Massive Vector Scattering in Lee-Wick Gauge Theory

TL;DR

This paper shows that in Lee-Wick gauge theory, scattering amplitudes of massive vector bosons do not grow with energy, maintaining perturbative unitarity, unlike in the Standard Model with a heavy Higgs.

Contribution

It proves that Lee-Wick gauge theories preserve unitarity at all orders, under certain operator dimension restrictions, contrasting with the Standard Model's unitarity violation.

Findings

Longitudinal vector boson scattering amplitudes are energy-independent.

Perturbative unitarity holds in Lee-Wick gauge theories.

Results are valid to all orders of perturbation theory.

Abstract

We demonstrate that amplitudes describing scattering of longitudinally polarized massive vector bosons present in non-Abelian Lee-Wick gauge theory do not grow with energy and, hence, satisfy the constraints imposed by perturbative unitarity. This result contrasts with the widely-known violation of perturbative unitarity in the standard model with a very heavy Higgs. Our conclusions are valid to all orders of perturbation theory and depend on the existence of a formulation of the theory in which all operators are of dimension four or less. This can be thought of as a restriction on the kinds of higher dimension operator which can be included in the higher derivative formulation of the theory.