The luminosity determination of electron-positron colliders operating in th
e region of low-lying hadronic resonances (E-cm similar or equal to 1-10 Ge
V), such as BEPC/BES, DA Phi NE, KEKB, PEP-II and VEPP-2M, requires the pre
cision calculation of the Bhabha process at large scattering angles. In ord
er to achieve a theoretical accuracy at a few 0.1% level, the inclusion of
radiative corrections is mandatory, The phenomenologically relevant effect
of QED corrections is taken into account in the framework of the Parton Sho
wer (PS) method, which is employed both for cross section calculation and e
vent generation. To test the reliability of the approach, a benchmark calcu
lation, including exact O(alpha) corrections and higher-order leading logar
ithmic contributions, is developed as well and compared in detail with the
PS predictions. The effect of O(alpha) next-to-leading and higher-order lea
ding corrections is investigated in the presence of realistic event selecti
ons for the Bhabha process at the Phi factories. A new Monte Carlo generato
r for data analysis (BABAYAGA) is presented, with an estimated accuracy of
0.5%. Possible developments aiming at improving its precision and range of
applicability are discussed. (C) 2000 Elsevier Science B.V. All rights rese
rved.