Soft High Energy Scattering in Nonperturbative QCD

In this report diffractive high energy reactions are discussed in a functional integral approach where hadronic amplitudes are calculated from vacuum expectation values of lightlike Wegner-Wilson loops. In the first part we calculate elastic differential cross sections for high energy and small momentum transfer elastic proton-proton (pp) scattering which are in reasonable agreement with the experimental data. In the second part we consider exclusive $\pi^0$ production in ep-scattering. At high energies photon and odderon exchange contribute to this reaction. We show that odderon exchange leads to a much larger inelastic than elastic $\pi^0$ production cross section, dominating the $\gamma$ contribution by orders of magnitude. Observing our process at HERA would establish the soft odderon.Comment: Talk given at the International Conference on Elastic and Diffractive Scattering (EDS 99), Protvino, Russia, 28 June-2 July 199

Differential cross sections for high energy elastic hadron-hadron scattering in nonperturbative QCD

Total and differential cross sections for high energy and small momentum transfer elastic hadron-hadron scattering are studied in QCD using a functional integral approach. The hadronic amplitudes are governed by vacuum expectation values of lightlike Wegner-Wilson loops, for which a matrix cumulant expansion is derived. The cumulants are evaluated within the framework of the Minkowskian version of the model of the stochastic vacuum. Using the second cumulant, we calculate elastic differential cross sections for hadron-hadron scattering. The agreement with experimental data is good.Comment: 30 pages, 14 figure

Training samples in objective Bayesian model selection

Central to several objective approaches to Bayesian model selection is the use of training samples (subsets of the data), so as to allow utilization of improper objective priors. The most common prescription for choosing training samples is to choose them to be as small as possible, subject to yielding proper posteriors; these are called minimal training samples. When data can vary widely in terms of either information content or impact on the improper priors, use of minimal training samples can be inadequate. Important examples include certain cases of discrete data, the presence of censored observations, and certain situations involving linear models and explanatory variables. Such situations require more sophisticated methods of choosing training samples. A variety of such methods are developed in this paper, and successfully applied in challenging situations

An inverse of the evaluation functional for typed Lambda-calculus

In any model of typed λ-calculus conianing some basic arithmetic, a functional p - * (procedure—* expression) will be defined which inverts the evaluation functional for typed X-terms, Combined with the evaluation functional, p-e yields an efficient normalization algorithm. The method is extended to X-calculi with constants and is used to normalize (the X-representations of) natural deduction proofs of (higher order) arithmetic. A consequence of theoretical interest is a strong completeness theorem for βη-reduction, generalizing results of Friedman [1] and Statman [31: If two Xterms have the same value in some model containing representations of the primitive recursive functions (of level 1) then they are provably equal in the βη- calculus

Program logics for homogeneous meta-programming.

A meta-program is a program that generates or manipulates another program; in homogeneous meta-programming, a program may generate new parts of, or manipulate, itself. Meta-programming has been used extensively since macros were introduced to Lisp, yet we have little idea how formally to reason about metaprograms. This paper provides the first program logics for homogeneous metaprogramming – using a variant of MiniMLe by Davies and Pfenning as underlying meta-programming language.We show the applicability of our approach by reasoning about example meta-programs from the literature. We also demonstrate that our logics are relatively complete in the sense of Cook, enable the inductive derivation of characteristic formulae, and exactly capture the observational properties induced by the operational semantics

325 MHz VLA Observations of Ultracool Dwarfs TVLM 513-46546 and 2MASS J0036+1821104

We present 325 MHz (90 cm wavelength) radio observations of ultracool dwarfs TVLM 513-46546 and 2MASS J0036+1821104 using the Very Large Array (VLA) in June 2007. Ultracool dwarfs are expected to be undetectable at radio frequencies, yet observations at 8.5 GHz (3.5 cm) and 4.9 GHz (6 cm) of have revealed sources with > 100 {\mu}Jy quiescent radio flux and > 1 mJy pulses coincident with stellar rotation. The anomalous emission is likely a combination of gyrosynchrotron and cyclotron maser processes in a long-duration, large-scale magnetic field. Since the characteristic frequency for each process scales directly with the magnetic field magnitude, emission at lower frequencies may be detectable from regions with weaker field strength. We detect no significant radio emission at 325 MHz from TVLM 513-46546 or 2MASS J0036+1821104 over multiple stellar rotations, establishing 2.5{\sigma} total flux limits of 795 {\mu}Jy and 942 {\mu}Jy respectively. Analysis of an archival VLA 1.4 GHz observation of 2MASS J0036+1821104 from January 2005 also yields a non-detection at the level of < 130 {\mu}Jy . The combined radio observation history (0.3 GHz to 8.5 GHz) for these sources suggests a continuum emission spectrum for ultracool dwarfs which is either flat or inverted below 2-3 GHz. Further, if the cyclotron maser instability is responsible for the pulsed radio emission observed on some ultracool dwarfs, our low-frequency non-detections suggest that the active region responsible for the high-frequency bursts is confined within 2 stellar radii and driven by electron beams with energies less than 5 keV.Comment: 11 pages, 5 figures, submitted to A

Lasercooled RaF as a promising candidate to measure molecular parity violation

The parameter $W_\mathrm{a}$, which characterizes nuclear spin-dependent parity violation effects within the effective molecular spin-rotational Hamiltonian, was computed for the electronic ground state of radium fluoride (RaF) and found to be one of the largest absolute values predicted so far. These calculations were performed with the complex generalised Hartree-Fock method within a two-component (quasi-relativistic) zeroth-order regular approximation framework. Peculiarities of the molecular electronic structure of RaF lead to highly diagonal Franck-Condon matrices between vibrational states of the electronic ground and first excited states, which renders the molecule in principle suitable for direct laser cooling. As a trapped gas of cold molecules offers a superior coherence time, RaF can be considered a promising candidate for high-precision spectroscopic experiments aimed at the search of molecular parity-violation effects.Comment: 4.5 pages, 1 figure, 2 tables. Supplementary material can be requested from the authors. Minor changes to version