Off-shell $W$-pair production in $e^+ e^-$-annihilation. Initial state radiation

Abstract

With a current-splitting technique, we calculate the gauge-invariant initial-state radiation to order \oalf\ with soft-photon exponentiation for on- and off-shell $W$-pair production. This result generalizes the convolution formula, which is known from the description of the $Z$ resonance, to the case of the production of two $W$-bosons. After up to eightfold analytical integrations, a sufficiently smooth integral over three invariant masses remains to be treated numerically. Including the Coulomb singularity, the largest corrections are covered. We discuss the corrections in a large energy range up to $\sqrt{s}$=1~TeV and draw numerical conclusions on their influence on the $W$-mass determination at LEP~200. Table~1 and figure~5 are revised after correcting the analytical formulae for the nonuniversal corrections.

12 pages, latex, 5 figures, 1 table, a uuencoded file containing the latex file and figures is available via anonymous ftp at ftp://ftp.ifh.de/pub/preprint/desy93-035rev.uu Note: paper publ. in Phys. Lett. B308 (1993) 403, is revised now. second submission due to syntax error, no changes of the paper