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Manuscript Title: WTO - a deterministic approach to 4-Fermion physics.
Authors: G. Passarino
Program title: WTO
Catalogue identifier: ADDK_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 97(1996)261
Programming language: Fortran.
Computer: Alpha AXP-2100.
Operating system: Open VMS, VMS.
RAM: 4K words
Word size: 64
Keywords: Particle physics, Elementary, Event simulation, E+e- annihilation into Four fermions, Lep 2, Properties of the w Vector boson, Higgs boson, Initial and final, State qed radiation, Corrections qcd, Minimal standard model, Cross sections and Moments of distributions, Gauge invariance, Theoretical error, Deterministic Integration.
Classification: 11.2.

Nature of problem:
An accurate description of the process e+e- -> 4 fermions is needed in order to fully describe the physics available at LEP 2 and at higher energies. In particular the properties of the W boson can be correctly analyzed around and above the threshold only when the full gauge- invariant set of diagrams contributing to a given final state is included. Similarly the Z - Z production and the Higgs boson production can be studied within the minimal standard model. Indeed from a field theoretical point of view both the W and the Z bosons (and the Higgs boson too) are unstable particles and a full description of their production can only proceed through the complete set of matrix elements for the 4-fermion processes. Although at typical LEP 2 energies the difference between the full calculation and the double resonant approximation for a process like e+e- -> mu- nubarmu nutau tau+ is totally negligible, the same is certainly not true anymore when we consider e+e- -> e- nubare numu mu+ or any of the neutral current processes.

Solution method:
The helicity amplitudes for each given process are given, according to the formalism of ref. [2], in terms of the 7 independent invariant which characterize the phase space. The phase space itself, including all realistic kinematical cuts, is also described in terms of invariants. Initial state QED radiation is included by means of the structure function approach. Upon initialization the final state QCD corrections are included by adopting a naive approach (NQCD). The numerical integration, with complete cut-availability, is performed with the help of a deterministic integration routine which makes use of quasi-random, deterministic number sets, the shifted Korobov sets. The boundaries of the phase space, with kinematical cuts, are reconstructed through a backwards propagation of constraints.

Restrictions:
The theoretical formulation is specifically worked out for massless fermions, although this is not a limitation of principle. Emission of photons is strictly collinear and not pt is therefore included. No interface exists with the standard packages for hadronization.

Unusual features:
NAGLIB [1] subroutines used.

Running time:
Dependent on the process and on the required accuracy. For example a 0.1% accuracy for a CC11 process requires something of the order of 440 CPU seconds for Alpha AXP-2100. On the other extreme a 0.5% accuracy for some (but not all) of the NC processes requires approximately 12 CPU hours on the same computer.

References:
[1] NAG Fortran Library Manual Mark 15 (Numerical Algorithms Group, Oxford, 1991).
[2] G. Passarino, Nucl. Phys. B 237 (1984) 249.