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.1

We examine dimension-six extensions of the standard electroweak Lagrangian which are invariant under local SU(2) L × U(1) Y -transformations. The dimensionfour trilinear and quadrilinear effective interactions of the vector bosons with one another are found to coincide with the vector boson interactions previously derived from global SU(2) weak isospin symmetry broken by electromagnetism. Supplementing the model by a well-known dimension-six single-parameter quadrupole interaction leads to the most general vector boson self-couplings that can be obtained by addition of dimension-six terms to the standard Lagrangian. We examine in some detail another SU(2) L × U(1) Y -symmetric interaction which contains W 3 B mixing and modifies both vector boson self-couplings and fermionic interactions. Independently of being strongly constrained by the LEP 1 data, the addition of this interaction to the above-mentioned non-standard ones does not change the form of the trilinear and quadrilinear non-standard self-couplings of the vector bosons. Therefore, while being interesting in itself with respect to LEP 1 physics, this term is irrelevant with respect to the phenomenology of the vector-boson self-interactions.

We point out that the equivalence theorem, which relates the amplitude for a process with external longitudinally polarized vector bosons to the amplitude in which the longitudinal vector bosons are replaced by the corresponding pseudo-Goldstone bosons, is not valid for effective Lagrangians. However, a more general formulation of this theorem also holds for effective interactions. The generalized theorem can be utilized to determine the high-energy behaviour of scattering processes just by power counting and to simplify the calculation of the corresponding amplitudes. We apply this method to the phenomenologically most interesting terms describing effective interactions of the electroweak vector and Higgs bosons in order to examine their effects on vector-boson scattering and on vector-boson-pair production in ff annihilation. The use of the equivalence theorem in the literature is examined. *

An improved effective vector-boson approximation is applied to hadron-hadron collisions. The effective vector-boson approximation in this form is accurate enough to reproduce the result of a complete perturbative calculation for the specific example of ZZ production within 10%. This is true even far away from a possible Higgs boson resonance and thus in a region where the transverse intermediate vector bosons give the dominant contribution. Simple approximate formulas which greatly reduce the calculational effort are derived. The full information about the kinematics is, however, lost in these approximations. A comparison between the improved, the approximate, and existing formulations is presented. ͓S0556-2821͑97͒03109-3͔

Application of a Stueckelberg transformation allows one to connect various Lagrangians which have been independently proposed for non-standard couplings. We discuss the reduction of the number of independent parameters in the Lagrangian and compare symmetry arguments with dimensional arguments.