Unitarity in gauge symmetry breaking on an orbifold

We study the unitarity bounds of scattering amplitudes in extra-dimensional gauge theory, in which the gauge symmetry is broken by the boundary conditions. The evaluation of the amplitude of the diagram including four massive gauge bosons in the external lines shows that the asymptotic power behavior of the amplitude is canceled. The calculation is carried out with the 5-dimensional standard model and the SU(5) grand unified theory, whose 5th dimensional coordinate is compactified on S-1/Z(2). The gauge theories broken through the orbifolding preserve unitarity at high energies, similarly to the broken gauge theories in which the gauge bosons acquire masses through the Higgs mechanism. We show that the contributions of the Kaluza-Klein states play a crucial role in conserving the unitarity.