Representations for Three-Body T-Matrix on Unphysical Sheets: Proofs

A proof is given for the explicit representations which have been formulated in the author's previous work (nucl-th/9505028) for the Faddeev components of three-body T-matrix continued analytically on unphysical sheets of the energy Riemann surface. Also, the analogous representations for analytical continuation of the three-body scattering matrices and resolvent are proved. An algorithm to search for the three-body resonances on the base of the Faddeev differential equations is discussed.Comment: 98 Kb; LaTeX; Journal-ref was added (the title changed in the journal

Representations for Three-Body T-Matrix on Unphysical Sheets

Explicit representations are formulated for the Faddeev components of three-body T-matrix continued analytically on unphysical sheets of the energy Riemann surface. According to the representations, the T-matrix on unphysical sheets is obviously expressed in terms of its components taken on the physical sheet only. The representations for T-matrix are used then to construct similar representations for analytical continuation of three-body scattering matrices and resolvent. Domains on unphysical sheets are described where the representations obtained can be applied.Comment: 123 Kb; LaTeX; Journal-ref was added (the title changed in the journal

Electroweak higher-order effects and theoretical uncertainties in deep-inelastic neutrino scattering

A previous calculation of electroweak O(alpha) corrections to deep-inelastic neutrino scattering, as e.g. measured by NuTeV and NOMAD, is supplemented by higher-order effects. In detail, we take into account universal two-loop effects from \Delta\alpha and \Delta\rho as well as higher-order final-state photon radiation off muons in the structure function approach. Moreover, we make use of the recently released O(alpha)-improved parton distributions MRST2004QED and identify the relevant QED factorization scheme, which is DIS like. As a technical byproduct, we describe slicing and subtraction techniques for an efficient calculation of a new type of real corrections that are induced by the generated photon distribution. A numerical discussion of the higher-order effects suggests that the remaining theoretical uncertainty from unknown electroweak corrections is dominated by non-universal two-loop effects and is of the order 0.0003 when translated into a shift in sin^2\theta_W=1-MW^2/MZ^2. The O(alpha) corrections implicitly included in the parton distributions lead to a shift of about 0.0004.Comment: 25 pages, latex, 8 postscript figure

The FORS Deep Field: Field selection, photometric observations and photometric catalog

The FORS Deep Field project is a multi-colour, multi-object spectroscopic investigation of an approx. 7 times 7 region near the south galactic pole based mostly on observations carried out with the FORS instruments attached to the VLT telescopes. It includes the QSO Q 0103-260 (z = 3.36). The goal of this study is to improve our understanding of the formation and evolution of galaxies in the young Universe. In this paper the field selection, the photometric observations, and the data reduction are described. The source detection and photometry of objects in the FORS Deep Field is discussed in detail. A combined B and I selected UBgRIJKs photometric catalog of 8753 objects in the FDF is presented and its properties are briefly discussed. The formal 50% completeness limits for point sources, derived from the co-added images, are 25.64, 27.69, 26.86, 26.68, 26.37, 23.60 and 21.57 in U, B, g, R, I, J and Ks (Vega-system), respectively. A comparison of the number counts in the FORS Deep Field to those derived in other deep field surveys shows very good agreement.Comment: 15 pages, 11 figures (included), accepted for publication in A&

Current-density functional theory of time-dependent linear response in quantal fluids: recent progress

Vignale and Kohn have recently formulated a local density approximation to the time-dependent linear response of an inhomogeneous electron system in terms of a vector potential for exchange and correlation. The vector potential depends on the induced current density through spectral kernels to be evaluated on the homogeneous electron-gas. After a brief review of their theory, the case of inhomogeneous Bose superfluids is considered, with main focus on dynamic Kohn-Sham equations for the condensate in the linear response regime and on quantal generalized hydrodynamic equations in the weak inhomogeneity limit. We also present the results of calculations of the exchange-correlation spectra in both electron and superfluid boson systems.Comment: 12 pages, 2 figures, Postscript fil

An optimal gap theorem

By solving the Cauchy problem for the Hodge-Laplace heat equation for $d$-closed, positive $(1, 1)$-forms, we prove an optimal gap theorem for K\"ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius $r$ centered at any fixed point $o$ is a function of $o(r^{-2})$. Furthermore via a relative monotonicity estimate we obtain a stronger statement, namely a `positive mass' type result, asserting that if $(M, g)$ is not flat, then $\liminf_{r\to \infty} \frac{r^2}{V_o(r)}\int_{B_o(r)}\mathcal{S}(y)\, d\mu(y)>0$ for any $o\in M$

Separated cross sections in \pi^0 electroproduction at threshold at Q^2 = 0.05 GeV^2/c^2

The differential cross sections \sigma_0=\sigma_T+\epsilon \sigma_L, \sigma_{LT}, and \sigma_{TT} of \pi^0 electroproduction from the proton were measured from threshold up to an additional center of mass energy of 40 MeV, at a value of the photon four-momentum transfer of Q^2= 0.05 GeV^2/c^2 and a center of mass angle of \theta=90^\circ. By an additional out-of-plane measurement with polarized electrons \sigma_{LT'} was determined. This showed for the first time the cusp effect above the \pi^+ threshold in the imaginary part of the s-wave. The predictions of Heavy Baryon Chiral Perturbation Theory are in disagreement with these data. On the other hand, the data are somewhat better predicted by the MAID phenomenological model and are in good agreement with the dynamical model DMT.Comment: 6 pages, 4 figure

Observation of Lambda H-4 hyperhydrogen by decay-pion spectroscopy in electron scattering

At the Mainz Microtron MAMI, the first high-resolution pion spectroscopy from decays of strange systems was performed by electron scattering off a Be-9 target in order to study the ground-state masses of Lambda-hypernuclei. Positively charged kaons were detected by a short-orbit spectrometer with a broad momentum acceptance at zero degree forward angles with respect to the beam, efficiently tagging the production of strangeness in the target nucleus. In coincidence, negatively charged decay-pions were detected by two independent high-resolution spectrometers. About 10^3 pionic weak decays of hyperfragments and hyperons were observed. The pion momentum distribution shows a monochromatic peak at p_pi ~ 133 MeV/c, corresponding to the unique signature for the two-body decay of hyperhydrogen Lambda H-4 -> He-4 + pi-, stopped inside the target. Its binding energy was determined to be B_Lambda = 2.12 +- 0.01 (stat.) +- 0.09 (syst.) MeV with respect to the H-3 + Lambda mass

Photospheric Magnetic Fields of the Trailing Sunspots in Active Region NOAA 12396

The solar magnetic field is responsible for all aspects of solar activity. Sunspots are the main manifestation of the ensuing solar activity. Combining high-resolution and synoptic observations has the ambition to provide a comprehensive description of the sunspot growth and decay processes. Active region NOAA 12396 emerged on 2015 August 3 and was observed three days later with the 1.5-meter GREGOR solar telescope on 2015 August 6. High-resolution spectropolarimetric data from the GREGOR Infrared Spectrograph (GRIS) are obtained in the photospheric Si I $\lambda$ 1082.7 nm and Ca I $\lambda$1083.9 nm lines, together with the chromospheric He I $\lambda$1083.0 nm triplet. These near-infrared spectropolarimetric observations were complemented by synoptic line-of-sight magnetograms and continuum images of the Helioseismic and Magnetic Imager (HMI) and EUV images of the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO).Comment: 4 pages, 2 figures, to be published in "Solar Polarization Workshop 8", ASP Proceedings, Luca Belluzzi (eds.

New detectors for the kaon and hypernuclear experiments with KaoS at MAMI and with PANDA at GSI

The KaoS spectrometer at the Mainz Microtron MAMI, Germany, is perceived as the ideal candidate for a dedicated spectrometer in kaon and hypernuclei electroproduction. KaoS will be equipped with new read-out electronics, a completely new focal plane detector package consisting of scintillating fibres, and a new trigger system. First prototypes of the fibre detectors and the associated new front-end electronics are shown in this contribution. The Mainz hypernuclei research program will complement the hypernuclear experiments at the planned FAIR facility at GSI, Germany. At the proposed antiproton storage ring the spectroscopy of double Lambda hypernuclei is one of the four main topics which will be addressed by the PANDA Collaboration. The experiments require the operation of high purity germanium (HPGe) detectors in high magnetic fields (B= 1T) in the presence of a large hadronic background. The performance of high resolution Ge detectors in such an environment has been investigated.Comment: Presentation at International Symposium on the Development of Detectors for Particle, Astroparticle and Synchrotron Radiation Experiments, Stanford, Ca (SNIC06), 6 pages, LaTeX, 11 eps figure