Unitarity in gauge symmetry breaking on orbifold

TL;DR

This paper investigates how unitarity is preserved in gauge theories with extra dimensions where symmetry breaking occurs via boundary conditions, emphasizing the role of Kaluza-Klein states in maintaining high-energy consistency.

Contribution

It demonstrates that unitarity is preserved in orbifold gauge symmetry breaking models, highlighting the importance of Kaluza-Klein modes in this process.

Findings

Unitarity bounds are maintained in 5D models with boundary condition breaking.

Kaluza-Klein states are essential for unitarity conservation.

High-energy amplitude behavior is canceled by extra-dimensional effects.

Abstract

We study the unitarity bounds of the scattering amplitudes in the extra dimensional gauge theory where the gauge symmetry is broken by the boundary condition. The estimation 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 will be done in the 5 dimensional standard model and the SU(5) grand unified theory, whose 5th dimensional coordinate is compactified on $S^1/Z_2$. The broken gauge theories through the orbifolding preserve the unitarity at high energies similarly to the broken gauge theories where the gauge bosons obtain their masses through the Higgs mechanism. We show that the contributions of the Kaluza-Klein states play a crucial role in conserving the unitarity.