Extended Modified Observable Technique for a Multi-Parametric Trilinear Gauge Coupling Estimation at LEP II

This paper describes the extension of the Modified Observables technique in estimating simultaneously more than one Trilinear Gauge Couplings. The optimal properties, unbiasedness and consistent error estimation of this method are demonstrated by Monte Carlo experimentation using $\ell \nu jj$ four-fermion final state topologies. Emphasis is given in the determination of the expected sensitivities in estimating the $\lambda_{\gamma} - \Delta g_{1}^{z}$ and $\Delta k_{\gamma} - \Delta g_{1}^{z}$ pair of couplings with data from the 183 GeV LEPII run.Comment: (17 pages, 8 figures

Multidimensional Binning Techniques for a Two Parameter Trilinear Gauge Coupling Estimation at LEP II

This paper describes two generalization schemes of the Optimal Variables technique in estimating simultaneously two Trilinear Gauge Couplings. The first is an iterative procedure to perform a 2-dimensional fit using the linear terms of the expansion of the probability density function with respect to the corresponding couplings, whilst the second is a clustering method of probability distribution representation in five dimensions. The pair production of W's at 183 GeV center of mass energy, where one W decays leptonically and the other hadronically, was used to demonstrate the optimal properties of the proposed estimation techniques.Comment: (25 pages, 11 figures

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

The effects of organic farming on the soil physical environment

The aim of this research was to investigate the effects of organic farming practices on the development of soil physical properties, and in particular, soil structure in comparison with conventional agricultural management. The soil structure of organically and conventionally managed soils at one site was compared in a quantitative manner at different scales of observations using image analysis. Key soil physical and chemical properties were measured as well as the pore fractal geometry to characterise pore roughness. Organically managed soils had higher organic matter content and provided a more stable soil structure than conventionally managed soils. The higher porosity (%) at the macroscale in soil under conventional management was due to fewer larger pores while mesoand microscale porosity was found to be greater under organic management. Organically managed soils typically provided spatially well distributed pores of all sizes and of greater roughness compared to those under conventional management. These variations in the soil physical environment are likely to impact significantly on the performance of these soils for a number of key processes such as crop establishment and water availabilit

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