Upgrade of the Monte Carlo program BHLUMI for Bhabha scattering at low angles to version 4.04

The new version of the Monte Carlo program for small-angle Bhabha scattering BHLUMI with an overall precision of 0.11% is presented. The main improvements are in the matrix element of the main multi-photon sub-generator based on the Yennie-Frautschi-Suura exponentiation, where the missing second-order terms in the leading-logarithmic (LL) approximation are supplemented and the contribution from the Z resonance is improved. In the LUMLOG sub-generator based on the LL approximation, we implement collinear photon emission in the nal state and we also add a down-graded third-order LL matrix element, which has exactly the same incomplete third-order LL contribution as the multi-photon BHLUMI. The new LUMLOG is therefore capable of calculating the missing third-order LL part in the cross sections obtained from the main multi-photon event generator, for arbitrary event selection. The rst-order event generator OLDBIS remains unchanged. Submitted to Computer Physics Communications x Work supported in part by the US DoE contract DE-FG05-91ER40627, Polish Government grants KBN 2P30225206, 2P03B17210, the European Union contract No. ERB-CIPD-CT94-0016 and Polish-French Collaboration within IN2P3. y On leave of absence from Institute of Computer Science, Jagellonian University, Krak ow, Poland. CERN-TH/96-158 UTHEP-96-0601 June 1996