SEMIANALYTICAL 3RD-ORDER CALCULATIONS OF THE SMALL-ANGLE BHABHA CROSS-SECTIONS

We integrate analytically the total cross section of the small-angle B habha scattering over the complete multiple photon phase space. Some i nclusive distributions are also obtained. The differential distributio ns are taken from the Monte Carlo event generator BHLUMI and correspon d to the second-order matrix element with Yennie-Frautschi-Suura (YFS) exponentiation. In the integration we control terms up to leading thi rd-order and sub-leading second-order, in the leading-logarithmic appr oximation. The analytical results provide a vital cross-check of the c orrectness of the BHLUMI program. The analytical and Monte Carlo resul ts agree to within 1.7 x 10(-4). On the other hand, the calculation gi ves us unique insight into the relation between exclusive YFS exponent iation and naive inclusive exponentiation.