GENTLE/4fan: a package of Fortran programs for the description of e+ e- annihilation into four fermions

We describe the program package gentle/4fan, which consists of the Fortran codes gentle\_4fan.f, 4fan.f, and gentle\_nc\_qed.f and is devoted to the description of e+ e- annihilation into four fermions. The codes are based on the semi-analytical approach. Initial state QED corrections are taken into account. The program versions, which are described here were used in the 1995 workshop `Physics at LEP~2'

Semi-analytical approach to off-shell W and Z pair production

We give a short review of the results for four fermion production, which have been obtained by the semi-analytical approach. The angular degrees of freedom (typically five or more) are integrated over analytically while the integrations over invariant fermion pair masses (typically two or more) remain to be performed by numerical methods. In addition to doubly resonating cross sections from virtual two boson production, QED corrections and background contributions were determined. However, a large variety of final state topologies has not been treated so far

Semi-analytical approach to four-fermion production in e+e- annihilation

A study of the semi-analytical approach to four-fermion production in e^+ e^- annihilation is presented. We classify all possible four-fermion final states and present results of new calculations for the `basic' processes with the WW,ZZ, and ZH off-shell production together with some examples of `background' processes. The Initial State Radiative corrections are included for the basic processes. Several numerical examples are given in the energy range from LEP2 up to \sqrt{s}=1 TeV

Measurements of the leptonic branching fractions of the τ\tau

Data collected with the DELPHI detector from 1993 to 1995 combined with previous DELPHI results for data from 1991 and 1992 yield the branching fractions B({\tau \rightarrow \mbox{\rm e} \nu \bar{\nu}}) = (17.877 \pm 0.109_{stat} \pm 0.110_{sys} )\% and $B({\tau \rightarrow \mu \nu \bar{\nu}}) = (17.325 \pm 0.095_{stat} \pm 0.077_{sys} )\%$

Measurement of inclusive π0\pi^{0} production in hadronic Z0Z^{0} decays

An analysis is presented of inclusive \pi^0 production in Z^0 decays measured with the DELPHI detector. At low energies, \pi^0 decays are reconstructed by \linebreak using pairs of converted photons and combinations of converted photons and photons reconstructed in the barrel electromagnetic calorimeter (HPC). At high energies (up to x_p = 2 \cdot p_{\pi}/\sqrt{s} = 0.75) the excellent granularity of the HPC is exploited to search for two-photon substructures in single showers. The inclusive differential cross section is measured as a function of energy for {q\overline q} and {b \bar b} events. The number of \pi^0's per hadronic Z^0 event is N(\pi^0)/ Z_{had}^0 = 9.2 \pm 0.2 \mbox{(stat)} \pm 1.0 \mbox{(syst)} and for {b \bar b}~events the number of \pi^0's is {\mathrm N(\pi^0)/ b \overline b} = 10.1 \pm 0.4 \mbox{(stat)} \pm 1.1 \mbox{(syst)} . The ratio of the number of \pi^0's in b \overline b events to hadronic Z^0 events is less affected by the systematic errors and is found to be 1.09 \pm 0.05 \pm 0.01. The measured \pi^0 cross sections are compared with the predictions of different parton shower models. For hadronic events, the peak position in the \mathrm \xi_p = \ln(1/x_p) distribution is \xi_p^{\star} = 3.90^{+0.24}_{-0.14}. The average number of \pi^0's from the decay of primary \mathrm B hadrons is found to be {\mathrm N} (B \rightarrow \pi^0 \, X)/\mbox{B hadron} = 2.78 \pm 0.15 \mbox{(stat)} \pm 0.60 \mbox{(syst)}