T. Riemann

ZFITTER v.6.21: A semi-analytical program for fermion pair production in e+e− annihilation

We describe ZFITTER, a Fortran program based on a semi-analytical approach to fermion pair production in e+e− annihilation at a wide range of centre-of-mass energies, including the PETRA, TRISTAN, LEP1/SLC, and LEP2 energies. A flexible treatment of complete O(α) QED corrections and of some higher order contributions is made possible with three calculational chains containing different realistic sets of restrictions in the photon phase space. Numerical integrations are at most one-dimensional. Complete O(α) weak loop corrections supplemented by selected higher-order terms may be included. The program calculates Δr, the Z width, differential cross-sections, total cross-sections, integrated forward–backward asymmetries, left–right asymmetries, and for τ pair production also final-state polarization effects. Various interfaces allow fits to be performed with different sets of free parameters.

QED corrections with partial angular integration to fermion pair production in e+ e- annihilation

Abstract Analytic formulae are derived for the complete photon energy spectrum due to QED corrections to fermion pair production in the case of a limited angular acceptance for the final state fermions. After a numerical integration over the energy of non-observed photons, this corresponds to typical experimental conditions at LEP/SLC.

HECTOR 1.00 a program for the calculation of QED, QCD and electroweak corrections to ep and l± N deep inelastic neutral and charged current scattering

Abstract A description of the Fortran program HECTOR for a variety of semi-analytical calculations of radiative QED, QCD, and electroweak corrections to the double-differential cross sections of NC and CC deep inelastic charged lepton proton (or lepton deuteron) scattering is presented. HECTOR originates from the substantially improved and extended earlier programs HELIOS and TERAD91. It is mainly intended for applications at HERA or LEP⊗LHC, but may be used also for μN scattering in fixed target experiments. The QED corrections may be calculated in different sets of variables: leptonic, hadronic, mixed, Jaquet-Blondel, double angle etc. Besides the leading logarithmic approximation up to order O ( α 2 ), exact O ( α ) corrections and inclusive soft photon exponentiation are taken into account. The photoproduction region is also covered.

Bhabha scattering with higher order weak loop corrections

We present a compact incorporation of the weak loop effects in the Bhabha cross section with the accuracy required by the present precision experiments. Special care is taken of the leading 2-loop effects from a heavy top quark which are of the type α2(mt/MZ)4. We find very satisfactory agreement between two independent calculations which are based on different gauges and different renormalizations. The compact formulation in terms of form factors allows a straight-forward implementation into analytic or Monte Carlo QED calculations.

Off-shell W-pair production in e+e−-annihilation. Initial state radiation

Abstract With a current-splitting technique, we calculate the gauge-invariant initial-state radiation to order O(α) with soft-photon exponentiation for on- and off-shell W -pair production. This result generalizes the convolution formula, which is known from the description of the Z resonance, to the case of the production of two W -bosons. After up to eightfold analytical integrations, a sufficiently smooth integral over three invariant masses remains to be treated numerically. Including the Coulomb singularity, the largest corrections are covered. We discuss the corrections in a large energy range up to √ s = 1 TeV and draw numerical conclusions on their influence on the W -mass determination at LEP 200.

The convolution integral for the forward-backward asymmetry in e+e− annihilation

Abstract The complete convolution integral for the forward-backward asymmetry AFB in e+e− annihilation is obtained in order O (α) with soft photon exponentiation. The influence of these QED corrections on AFB in the vicinity of the Z peak is discussed. The results are used to comment on a recent ad hoc ansatz using convolution weights derived for the total cross section.

GENTLE/4fan v. 2.0 A program for the semi-analytic calculation of predictions for the process e+e− → 4f

Abstract 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 four-fermion 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.

Off-shell

The various four-fermion production channels in e+e− annihilation are discussed and the CC11 process e+e− → ƒ1μ ƒ1d ƒ2μ ƒ2d ƒ ≠ e, is studied in section d2σ/ds1 ds2, with s1, s2 being the invariant masses squared of the two fermion pairs, may be expressed by six generic functions. All but one may be found in the literature. The cross section, including initial-state radiation and the Coulomb correction, is discussed and compared with other calculations from low energies up to √s = 2 TeV.

W

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 LEP 2 up to s = 1 TeV.

pair production in

Electroweak radiative corrections to the Z peak are determined in the unitary gauge. Peculiarities of this gauge are discussed. A gauge-invariant expression for the weak loop corrections is presented. An approximate cross section formula based on partial Z widths may be derived from the exact one loop calculations.