arXiv subjects
Publications and source records attributed to A. van Hameren.
The usefulness of recursive equations to compute scattering matrix elements for arbitrary processes is discussed. Explicit results at tree and one-loop order, obtained by the HELAC/PHEGAS package that is based on the Dyson-Schwinger recursive equations approach, are briefly presented.
The physics of high-energy collider experiments asks for delicate comparisons between theoretical predictions and experimental data. Signals and potential backgrounds for new physics have to be predicted at sufficient accuracy. The accuracy as well as the computational complexity of the calculations leading to the predictions depend on both the number of external particles in the process analyzed and the order of the quantum corrections, the number of loops, included in the calculation. We present some approaches to problems occurring in these calculations regarding the integration of phase-space and the inclusion of one-loop corrections.
A method is presented to construct goodness-of-fit statistics in many dimensions for which the distribution of all possible test results in the limit of an infinite number of data becomes Gaussian if also the number of dimensions becomes infinite. Furthermore, an explicit example is presented, for which this distribution as good as only depends on the expectation value and the variance of the statistic for any dimension larger than one.
The adaptive multi-channel method is applied to derive probability distributions from data samples. Moreover, an explicit algorithm is introduced, for which both the channel weights and the channels themselves are adaptive, and which can be used both for data analysis and for importance sampling in Monte Carlo integration. Finally, it is pointed out how the usefulness for data analysis can be used to optimize the integration procedure.
A small comment on the paper with the mentioned title by Carl M. Bender, Dorje C. Brody and Hugh F. Jones.
We present a ``hierarchical'' strategy for phase space generation in order to efficiently map the antenna momentum structures, typically occurring in QCD amplitudes.
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.
An extension of the SARGE-algorithm of \cite{HKD} is introduced, which includes the incoming momenta in the kinematical pole structure of the density with which the momenta are generated. The algorithm is compared with RAMBO in the integration of QCD-amplitudes in the SPHEL-approximation, and the computing times are extrapolated to those for the calculation with exact matrix elements.
We describe a uniformly fast algorithm for generating points \vec{x} uniformly in a hypercube with the restriction that the difference between each pair of coordinates is bounded. We discuss the quality of the algorithm in the sense of its usage of pseudo-random source numbers, and present an interesting result on the correlation between the coordinates.
We present an algorithm to generate any number of random massless momenta in phase space, with a distribution that contains the kinematical pole structure that is typically found in multi-parton QCD-processes. As an application, we calculate the cross-section of some \eplus\eminus \to partons processes, and compare SARGE's performance with that of the uniform-phase space generator RAMBO.
For the Lego discrepancy with M bins, which is equivalent with a chi^2-statistic with M bins, we present a procedure to calculate the moment generating function of the probability distribution perturbatively if M and N, the number of uniformly and randomly distributed data points, become large. Furthermore, we present a phase diagram for various limits of the probability distribution in terms of the standardized variable if M and N become infinite.
We calculate the 1/N corrections to the probability distributions of quadratic discrepancies for sets of N random points. This is achieved by the introduction of fermionic variables. We give the diagrammatic expansion up to and including the second order in 1/N. For some discrepancies, we give the explicit expansion to first order.
The concept of discrepancy plays an important role in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem of calculating the probability density of (quadratic) discrepancies into that of evaluating certain path integrals. Both their perturbative and non-perturbative properties are discussed.
We report on experience with an investigation of the analytic structure of the solution of certain algebraic complex equations. In particular the behavior of their series expansions around the origin is discussed. The investigation imposes the need for an analysis of the singularities and the Riemann sheets of the solution, in which numerical methods are used.