Missing third-order leading-log corrections in the small-angle Bhabha calculation

We calculate the missing third-order leading-log (LL) contribution in the second-order cross section of the small-angle Bhabha process for a realistic event selection. We find that, for the second-order calculation with Yennie-Frautschi-Suura exponentiation, the missing third-order LL correction is below 2 × 10−4 and is therefore negligible with respect to the current experimental LEP precision, while for the second-order calculation without exponentiation it can be closer to or even comparable with the experimental precision, at least for certain event selections. The calculation is implemented the LUMLOG Monte Carlo event generator.