158 research outputs found

    Wave operator bounds for 1-dimensional Schr\"odinger operators with singular potentials and applications

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    Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.Comment: 16 pages, 0 figure

    On the Quantitative Impact of the Schechter-Valle Theorem

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    We evaluate the Schechter-Valle (Black Box) theorem quantitatively by considering the most general Lorentz invariant Lagrangian consisting of point-like operators for neutrinoless double beta decay. It is well known that the Black Box operators induce Majorana neutrino masses at four-loop level. This warrants the statement that an observation of neutrinoless double beta decay guarantees the Majorana nature of neutrinos. We calculate these radiatively generated masses and find that they are many orders of magnitude smaller than the observed neutrino masses and splittings. Thus, some lepton number violating New Physics (which may at tree-level not be related to neutrino masses) may induce Black Box operators which can explain an observed rate of neutrinoless double beta decay. Although these operators guarantee finite Majorana neutrino masses, the smallness of the Black Box contributions implies that other neutrino mass terms (Dirac or Majorana) must exist. If neutrino masses have a significant Majorana contribution then this will become the dominant part of the Black Box operator. However, neutrinos might also be predominantly Dirac particles, while other lepton number violating New Physics dominates neutrinoless double beta decay. Translating an observed rate of neutrinoless double beta decay into neutrino masses would then be completely misleading. Although the principal statement of the Schechter-Valle theorem remains valid, we conclude that the Black Box diagram itself generates radiatively only mass terms which are many orders of magnitude too small to explain neutrino masses. Therefore, other operators must give the leading contributions to neutrino masses, which could be of Dirac or Majorana nature.Comment: 18 pages, 4 figures; v2: minor corrections, reference added, matches journal version; v3: typo corrected, physics result and conclusions unchange

    Surface Gap Soliton Ground States for the Nonlinear Schr\"{o}dinger Equation

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    We consider the nonlinear Schr\"{o}dinger equation (Δ+V(x))u=Γ(x)up1u(-\Delta +V(x))u = \Gamma(x) |u|^{p-1}u, xRnx\in \R^n with V(x)=V1(x)χ{x1>0}(x)+V2(x)χ{x1<0}(x)V(x) = V_1(x) \chi_{\{x_1>0\}}(x)+V_2(x) \chi_{\{x_1<0\}}(x) and Γ(x)=Γ1(x)χ{x1>0}(x)+Γ2(x)χ{x1<0}(x)\Gamma(x) = \Gamma_1(x) \chi_{\{x_1>0\}}(x)+\Gamma_2(x) \chi_{\{x_1<0\}}(x) and with V1,V2,Γ1,Γ2V_1, V_2, \Gamma_1, \Gamma_2 periodic in each coordinate direction. This problem describes the interface of two periodic media, e.g. photonic crystals. We study the existence of ground state H1H^1 solutions (surface gap soliton ground states) for 0<minσ(Δ+V)0<\min \sigma(-\Delta +V). Using a concentration compactness argument, we provide an abstract criterion for the existence based on ground state energies of each periodic problem (with VV1,ΓΓ1V\equiv V_1, \Gamma\equiv \Gamma_1 and VV2,ΓΓ2V\equiv V_2, \Gamma\equiv \Gamma_2) as well as a more practical criterion based on ground states themselves. Examples of interfaces satisfying these criteria are provided. In 1D it is shown that, surprisingly, the criteria can be reduced to conditions on the linear Bloch waves of the operators d2dx2+V1(x)-\tfrac{d^2}{dx^2} +V_1(x) and d2dx2+V2(x)-\tfrac{d^2}{dx^2} +V_2(x).Comment: definition of ground and bound states added, assumption (H2) weakened (sign changing nonlinearity is now allowed); 33 pages, 4 figure

    Atmospheric neutrino observations and flavor changing interactions

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    Flavor changing (FC) neutrino-matter interactions can account for the zenith-angle dependent deficit of atmospheric neutrinos observed in the SuperKamiokande experiment, without directly invoking neither neutrino mass, nor mixing. We find that FC νμ\nu_\mu-matter interactions provide a good fit to the observed zenith angle distributions, comparable in quality to the neutrino oscillation hypothesis. The required FC interactions arise naturally in many attractive extensions of the Standard Model.Comment: RevTex, 4 pages, 2 postscript figures, some minor modifications in the text and few new references are added, no change in the results and conclusions, final version to be published in Phys. Rev. Let

    Effective chiral Lagrangians for spin-1 mesons

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    The commonly used types of effective theory for vector mesons are reviewed and their relationships clarified. They are shown to correspond to different choices of field for spin-1 particles and the rules for transforming between them are described. The importance of respecting chiral symmetry is stressed. The choice of fields that transform homogeneously under the nonlinear realisation of chiral symmetry imposes no preconceptions about the types of coupling for the mesons. This representation thus provides a convenient framework for relating different theories. It is also used to elucidate the nature of the assumptions in specific hidden-gauge and massive Yang-Mills models that have been widely used.Comment: 46 pages (RevTeX

    Cross-Correlation of the Cosmic Microwave Background with the 2MASS Galaxy Survey: Signatures of Dark Energy, Hot Gas, and Point Sources

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    We cross-correlate the Cosmic Microwave Background (CMB) temperature anisotropies observed by the Wilkinson Microwave Anisotropy Probe (WMAP) with the projected distribution of extended sources in the Two Micron All Sky Survey (2MASS). By modelling the theoretical expectation for this signal, we extract the signatures of dark energy (Integrated Sachs-Wolfe effect;ISW), hot gas (thermal Sunyaev-Zeldovich effect;thermal SZ), and microwave point sources in the cross-correlation. Our strongest signal is the thermal SZ, at the 3.1-3.7 \sigma level, which is consistent with the theoretical prediction based on observations of X-ray clusters. We also see the ISW signal at the 2.5 \sigma level, which is consistent with the expected value for the concordance LCDM cosmology, and is an independent signature of the presence of dark energy in the universe. Finally, we see the signature of microwave point sources at the 2.7 \sigma level.Comment: 35 pages (preprint format), 8 figures. In addition to minor revisions based on referee's comments, after correcting for a bug in the code, the SZ detection is consistent with the X-ray observations. Accepeted for publication in Physical Review

    Orientation bias of optically selected galaxy clusters and its impact on stacked weak-lensing analyses

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    Weak-lensing measurements of the averaged shear profiles of galaxy clusters binned by some proxy for cluster mass are commonly converted to cluster mass estimates under the assumption that these cluster stacks have spherical symmetry. In this paper, we test whether this assumption holds for optically selected clusters binned by estimated optical richness. Using mock catalogues created from N-body simulations populated realistically with galaxies, we ran a suite of optical cluster finders and estimated their optical richness. We binned galaxy clusters by true cluster mass and estimated optical richness and measure the ellipticity of these stacks. We find that the processes of optical cluster selection and richness estimation are biased, leading to stacked structures that are elongated along the line of sight. We show that weak-lensing alone cannot measure the size of this orientation bias. Weak-lensing masses of stacked optically selected clusters are overestimated by up to 3–6 per cent when clusters can be uniquely associated with haloes. This effect is large enough to lead to significant biases in the cosmological parameters derived from large surveys like the Dark Energy Survey, if not calibrated via simulations or fitted simultaneously. This bias probably also contributes to the observed discrepancy between the observed and predicted Sunyaev–Zel’dovich signal of optically selected clusters

    The Sloan Digital Sky Survey Quasar Lens Search. VI. Constraints on Dark Energy and the Evolution of Massive Galaxies

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    We present a statistical analysis of the final lens sample from the Sloan Digital Sky Survey Quasar Lens Search (SQLS). The number distribution of a complete subsample of 19 lensed quasars selected from 50,836 source quasars is compared with theoretical expectations, with particular attention to the selection function. Assuming that the velocity function of galaxies does not evolve with redshift, the SQLS sample constrains the cosmological constant to \Omega_\Lambda=0.79^{+0.06}_{-0.07}(stat.)^{+0.06}_{-0.06}(syst.) for a flat universe. The dark energy equation of state is found to be consistent with w=-1 when the SQLS is combined with constraints from baryon acoustic oscillation (BAO) measurements or results from the Wilkinson Microwave Anisotropy Probe (WMAP). We also obtain simultaneous constraints on cosmological parameters and redshift evolution of the galaxy velocity function, finding no evidence for redshift evolution at z<1 in any combinations of constraints. For instance, number density evolution quantified as \nu_n=d\ln\phi_*/d\ln(1+z) and the velocity dispersion evolution \nu_\sigma=d\ln\sigma_*/d\ln(1+z) are constrained to \nu_n=1.06^{+1.36}_{-1.39}(stat.)^{+0.33}_{-0.64}(syst.) and \nu_\sigma=-0.05^{+0.19}_{-0.16}(stat.)^{+0.03}_{-0.03}(syst.) respectively when the SQLS result is combined with BAO and WMAP for flat models with a cosmological constant. We find that a significant amount of dark energy is preferred even after fully marginalizing over the galaxy evolution parameters. Thus the statistics of lensed quasars robustly confirm the accelerated cosmic expansion.Comment: 44 pages, 12 figures, 4 tables, accepted for publication in A

    The Sloan Digital Sky Survey Quasar Lens Search. V. Final Catalog from the Seventh Data Release

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    We present the final statistical sample of lensed quasars from the Sloan Digital Sky Survey (SDSS) Quasar Lens Search (SQLS). The well-defined statistical lens sample consists of 26 lensed quasars brighter than i=19.1 and in the redshift range of 0.6<z<2.2 selected from 50,836 spectroscopically confirmed quasars in the SDSS Data Release 7 (DR7), where we restrict the image separation range to 1"<\theta<20" and the i-band magnitude differences in two image lenses to be smaller than 1.25 mag. The SDSS DR7 quasar catalog also contains 36 additional lenses identified with various techniques. In addition to these lensed quasars, we have identified 81 pairs of quasars from follow-up spectroscopy, 26 of which are physically associated binary quasars. The statistical lens sample covers a wide range of image separations, redshifts, and magnitudes, and therefore is suitable for systematic studies of cosmological parameters and surveys of the structure and evolution of galaxies and quasars.Comment: 42 pages, 2 figures, 6 tables, accepted for publication in AJ; see http://www-utap.phys.s.u-tokyo.ac.jp/~sdss/sqls/ for supplemental informatio
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