The anatomy of a quadruply imaged gravitational lens system

The key to using a strong gravitational lens system to measure the Hubble constant is to obtain an accurate model of the lens potential. In this paper, we investigate the properties of gravitational lens B1608+656, a quadruply-imaged lens system with an extended source intensity distribution. Our analysis is valid for generic quadruply-lensed systems. Limit curves and isophotal separatrices are defined for such systems, and we show that the isophotal separatrices must intersect at the critical curves and the satellite isophotes must be tangent to the limit curves. The current model of B1608+656 (Koopmans et al. 2003) satisfies these criteria for some, but not all, of the isophotal separatrices within the observational uncertainty. We study a non-parametric method of potential reconstruction proposed by Blandford, Surpi & Kundic (2001) and demonstrate that although the method works in principle and elucidates image formation, the initial potential only converges to the true model when it is within ~ 1 percent of the true model.Comment: 12 pages, 12 figures. Minor revisions based on referee's comments after initial submission to MNRA

A Bayesian analysis of regularised source inversions in gravitational lensing

Strong gravitational lens systems with extended sources are of special interest because they provide additional constraints on the models of the lens systems. To use a gravitational lens system for measuring the Hubble constant, one would need to determine the lens potential and the source intensity distribution simultaneously. A linear inversion method to reconstruct a pixellated source brightness distribution of a given lens potential model was introduced by Warren & Dye. In the inversion process, a regularisation on the source intensity is often needed to ensure a successful inversion with a faithful resulting source. In this paper, we use Bayesian analysis to determine the optimal regularisation constant (strength of regularisation) of a given form of regularisation and to objectively choose the optimal form of regularisation given a selection of regularisations. We consider and compare quantitatively three different forms of regularisation previously described in the literature for source inversions in gravitational lensing: zeroth-order, gradient and curvature. We use simulated data with the exact lens potential to demonstrate the method. We find that the preferred form of regularisation depends on the nature of the source distribution.Comment: 18 pages, 10 figures; Revisions based on referee's comments after initial submission to MNRA

On a theory of neutrino oscillations with entanglement

We show that, despite appearances, a theoretical approach to neutrino oscillation in which the neutrino and its interaction partners are entangled yields the standard result for the neutrino oscillation wavelength. We also shed some light on the question of why plane-wave approaches to the neutrino oscillation problem can yield the correct oscillation wavelength even though they do not explicitly account for the localization of the neutrino source and the detector.Comment: RevTeX 4, 12 pages, 1 figure; v2: Minor clarifications, references adde

Stacked Weak Lensing Mass Calibration: Estimators, Systematics, and Impact on Cosmological Parameter Constraints

When extracting the weak lensing shear signal, one may employ either locally normalized or globally normalized shear estimators. The former is the standard approach when estimating cluster masses, while the latter is the more common method among peak finding efforts. While both approaches have identical signal-to-noise in the weak lensing limit, it is possible that higher order corrections or systematics considerations make one estimator preferable over the other. In this paper, we consider the efficacy of both estimators within the context of stacked weak lensing mass estimation in the Dark Energy Survey (DES). We find the two estimators have nearly identical statistical precision, even after including higher order corrections, but that these corrections must be incorporated into the analysis to avoid observationally relevant biases in the recovered masses. We also demonstrate that finite bin-width effects may be significant if not properly accounted for, and that the two estimators exhibit different systematics, particularly with respect to contamination of the source catalog by foreground galaxies. Thus, the two estimators may be employed as a systematics cross-check of each other. Stacked weak lensing in the DES should allow for the mean mass of galaxy clusters to be calibrated to about 2% precision (statistical only), which can improve the figure of merit of the DES cluster abundance experiment by a factor of ~3 relative to the self-calibration expectation. A companion paper (Schmidt & Rozo, 2010) investigates how the two types of estimators considered here impact weak lensing peak finding efforts.Comment: 14 pages, 9 figures; comments welcom

Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics

We develop and validate a density functional, XYG3, based on the adiabatic connection formalism and the Görling–Levy coupling-constant perturbation expansion to the second order (PT2). XYG3 is a doubly hybrid functional, containing 3 mixing parameters. It has a nonlocal orbital-dependent component in the exchange term (exact exchange) plus information about the unoccupied Kohn–Sham orbitals in the correlation part (PT2 double excitation). XYG3 is remarkably accurate for thermochemistry, reaction barrier heights, and nonbond interactions of main group molecules. In addition, the accuracy remains nearly constant with system size

Search for Electron Neutrino Appearance in MINOS

The MINOS Collaboration continues its search for {nu}{sub e} appearance in the NuMI (Neutrinos at the Main Injector) beam at Fermilab. Neutrinos in the beam interact in the Near Detector, located 1 km from the beam source, allowing us to characterize the backgrounds present in our analysis. In particular, we can estimate the number of {nu}{sub e} candidate events we expect to see in the Far Detector (735 km away, in the Soudan mine in northern Minnesota) in the presence or absence of {nu}{sub {mu}} {yields} {nu}{sub e} oscillation. Recent efforts to improve the sensitivity of the analysis, including upgrades to the event identification algorithm and fitting procedure, are discussed, and the latest results from the search are presented

Radiative Leptonic B Decays

We present the results of a search for B{sup +} meson decays into {gamma}{ell}{sup +}{nu}{sub {ell}}, where {ell} = e,{mu}. We use a sample of 232 million B{bar B} meson pairs recorded at the {Upsilon}(4S) resonance with the BABAR detector at the PEP-II B factory. We measure a partial branching fraction {Delta}{beta} in a restricted region of phase space that reduces the effect of theoretical uncertainties, requiring the lepton energy to be in the range 1.875 and 2.850 GeV, the photon energy to be in the range 0.45 and 2.35 GeV, and the cosine of the angle between the lepton and photon momenta to be less than -0.36, with all quantities computed in the {Upsilon}(4S) center-of-mass frame. We find {Delta}{Beta}(B{sup +} {yields} {gamma}{ell}{sup +}{nu}{sub {ell}}) = (-0.3{sub 1.5}{sup +1.3}(statistical){sub -0.6}{sup +0.6}(systematic) {+-} 0.1(theoretical)) x 10{sup -6}, under the assumption of lepton universality. Interpreted as a 90% confidence-level Bayesian upper limit, the result corresponds to 1.7 x 10{sup -6} for a prior at in amplitude, and 2.3 x 10{sup -6} for a prior at in branching fraction

Neutral Currents - The Structure of the Coupling

The authors report here on latest results from an investigation of the form of the neutral current coupling in the inclusive channels {nu}{sub {mu}} + N {yields} {nu}{sub {mu}} + hadrons and {bar {nu}}{sub {mu}} + N {yields} {bar {nu}}{sub {mu}} + hadrons. The experiment was conducted by the Caltech-Fermilab group in October 1974. The data were taken in the Fermilab narrow band beam set to a mean secondary hadron energy of {+-} 170 GeV. The distributions of total energy, observed in the target calorimeter, for charged current events in which the muon momentum was measured, shown in figure 1, reflect the dichromatic structure of the beam, with average energies for neutrinos from pion and kaon decay of 50 and 150 GeV, respectively. The two main sources of background present in the data sample come from cosmic ray interactions. and from neutrinos (and anti-neutrinos) which are produced by decays before momentum and sign selection has occurred (wide-band background). Both backgrounds are measured and empirically subtracted from the data. The first (cosmic rays) is measured in an off-beam gate. The second (wide-band) is measured by closing a slit at the entrance to the decay pipe. Thus, the data sample contains beam associated neutrinos (or anti-neutrinos) with little or no contamination from the neutrino of opposite helicity