Complete Initial State QED Corrections to Off-Shell Gauge Boson Pair   Production in e+e- Annihilation
  We study Standard Model four-fermion production in e+ e- annihilation at LEP2 energies and above using a semi-analytical approach. We derive the complete QED initial state corrections (ISR) to the reactions e+e- -> ZZ -> $f_1\bar{f_1}f_2\bar{f_2}$ and e+e- -> W+W- -> ${\bar f}_1^u f_1^d f_2^u {\bar f}_2^d$ with $f_1\neq f_2$~and $f_i \neq e^\pm, \nu_e$. As compared to the well-known universal s-channel ISR, additional complexity arises due to non-universal, process-dependent ISR contributions from t- and u-channel fermion exchanges. The full set of formulae needed to perform numerical calculations is given together with samples of numerical results. 
Dima Bardin, Dietrich Lehner, Tord Riemann