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 re
sult 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.
We construct a modification of the standard model which stabilizes the Higgs mass against quadratically divergent radiative corrections, using ideas originally discussed by Lee and Wick in the context of a finite theory of quantum electrodynamics. Th
e Lagrangian includes new higher derivative operators. We show that the higher derivative terms can be eliminated by introducing a set of auxiliary fields; this allows for convenient computation and makes the physical interpretation more transparent. Although the theory is unitary, it does not satisfy the usual analyticity conditions.
