We study the constraints on the Lee-Wick Higgs sector arising from direct collider searches. We work in an effective-field theory framework, where all of the Lee-Wick partners are integrated out, with the sole exception of the Lee-Wick Higgs bosons. The resulting theory is a two-Higgs doublet model where the second doublet has wrong-sign kinetic and mass terms. We include the bounds coming from direct Higgs searches at both LEP and Tevatron using the code HiggsBounds, and show the currently excluded parameter space. We also analyze the prospects of LHC Run-I, finding that with a total integrated luminosity of 5 fb $^{-1}$ and a center-of-mass energy of 7 TeV, most of the parameter space for the SM-like CP-even Higgs will be probed.
The Lee-Wick Standard Model is a highly constrained model which solves the gauge hierarchy problem at the expense of including states with negative norm. It appears to be macroscopically causal and consistent. This model is extended by considering the two-Higgs doublet extension of the Lee-Wick model. Rewriting the Lagrangian using auxiliary fields introduces two additional doublets of Lee-Wick partners. The model is highly constrained, with only one or two additional parameters beyond that of the usual two-Higgs doublet model, and yet there are four doublets. Mass relations are established by…
Precision Electroweak Constraints on the N=3 Lee-Wick Standard Model
高导数理论的李-威克（Lee-Wick，LW）公式可以从一个额外的自由度被表示为每个已知粒子（N=2）的单个重的负范数伙伴的公式，扩展到一个出现第二个正范数伙伴的公式（N=3）。我们探讨了LW标准模型中这些额外状态的存在对精确电弱观测量的影响程度，并发现它们往往具有边际效应（例如，T上的夸克伙伴），或实质上有益的效果（例如，Higgs partners on the Zbb couplings）。我们发现，精度的限制，使LW的合作伙伴存在于广泛的区域的质量参数空间访问的大型强子对撞机，使LW理论一个可行的超越标准模型的候选人。
Most discussions of propagators in Lee-Wick theories focus on the presence of two massive complex conjugate poles in the propagator. We show that there is in fact only one pole near the physical region, or in another representation three pole-like structures with compensating extra poles. The latter modified Lehmann representation is useful caculationally and conceptually only if one includes the resonance structure in the spectral integral.
We study perturbative unitarity in a Lorentz-symmetry-violating QED model with higher-order derivative operators in the light of the results of Lee and Wick to preserve unitarity in indefinite metric theories. Specifically, we consider the fermionic sector of the Myers-Pospelov model, which includes dimension-five operators, coupled to standard photons. We canonically quantize the model, paying attention to its effective character, and show that its Hamiltonian is stable, emphasizing the exact stage at which the indefinite metric appears and decomposes into a positive-metric sector and a negat…
The Lee-Wick models are higher-derivative theories that are claimed to be unitary thanks to a peculiar cancelation mechanism. In this paper, we provide a new formulation of the models, to clarify several aspects that have remained quite mysterious, so far. Specifically, we define them as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions, which can be related to one another by a well-defined, albeit nonanalytic procedure. Working in a generic Lorentz frame, the models are intrinsically equipped with the right recipe to treat the pinch…
We study the perturbative unitarity of the Lee-Wick models, formulated as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions and the values of a loop integral in the various regions are related to one another by a nonanalytic procedure. We show that the one-loop diagrams satisfy the expected, unitary cutting equations in each region: only the physical degrees of freedom propagate through the cuts. The goal can be achieved by working in suitable subsets of each region and proving that the cutting equations can be analytically continued…
In this work, in the light of the developments for indefinite metric theories made by Lee and Wick, we study perturbative unitarity in a Lorentz-invariance violating QED model with higher-order operators. We show that by following the Lee-Wick prescription it is possible to preserve unitarity in the model at one-loop order in the coupling.
We reconsider the Lee-Wick (LW) models and compare their properties to the properties of the models that contain purely virtual particles. We argue against the LW premise that unstable particles can be removed from the sets of incoming and outgoing states in scattering processes. The removal leads to a non-Hermitian classical limit, besides clashing with the observation of the muon. If, on the other hand, all the states are included, the LW models have a Hamiltonian unbounded from below or negative norms. Purely virtual particles, on the contrary, lead to a Hermitian classical limit and are ab…
The "fakeon" is a fake degree of freedom, i.e. a degree of freedom that does not belong to the physical spectrum, but propagates inside the Feynman diagrams. Fakeons can be used to make higher-derivative theories unitary. Moreover, they help us clarify how the Lee-Wick models work. In this paper we study the fakeon models, that is to say the theories that contain fake and physical degrees of freedom. We formulate them by (nonanalytically) Wick rotating their Euclidean versions. We investigate the properties of arbitrary Feynman diagrams and, among other things, prove that the fakeon models are…
We propose a class of multidimensional higher derivative theories of gravity without extra real degrees of freedom besides the graviton field. The propagator shows up the usual real graviton pole and extra complex conjugates poles that do not contribute to the absorptive part of the physical scattering amplitudes. Indeed, they may consistently be excluded from the asymptotic observable states of the theory making use of the Lee-Wick and Cutkoski, Landshoff, Olive and Polkinghorne prescription for the construction of a unitary S-matrix. Therefore, the spectrum consists on the graviton and short…
We construct a theory of real scalar fields that interpolates between two different theories: a Lee-Wick theory with $N$ propagator poles, including $N-1$ Lee-Wick partners, and a nonlocal infinite-derivative theory with kinetic terms modified by an entire function of derivatives with only one propagator pole. Since the latter description arises when taking the $N\rightarrow\infty$ limit, we refer to the theory as "asymptotically nonlocal." Introducing an auxiliary-field formulation of the theory allows one to recover either the higher-derivative form (for any $N$) or the Lee-Wick form of the …
Asymptotically nonlocal field theories represent a sequence of higher-derivative theories whose limit point is a ghost-free, infinite-derivative theory. Here, we extend previous work on pure scalar and Abelian gauge theories to asymptotically nonlocal non-Abelian theories. In particular, we confirm that there is a limit in which the Lee-Wick spectrum can be decoupled, but where the hierarchy problem is resolved via an emergent nonlocal scale that regulates loop diagrams and that is hierarchically smaller than the lightest Lee-Wick resonance.
We consider unitarity and causality in a higher-derivative theory of infinite order, where propagators fall off more quickly in the ultraviolet due to the presence of a transcendental entire function of the momentum. Like Lee-Wick theories, these field theories might provide new avenues for addressing the hierarchy problem; unlike Lee-Wick theories, tree-level propagators do not have additional poles corresponding to unobserved particles with unusual properties. We consider microscopic acausality in these nonlocal theories. The acausal ordering of production and decay vertices for ordinary res…
We study perturbative unitarity in the scalar sector of the Myers-Pospelov model. The model introduces a preferred four-vector $n$ which breaks Lorentz symmetry and couples to a five-dimension operator. When the preferred four-vector is chosen in the pure timelike or lightlike direction, the model becomes a higher time derivative theory, leading to a cubic dispersion relation. Two of the poles are shown to be perturbatively connected to the standard ones, while a third pole, which we call the Lee-Wick-like pole, is associated to a negative metric, in Hilbert space, threatening the preservation…
We study the main options for a unitary and renormalizable, local quantum field theory of the gravitational interactions. The first model is a Lee-Wick superrenormalizable higher-derivative gravity, formulated as a nonanalytically Wick rotated Euclidean theory. We show that, under certain conditions, the $S$ matrix is unitary when the cosmological constant vanishes. The model is the simplest of its class. However, infinitely many similar options are allowed, which raises the issue of uniqueness. To deal with this problem, we propose a new quantization prescription, by doubling the unphysical p…
Based on the weakly-coupled two-Higgs-doublet model with spontaneous CP-violation (named Lee model) and the mechanism to generate the correlation between smallness of CP-violation and lightness of scalar mass, as we proposed earlier, we predicted a light CP-mixing scalar $η$ in which pseudoscalar component is dominant. It is a natural scenario in which $m_η\sim\mathcal{O}(10\textrm{GeV})\ll v$. Masses of all other scalars ($h$, $H$, $H^\pm$) should be around the electro-weak scale $v$. Among them, the 125 GeV Higgs ($h$) couplings are standard-model like, and the charged Higgs ($H^\pm$) mass s…
