Final-state QED Multipole Radiation in Antenna Parton Showers

We present a formalism for a fully coherent QED parton shower. The complete multipole structure of photonic radiation is incorporated in a single branching kernel. The regular on-shell 2 to 3 kinematic picture is kept intact by dividing the radiative phase space into sectors, allowing for a definition of the ordering variable that is similar to QCD antenna showers. A modified version of the Sudakov veto algorithm is discussed that increases performance at the cost of the introduction of weighted events. Due to the absence of a soft singularity, the formalism for photon splitting is very similar to the QCD analogon of gluon splitting. However, since no color structure is available to guide the selection of a spectator, a weighted selection procedure from all available spectators is introduced.Comment: 33 pages, 12 figures. Added subsection 4.3 and some comments and references per reviewer request. Version accepted by JHE

Competing Sudakov Veto Algorithms

We present a way to analyze the distribution produced by a Monte Carlo algorithm. We perform these analyses on several versions of the Sudakov veto algorithm, adding a cutoff, a second variable and competition between emission channels. The analysis allows us to prove that multiple, seemingly different competition algorithms, including those that are currently implemented in most parton showers, lead to the same result. Finally, we test their performance and show that there are significantly faster alternatives to the commonly used algorithms.Comment: 16 pages, 1 figur

BBBREM - Monte Carlo simulation of radiative Bhabha scattering in the very forward direction

A fast and simple Monte Carlo program is presented that simulates single Bremsstrahlung in Bhabha scattering, e+e- --> e+e-gamma, without constraints on scattering angles. This allows the study of this process at arbitrarily small, or even vanishing, scattering angles. Experimental cuts can be imposed on an event-by-event basis, allowing for detailed studies of the process as a limitation to beam lifetimes, or a luminosity-measuring device, in e+e- storage rings. As an application, we show that the easy introduction of a cutoff parameter, corresponding to the characteristic distance between particles in the bunches, gives a reduced cross section that is in good agreement with observation.Comment: 14 pages, NIKHEF-H/94-01 and CERN SL/94-03 (OP

Discrepancy-based error estimates for Quasi-Monte Carlo. III: Error distributions and central limits

In Quasi-Monte Carlo integration, the integration error is believed to be generally smaller than in classical Monte Carlo with the same number of integration points. Using an appropriate definition of an ensemble of quasi-randompoint sets, we derive various results on the probability distribution of the integration error, which can be compared to the standard Central Limit theorem for normal stochastic sampling. In many cases, a Gaussian error distribution is obtained.Comment: 15 page

Singular Cross Sections in Muon Colliders

We address the problem that the cross section for the collisions of unstable particles diverges, if calculated by standard methods. This problem is considered for beams much smaller than the decay length of the unstable particle, much larger than the decay length and finally also for pancake- shaped beams. We find that in all cases this problem can be solved by taking into account the production/propagation of the unstable particle and/or the width of the incoming wave packets in momentum space.Comment: 12 pages, 3 figures. References corrected. Removed one sentence about a fact that was known. Added explaination why one of our graphs is different as compared to one of the references. Clearified explaination in sec. 3.

Counting tree diagrams: asymptotic results for QCD-like theories

We discuss the enumeration of Feynman diagrams at tree order for processes with external lines of different types. We show how this can be done by iterating algebraic Schwinger-Dyson equations. Asymptotic estimates for very many external lines are derived. Applications include QED, QCD and scalar QED, and the asymptotic estimates are numerically confronted with the exact results.Comment: 16 page

The Electroweak Standard Model in the Axial Gauge

We derive the Feynman rules of the standard model in the axial gauge. After this we prove that the fields $\phi_W$ and $\phi_Z$ do not correspond to physical particles. As a consequence, these fields cannot appear as incoming or outgoing lines in Feynman graphs. We then calculate the contribution of these fields in the case of a particular decay mode of the top quark.Comment: 16 pages, no figures. Added derivation of polarization su