On amplitude zeros at threshold

The occurrence of zeros of 2 to n amplitudes at threshold in scalar theories is studied. We find a differential equation for the scalar potential, which incorporates all known cases where the 2 to n amplitudes at threshold vanish for all sufficiently large $n$, in all space-time dimensions, $d\ge 1$. This equation is related to the reflectionless potentials of Quantum Mechanics and to integrable theories in 1+1 dimensions. As an application, we find that the sine-Gordon potential and its hyperbolic version, the sinh-Gordon potential, also have amplitude zeros at threshold, ${\cal A}(2\to n)=0$, for $n\ge 4$ and $d\ge 2$, independently of the mass and the coupling constant.Comment: 6 pages, Latex, CERN-TH.6762/9

Multiscalar production amplitudes beyond threshold

We present exact tree-order amplitudes for $H^* \to n~H$, for final states containing one or two particles with non-zero three-momentum, for various interaction potentials. We show that there are potentials leading to tree amplitudes that satisfy unitarity, not only at threshold but also in the above kinematical configurations and probably beyond. As a by-product, we also calculate $2\to n$ tree amplitudes at threshold and show that for the unbroken $\phi^4$ theory they vanish for $n>4~$, for the Standard Model Higgs they vanish for $n\ge 3~$ and for a model potential, respecting tree-order unitarity, for $n$ even and $n>4~$. Finally, we calculate the imaginary part of the one-loop $1\to n$ amplitude in both symmetric and spontaneously broken $\phi^4$ theory.Comment: 11 pages, Latex, 3 figures (available on request

(1,0) superconformal theories in six dimensions and Killing spinor equations

We solve the Killing spinor equations of 6-dimensional (1,0) superconformal theories in all cases. In particular, we derive the conditions on the fields imposed by the Killing spinor equations and demonstrate that these depend on the isotropy group of the Killing spinors. We focus on the models proposed by Samtleben et al in \cite{ssw} and find that there are solutions preserving 1,2, 4 and 8 supersymmetries. We also explore the solutions which preserve 4 supersymmetries and find that many models admit string and 3-brane solitons as expected from the M-brane intersection rules. The string solitons are smooth regulated by the moduli of instanton configurations.Comment: 26 page

Zero-dimensional field theory

A study of zero-dimensional theories, based on exact results, is presented. First, relying on a simple diagrammatic representation of the theory, equations involving the generating function of all connected Green's functions are constructed. Second, exact solutions of these equations are obtained for several theories. Finally, renormalization is carried out. Based on the anticipated knowledge of the exact solutionsthe full dependence on the renormalized coupling constant is studied.Comment: 38 pages, LaTe

Recursive actions for scalar theories

We introduce a class of self-interacting scalar theories in which the various coupling contants obey a recursive relation. These imply a particularly simple form for the generating function of the Feynman amplitudes with vanishing external momenta, as well as for the effective potential. In addition we discuss an interesting duality inherent in these models. Specializing to the case of zero spacetime dimensions we find intriguing nullification properties for the amplitudes.Comment: 28 pages, 2 figures Replaced contract numbe

Tsunami hazards in the Eastern Mediterranean: strong earthquakes and tsunamis in the East Hellenic Arc and Trench system

International audienceData on tsunami phenomena occurring in the East Hellenic Arc and Trench system (HA-T) from antiquity up to the present have been updated, critically evaluated and compiled in the standard GITEC format developed in the last decade for the New European Tsunami Catalogue. New field observations are presented for the tsunamis of 9 February 1948 and 24 March 2002. From the 18 tsunamis reported eight are rather well-documented while another nine remain doubtful. The mean recurrence of strong tsunamis is likely equal to about 142 years. Most of the tsunamis documented are caused by strong earthquakes occurring in the area offshore Rhodes to the east or northeast of the island. However, there are large earthquakes near Rhodes that do not cause tsunamis, like the 1926 and 1957 ones, which is of particular importance for the tsunami hazard assessment

Stable Calculations for Unstable Particles: Restoring Gauge Invariance

We discuss theoretical and phenomenological aspects of the use of boson propagators with energy-dependent widths in predictions for high-energy scattering processes. In general, gauge invariance is violated in such calculations. We discuss several approaches to restore gauge invariance, necessary for a reliable result. The most promising method is the addition of the relevant parts of the fermionic corrections, which fulfills all Ward identities. The numerical difference between this and other approaches is studied. A number of recommendations are given for LEP2 computations.Comment: 13 pages LaTeX inc 1 figure, uses epsf, axodraw. The ps file is available as ftp://rulgm4.leidenuniv.nl/pub/preprints/stable.ps or on http://rulgm4.leidenuniv.nl/ under preprints. Added two reference