In quantum mechanics the deterministic property of classical physics is an emergent phenomenon appropriate only on macroscopic scales. Lee and Wick introduced Lorentz invariant quantum theories where causality is an emergent phenomenon appropriate fo
r macroscopic time scales. In this paper we analyze a Lee-Wick version of the O(N) model. We argue that in the large N limit this theory has a unitary and Lorentz invariant S matrix and is therefore free of paradoxes in scattering experiments. We discuss some of its acausal properties.
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.
It is likely that the LHC will observe a color- and charge-neutral scalar whose decays are consistent with those of the Standard Model (SM) Higgs boson. The Higgs interpretation of such a discovery is not the only possibility. For example, electrowea
k symmetry breaking (EWSB) could be triggered by a spontaneously broken, nearly conformal sector. The spectrum of states at the electroweak scale would then contain a narrow scalar resonance, the pseudo-Goldstone boson of conformal symmetry breaking, with Higgs-like properties. If the conformal sector is strongly coupled, this pseudo-dilaton may be the only new state accessible at high energy colliders. We discuss the prospects for distinguishing this mode from a minimal Higgs boson at the LHC and ILC. The main discriminants between the two scenarios are (1) cubic self-interactions and (2) a potential enhancement of couplings to massless SM gauge bosons. A particularly interesting situation arises when the scale f of conformal symmetry breaking is approximately the electroweak scale v~246 GeV. Although in this case the LHC may not be able to tell apart a pseudo-dilaton from the Higgs boson, the self-interactions differ in a way that depends only on the scaling dimension of certain operators in the conformal sector. This opens the possibility of using dilaton pair production at future colliders as a probe of EWSB induced by nearly conformal new physics.
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.
