On a semi-analytical and realistic approach to e +e − annihilation into fermion pairs and to Bhabha scattering within the minimal standard model at LEP energies

Abstract

Theoretical predictions for the annihilation of e +e − into fermion pairs as well as for e +e − → e +e − around the Z 0 peak are reported. Different observables are considered, including the possibility of a realistic set-up for LEP physics, i.e. with cuts on acollinearity angle, energies or invariant mass and angular acceptance for the outgoing fermions. Pure weak corrections at the one-loop level are included in the formulation and leading higher order corrections due to a potentially large top quark mass are taken into account. Depending on the experimental set-up the initial state QED corrections are included by a convolution of the weakly corrected kernel distributions with a radiator function or with structure functions, where resummation of soft photon effects and hard photon emission up to O( α 2) are taken into account. Final state QED radiation, even in the presence of kinematical cuts, is treated analytically and exactly at O(α), and higher order contributions are taken into account. QCD effects are discussed for the parameters of the Z 0 resonance and for s-dependent quantities. Results and considerations for quantities which are physically observable at LEP are presented and discussed. The interplay with the experimental results is shown through an analysis of the LEP data, both at the level of the Z 0 parameters are given by the four LEP collaborations and at the level of the published results for the lineshape and asymmetry data. As a consequence constraints on the unknown parameters of the minimal standard model are deduced and analyzed. The features of a new semi-analytical computer program (TOPAZ0), which includes all the physical effects previously discussed, are briefly introduced. The numerical relevance of recently proposed higher order corrections, as initial state leptonic and hadronic pair production or O( G F 2 m t 4), O( α S G F m 2), O( α S 3), is analyzed in detail. A careful comparison with the existing programs is shown, indicating the overall agreement in the light of the present experimental errors and within the same choice of parameters, kinematical cuts and correction factor.