Pair production in small-angle Bhabha scattering

The radiative corrections due to pair production in small-angle high-energy e(+)e(-) Bhabha scattering are considered. The corrections due to the production of virtual pairs as well as real soft and hard pairs are calculated analytically. The collinear and semi-collinear kinematical regions of hard pair production are taken into account. The results in the leading and next-to-leading logarithmic approximations yield an accuracy similar to 0.1%. The results of numerical calculations show that the effects of pairs production must be taken into account in the precise luminosity determination at LEP.