direct or indirect WIMP signals should be seen, although direct detection of relic axions may be possible. For each DM scenario, we show results for the minimal AMSB model, as well as for the hypercharged and gaugino AMSB models.Comment: 29 pages including 13 figure

The Highest Energy Neutrinos

Measurements of the arrival directions of cosmic rays have not revealed their sources. High energy neutrino telescopes attempt to resolve the problem by detecting neutrinos whose directions are not scrambled by magnetic fields. The key issue is whether the neutrino flux produced in cosmic ray accelerators is detectable. It is believed that the answer is affirmative, both for the galactic and extragalactic sources, provided the detector has kilometer-scale dimensions. We revisit the case for kilometer-scale neutrino detectors in a model-independent way by focussing on the energetics of the sources. The real breakthrough though has not been on the theory but on the technology front: the considerable technical hurdles to build such detectors have been overcome. Where extragalactic cosmic rays are concerned an alternative method to probe the accelerators consists in studying the arrival directions of neutrinos produced in interactions with the microwave background near the source, i.e. within a GZK radius. Their flux is calculable within large ambiguities but, in any case, low. It is therefore likely that detectors that are larger yet by several orders of magnitudes are required. These exploit novel techniques, such as detecting the secondary radiation at radio wavelengths emitted by neutrino induced showers.Comment: 16 pages, pdflatex, 7 jpg figures, ICRC style files included. Highlight talk presented at the 30th International Cosmic Ray Conference, Merida, Mexico, 200

Constraining the Littlest Higgs

Little Higgs models offer a new way to address the hierarchy problem, and give rise to a weakly-coupled Higgs sector. These theories predict the existence of new states which are necessary to cancel the quadratic divergences of the Standard Model. The simplest version of these models, the Littlest Higgs, is based on an $SU(5)/SO(5)$ non-linear sigma model and predicts that four new gauge bosons, a weak isosinglet quark, $t'$, with $Q=2/3$, as well as an isotriplet scalar field exist at the TeV scale. We consider the contributions of these new states to precision electroweak observables, and examine their production at the Tevatron. We thoroughly explore the parameter space of this model and find that small regions are allowed by the precision data where the model parameters take on their natural values. These regions are, however, excluded by the Tevatron data. Combined, the direct and indirect effects of these new states constrain the `decay constant' f\gsim 3.5 TeV and m_{t'}\gsim 7 TeV. These bounds imply that significant fine-tuning be present in order for this model to resolve the hierarchy problem.Comment: 31 pgs, 26 figures; bound on t' mass fixed to mt'>2f, conclusions unchange

Solitons in one-dimensional interacting Bose-Einstein system

A modified Gross-Pitaevskii approximation was introduced recently for bosons in dimension $d\le2$ by Kolomeisky {\it et al.} (Phys. Rev. Lett. {\bf 85} 1146 (2000)). We use the density functional approach with sixth-degree interaction energy term in the Bose field to reproduce the stationary-frame results of Kolomeisky {\it et al.} for a one-dimensional Bose-Einstein system with a repulsive interaction. We also find a soliton solution for an attractive interaction, which may be boosted to a finite velocity by a Galilean transformation. The stability of such a soliton is discussed analytically. We provide a general treatment of stationary solutions in one dimension which includes the above solutions as special cases. This treatment leads to a variety of stationary wave solutions for both attractive and repulsive interactions.Comment: Latex, 14 pages, No figur

The Higgs intense--coupling regime in constrained SUSY models and its astrophysical implications

We analyze the Higgs intense--coupling regime, in which all Higgs particles of the Minimal Supersymmetric Standard Model are light with masses of the same order and the value of \tb the ratio of vacuum expectation values of the two Higgs fields is large, in the framework of Supergravity scenarios with non--universal soft Supersymmetry breaking scalar masses in the Higgs sector. In particular, we calculate the relic density abundance of the lightest neutralino candidate for cold dark matter and the rates in direct and indirect detection at present and future experiments. We first show that while in the mSUGRA model this regime is disfavored by present data, there are regions in the parameter space of models with non--universal Higgs masses where it can occur. We then show that because of the large value of $\tan\beta$ and the relatively low values of the neutral Higgs boson masses, the cross section for neutralino--nucleon scattering is strongly enhanced in this regime and would allow for the observation of a signal in direct detection experiments such as CDMS--Soudan. The expected sensitivity of gamma--ray detectors like GLAST might be also sufficient to observe the annihilation of neutralinos in such a regime.Comment: 19 pages, 5 figure

Vortices in Ginzburg-Landau billiards

We present an analysis of the Ginzburg-Landau equations for the description of a two-dimensional superconductor in a bounded domain. Using the properties of a special integrability point of these equations which allows vortex solutions, we obtain a closed expression for the energy of the superconductor. The role of the boundary of the system is to provide a selection mechanism for the number of vortices. A geometrical interpretation of these results is presented and they are applied to the analysis of the magnetization recently measured on small superconducting disks. Problems related to the interaction and nucleation of vortices are discussed.Comment: RevTex, 17 pages, 3 eps figure