${\cal O} (\alpha^2)$ Next-to-Leading Photonic Corrections to   Small-Angle Bhabha Scattering in the Structure Function Formalism
  A general method for computing ${\cal O} (\alpha^2)$ and higher-order next-to-leading photonic corrections is presented and applied to the precision calculation of the small-angle Bhabha scattering cross section in the phase-space region of interest for the luminosity measurement at LEP. The formulation is based on a proper matching of exact $\cal O (\alpha)$ results with higher-order corrections in the Structure Function formalism. The results of the approach are analytically compared with theoretical calculations, both for $s$- and $t$-channel processes, available for simple Event Selections. Numerical predictions for realistic Event Selections are also provided and critically compared with the ones existing in the literature. 
G. Montagna, O.Nicrosini and F. Piccinini