New results on the theoretical precision of the LEP/SLC luminosity

We consider the error budget ibr the calculation of the LEP/SLC luminosity in the Monte Carlo event generator BHLUMI4.04 from the standpoint of new calculations of the exact results fur the O(alpha(2)) contributions to the processes e(+)e(-) --> e(+)e(-) + (n)gamma, n = 0,1,2, in the low angle luminosity regime at SLC/LEP energies, in context of Yennie-Frautschi-Suura exponentiation. We find that the error on the O(alpha(2)) photonic correction can be reduced from the currently published value 0.1% to the value 0.027%. This leads to an over-all precision tag for the currently available program BHLUMI4.04 of 0.061%. This reduction of the precision of the calculation is important for the final LEP1 EW precision Z physics tests of the Standard Model. (C) 1999 Elsevier Science B.V. All rights reserved.