Cross section of the processes e++e−→e++e−(γ), π++π−(γ), μ++μ−(γ), γ+γ(γ) in the energy region 200MeV⩽2E⩽3GeV

The cross section for different processes induced by e+e− annihilation, in the kinematical limit , is calculated taking into account first order corrections to the amplitudes and the corrections due to soft emitted photons, with energy ω⩽ΔE⩽ϵ in the center of mass of the e+e− colliding beams. The results are given separately for charge-odd and charge-even terms in the final channels π+π−(γ) and μ+μ−(γ). In case of pions, form factors are taken into account. The differential cross sections for the processes: e++e−→e++e−(+γ), →π++π−(γ), →μ++μ−(γ), →γ+γ(γ) have been calculated and the corresponding formulas are given in the ultrarelativistic limit . For a quantitative evaluation of the contribution of higher order of the perturbation theory, the production of π+π−, including radiative corrections, is calculated in the approach of the lepton structure functions. This allows to estimate the precision of the obtained results as better than 0.5% outside the energy region corresponding to narrow resonances. A method to integrate the cross section, avoiding the difficulties which arise from singularities is also described.