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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. The 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.
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Recently an extension of the standard model (the Lee-Wick standard model) based on ideas of Lee and Wick (LW) was introduced. It does not contain quadratic divergences in the Higgs mass and hence solves the hierarchy puzzle. The LW-standard model contains new heavy LW-resonances at the TeV scale that decay to ordinary particles. In this paper we examine in more detail the flavor structure of the theory. We integrate out the heavy LW-fermions at tree level and find that this induces flavor changing Z boson couplings. However, these flavor changing neutral currents are acceptably small since they are automatically suppressed by small Yukawa couplings. This is the case even though the theory does not satisfy the principle of minimal flavor violation. New couplings of the charged W bosons to quarks and leptons are also induced. We also integrate out the LW-Higgs and examine the four-fermion operators induced.
Within the framework of the Lee Wick Standard Model (LWSM) we investigate Higgs pair production $gg to h_0 h_0$, $gg to h_0 tilde p_0$ and top pair production $gg to bar tt$ at the Large Hadron Collider (LHC), where the neutral particles from the Higgs sector ($h_0$, $tilde h_0$ and $tilde p_0$) appear as possible resonant intermediate states. We investigate the signal $gg to h_0 h_0 to bar b b gamma gamma$ and we find that the LW Higgs, depending on its mass-range, can be seen not long after the LHC upgrade in 2012. More precisely this happens when the new LW Higgs states are below the top pair threshold. In $gg to bar tt$ the LW states, due to the wrong-sign propagator and negative width, lead to a dip-peak structure instead of the usual peak-dip structure which gives a characteristic signal especially for low-lying LW Higgs states. We comment on the LWSM and the forward-backward asymmetry in view of the measurement at the TeVatron. Furthermore, we present a technique which reduces the hyperbolic diagonalization to standard diagonalization methods. We clarify issues of spurious phases in the Yukawa sector.
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.
Lee-Wick-like scalar model near a Dirichlet plate is considered in this work. The modified propagator for the scalar field due to the presence of a Dirichlet boundary is computed, and the interaction between the plate and a point-like scalar charge is analysed. The non-validity of the image method is investigated and the results are compared with the corresponding ones obtained for the Lee-Wick gauge field and for the standard Klein-Gordon field.
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 for 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.
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