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 W W, 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 LEP 2 up to √ s = 1 TeV.

We describe version 2.0 of the Fortran program GENTLE/4fan for the semi-analytic computation of cross-sections and distributions in four-fermion production in e + e − annihilation. GENTLE/4fan covers all charged current and neutral current fourfermion final states with no identical particles, no electrons, and no electron neutrinos in the final state. Initial state radiation representing the most relevant quantum corrections and anomalous triple gauge boson couplings have been included. Semi-analytic; numerical integration of analytic formulae: (i) Born approximation: Numerical integrations over two virtualities s 1 , s 2 plus optionally over the boson production angle θ; (ii) QED corrections in the flux function approach (FF): one additional numerical integration over virtuality s ′ ; (iii) QED corrections in the structure function approach (SF): alternatively to (ii), two additional numerical integrations over x 1 , x 2 Restrictions on complexity of the problem: Only selective experimental cuts are possible; the program calculates total cross-sections and the distribution in the boson production angle; background contributions are available only for selected final state configurations; no inclusion of pure weak corrections Typical running time:The running time strongly depends upon the options used; one finds e.g.: Born cross-section on-shell: below one sec., off-shell: few secs.; LLA QED corrections (FF) on-shell: few secs.; off-shell: few mins.; LLA QED corrections (SF) on-shell: few secs.; off-shell: several mins.; complete ISR (FF): on-shell: few mins., off-shell: several hours; with background: from few secs. (no QED) to several hours (with QED); with anomalous couplings: from few secs. (no QED) to several mins. (with QED)

We study Standard Model four-fermion production in e + e − annihilation at LEP2 energies and above using a semi-analytical approach. We derive the complete QED initial state corrections (ISR) to the reactionsν e . As compared to the well-known universal s-channel ISR, additional complexity arises due to nonuniversal, process-dependent ISR contributions from t-and u-channel fermion exchanges. The full set of formulae needed to perform numerical calculations is given together with samples of numerical results. the soft+virtual contributions S (k) J and the hard contributions H (k) J take the form S (k)

The process e + e ! l lf f, where l is a charged or a neutral lepton and f any charged fermion, is analyzed. The study uses the ALEPH data collected at LEP from 1989 to 1993 at centre-of-mass energies between 88 and 95 GeV, corresponding to almost two million hadronic Z decays and to a total integrated luminosity o f 79 pb 1 . F or all channels, the data agree well with the standard model expectation both in shape and normalization. The indication of an excess in the e + e ! + f f channel, reported by ALEPH in 1991, is not conrmed.

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