Frits A. Berends

Recursive Calculations for Processes with n Gluons

Abstract A method is presented in which multigluon processes are calculated recursively. The technique is explicitly developed for processes where only gluons are produced and processes where in addition to the gluons also a quark-antiquark pair with or without a vector boson or e + e − pair are present. The recursion relations are used to derive rigorously amplitudes for certain configurations, where most of the gluons have the same helicities. This proves a number of conjectures in the literature. Also expressions for amplitudes with collinear or soft gluons are derived.

The six-gluon process as an example of Weyl-van der Waerden spinor calculus

Abstract In this paper the use of Weyl-van der Waerden spinors and its related calculus with dotted and undotted indices is advocated for those high energy processes where masses can be neglected. The use of this spinor formalism for complicated tree diagram calculations is a logical further step implied by the previous CALKUL procedure and its improvements. In order to demonstrate the usefulness of the method a process is taken for which no simple expression exists: the process 2 → 4 gluons. A manageable formula for the amplitude is found and a method for obtaining its square is presented. A numerical evaluation of the found expressions turns out to be considerably faster than previous calculations. The systematics in the 2 → 2, 3 and 4 gluon processes is discussed. Also, QED calculations are shown to simplify in the spinor formalism.

Higher Order Radiative Corrections at LEP Energies

Abstract A complete two-loop O( α 2 ) initial state radiative correction to the Z-resonance shape is presented. The correction is compared with those expressions where only the soft-photon effects are resummed in all orders of perturbation theory. Our result shows that the soft-photon part constitutes the bulk of the radiative correction near the top of the Z-peak. The effect of non-photonic QED processes on the Z-resonance is found to be very small. The above results have been obtained by means of a standard Feynman diagram calculation. In addition we have also computed the cross sections by using the renormalization group method, where besides the leading logs ln( s / m 2 ), the next-to-leading ones also have been taken into account.

Complete Lowest Order Calculations for Four Lepton Final States in electron-Positron Collisions

We present a Monte Carlo procedure which enables us to calculate exact cross sections for processes such as e+e− → e+e−e+e−, e+e− → e+e−μ+μ−, e+e− → μ+μ−μ+μ−, e+e− → μ+μ−τ+τ−. In particular, attention is paid to the calculation of the complete matrix element squared including all interferences and all masses and to the method by which unweighted events are generated. This scheme can also be used to calculate cross sections for e+e− → e+e− qq or e+e− → μ+μ−qq.

On the Theoretical Problems in Constructing Interactions Involving Higher Spin Massless Particles

Abstract It is shown that a gauge theory of self-interacting massless spin-3 particles which is analogous to Yang-Mills or the theory of gravity does not exist. A way out may be the existence of an interacting infinite family of massless particles of various spins. The first-order interactions which are possible between such particles show a remarkable structure. This is established by explicit construction. Detailed results are obtained for the possible algebraic structures which one may obtain for gauge theories which are induced from the gauge invariance of free lagrangians.

Radiative corrections to Bhabha scattering at high energies: (II). Hard photon corrections and Monte Carlo treatment

Abstract The cross section for single hard photon bremsstrahlung in Bhabha scattering is presented, and its main qualitative features are reviewed. Subsequently, the structure of a Monte Carlo event generator for Bhabha scattering at LEP/SLC energies, including all one-loop electroweak corrections, is discussed, in which the results on the virtual and soft photon corrections, given in the first paper of this set, are incorporated. Finally, a number of numerical results is presented.

Multiple soft gluon radiation in parton processes

Abstract A previously introduced recursive calculational method is used to analyse the systematics of multiple soft gluon emission in multi-parton processes. Factorizaton properties in subamplitudes are discussed. The case of soft gluons with equal helicities leads to simple expressions. Explicit formulae for double soft gluon emission are given. The hard partons in the processes are gluons, a qq pair with or without a vector boson. The special assumption of strong ordering of soft gluon momenta transforms the general expression into the ones known from the literature. For pure gluonic processes a new relation between the subamplitudes is derived.

Distributions for electron-positron annihilation into two and three photons

Abstract In this paper a procedure is outlined to simulate events for the reactions e + e − → γγ and γγγ . Various distributions thus obtained are presented. The standard radiative corrections are also calculated in this way. Moreover, an analytical expression for the total annihilation cross section is given up to order α 3 .

Monte Carlo simulation of two-photon processes: II: Complete lowest order calculations for four-lepton production processes in electron-positron collisions

Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland (see application form in this Method of solution issue) The 36 diagrams are divided into four groups (see ref. [11).For each group we design a separate generator in which all the Computer: Amdahl V7B or IBM 370/158 phase-space variables have been chosen such that the peaking structure is well described. The interference between the groups Programming language used: FORTRAN H-EXT * is taken care of by the assignment of a weight to the events. High speed storage required: 256 K Each event is first obtained according to one out of four approximate distributions by the corresponding generator. We No. of bits in a word: 32 account for the approximations used by imposing a weight on the events. Upon the application of a rejection algorithm we

All electroweak four-fermion processes in electron-positron collisions

Abstract This paper studies the electroweak production of all possible four-fermion states in e + e − collisions. Since the methods employed to evaluate the complete matrix elements and phase space are very general, all four-fermion final states in which the charged particles are detected can be considered. Also all kinds of experimental cuts can be imposed. With the help of the constructed event generator a large number of illustrative results is obtained, which show the relevance of backgrounds to a number of signals. For LEP 200 the W-pair signal and its background are discussed, for higher energies also Z-pair and single W and Z signals and backgrounds are presented.This paper studies the electroweak production of all possible four fermion states in e+ e- collisions. Since the methods employed to evaluate the complete matrix elements and phase space are very general, all four fermion final states in which the charged particles are detected can be considered. Also all kinds of experimental cuts can be imposed. With the help of the constructed event generator a large number of illustrative results is obtained, which show the relevance of backgrounds to a number of signals. For LEP 200 the W-pair signal and its background are discussed, for higher energies also Z-pair and single W and Z signals and backgrounds are presented.