Luminosities for Vector-Boson Vector-Boson Scattering at High Energy Colliders

We derive exact expressions for luminosities of massive vector-boson pairs which can be used to describe the cross sections for processes in hadron collisions or $e^{+}{e}^{-}$ annihilation which proceed via two-vector-boson scattering. Our approach correctly takes into account the mutual influence of the emission of one vector boson on the emission of a second one. We show that only approximately the exact luminosities can be factorized into convolutions of single-vector-boson distributions. Numerical results are given and compared to simplified approaches.