arXiv subjects

Ronald Kleiss

Publications and source records attributed to Ronald Kleiss.

24 records · Page 2Linked to original sources

arXiv1996

Multidimensional sampling for simulation and integration: measures, discrepancies, and quasi-random numbers

This is basically a review of the field of Quasi-Monte Carlo intended for computational physicists and other potential users of quasi-random numbers. As such, much of the material is not new, but is presented here in a style hopefully more accessible to physicists than the specialized mathematical literature. There are also some new results: On the practical side we give important empirical properties of large quasi-random point sets, especially the exact quadratic discrepancies; on the theoretical side, there is the exact distribution of quadratic discrepancy for random point sets.

hep-ph↗

arXiv1996

Discrepancy-based error estimates for Quasi-Monte Carlo. II: Results in one dimension

The choice of a point set, to be used in numerical integration, determines, to a large extent, the error estimate of the integral. Point sets can be characterized by their discrepancy, which is a measure of its non-uniformity. Point sets with a discrepancy that is low with respect to the expected value for truly random point sets, are generally thought to be desirable. A low value of the discrepancy implies a negative correlation between the points, which may be usefully employed to improve the error estimate of a numerical integral based on the point set. We apply the formalism developed in a previous publication to compute this correlation for one-dimensional point sets, using a few different definitions of discrepancy.

hep-ph↗

arXiv1996

Definitions and upper bounds for unstable boson masses

We consider the problem of a proper definition of the mass of a heavy unstable boson. It is shown how various definitions are related by the renormalization-scheme independence of the full resummed amplitude. This is made explicit for the $W$ boson in the large $N_f$ limit, where we find an upper bound on the peak position of the lineshape and on the mass, provided a sensible definition of the mass is used. In more realistic models, we conjecture that under certain conditions the mass is similarly bounded. Using this approach an upper limit of about 1 TeV on the mass of the Minimal-Standard-Model Higgs boson is found, independent of any breakdown of perturbation theory.

hep-ph↗

arXiv1996

Discrepancy-based error estimates for Quasi-Monte Carlo. I: General formalism

We show how information on the uniformity properties of a point set employed in numerical multidimensional integration can be used to improve the error estimate over the usual Monte Carlo one. We introduce a new measure of (non-)uniformity for point sets, and derive explicit expressions for the various entities that enter in such an improved error estimate. The use of Feynman diagrams provides a transparent and straightforward way to compute this improved error estimate.

hep-ph↗

arXiv1995

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.

hep-ph↗

arXiv1993

The matrix element for radiative Bhabha scattering in the forward direction

We present an approximation to the matrix element for the process e+e- --> e+e-gamma, appropriate to the situation where one or both of the fermions are scattered over very small angles. The leading terms in the situation where all scattering angles are small contains not only terms quadratic in the electron mass, but also quartic and even sextic terms must be included. Special attention is devoted to the numerical stability of the resultant expression. Its relation to several existing formulae is discussed.

hep-ph↗