Unitarity Constraints for Transverse Gauge Bosons at LEP and Supercolliders

Abstract

Using asymptotic helicity amplitudes for Vector-Vector, Vector-Higgs and Higgs-Higgs scattering, we establish the unitarity constraints on the $SU(2)_c$ conserving and $W_\mu$ depending interactions, which at sufficiently high energies may create strong forces among the transverse vector boson and Higgs states. We then derive upper bounds for the couplings of these interactions, which depend on the high energy scale where unitarity is saturated. If \eg\, unitarity is saturated at 1TeV, then $\lambda_W \lsim 0.12$ is obtained. The implied relations between the present and future LEP results, and the possible observations of strong effects at supercolliders, are also discussed