The Lee-Wick Standard Model at temperatures near electroweak scale is considered, with the aim of studying the electroweak phase transition. While Lee-Wick theories possess states of negative norm, they are not pathological but instead are treated by imposing particular boundary conditions and using particular integration contours in the calculation of S-matrix elements. It is not immediately clear how to extend this prescription to formulate the theory at finite temperature; we explore two different pictures of finite-temperature LW theories, and calculate the thermodynamic variables and the (one-loop) thermal effective potential. We apply these results to study the Lee-Wick Standard Model and find that the electroweak phase transition is a continuous crossover, much like in the Standard Model. However, the high-temperature behavior is modified due to cancellations between thermal corrections arising from the negative- and positive-norm states.
Lee-Wick partners to the Standard Model Higgs doublet may appear at a mass scale that is significantly lower than that of the remaining Lee-Wick partner states. The relevant effective theory is a two-Higgs doublet model in which one doublet has wrong-sign kinetic and mass terms. We determine bounds on this effective theory, including those from neutral B-meson mixing, b --> X_s gamma, and Z --> b b-bar. The results differ from those of conventional two-Higgs doublet models and lead to meaningful constraints on the Lee-Wick Higgs sector.
We present the constraints on the parameter space of the Lee-Wick Standard Model coming from electroweak precision observables. The model predicts a large positive S and a negative T. We show that it is possible to find some regions in parameter space with a fermionic state as light as 2.4-3.5 TeV. We also propose a simple extension of the model including a fourth generation. In this case it is possible to pass the electroweak constraints with Lee-Wick fermionic masses of order 0.4-1.5 TeV and Lee-Wick gauge masses of order 3 TeV.
We examine the renormalization of Lee-Wick gauge theory to one loop order. We show that only knowledge of the wavefunction renormalization is necessary to determine the running couplings, anomalous dimensions, and vector boson masses. In particular, the logarithmic running of the Lee-Wick vector boson mass is exactly related to the running of the coupling. In the case of an asymptotically free theory, the vector boson mass runs to infinity in the ultraviolet. Thus, the UV fixed point of the pure gauge theory is an ordinary quantum field theory. We find that the coupling runs more quickly in Le…
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 integrat…
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…
This article reviews some recent work on a version of the standard model (the Lee-Wick standard model) that contains higher derivative kinetic terms that improve the convergence of loop diagrams removing the quadratic divergence in the Higgs boson mass. Naively higher derivative theories of this type are not acceptable since the higher derivative terms either cause instabilities (from negative energies) or a loss of unitarity (from negative norm states). Lee and Wick provided an interpretation for such theories arguing that theories with higher derivative kinetic terms can be unitary and stabl…
We determine constraints on the Lee-Wick Higgs sector obtained from the full LHC Higgs boson data set. We determine the current lower bound on the heavy neutral Lee-Wick scalar, as well as projected bounds at a 14 TeV LHC with 300 and 3000 inverse femtobarns of integrated luminosity. We point out that the first sign of new physics in this model may be the observation of a deviation from standard model expectations of the lighter neutral Higgs signal strengths corresponding to production via gluon-gluon fusion and decay to either tau or $Z$ pairs. The signal strength of the latter is greater th…
The process gg -> h_0 -> gamma gamma is studied in the Lee-Wick extension of the Standard Model (LWSM) proposed by Grinstein, O'Connell and Wise. In this model negative norm partners for each SM field are introduced with the aim to cancel quadratic divergences in the Higgs mass. All sectors of the model relevant to gg -> h_0 -> gamma gamma are diagonalized and results are commented on from the perspective of both the Lee-Wick and higher derivative formalisms. Deviations from the SM rate for gg -> h_0 are found to be of the order of 15% - 5% for Lee-Wick masses in the range 500GeV - 1000GeV. Ef…
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 the…
We consider a minimal Lee-Wick (LW) extension to the Standard Model in which the fields providing the most important contributions to the cancellation of quadratic divergences are the lightest. Partners to the SU(2) gauge bosons, Higgs, top quark, and left-handed bottom quark are retained in the low-energy effective theory, which is valid up to approximately 10 TeV; the remaining LW partners appear above this cutoff and complete the theory in the ultraviolet. We determine the constraints on the low-energy spectrum from the electroweak parameters S and T, and find LW states within the kinematic…
Recently, an extension of the standard model based on ideas of Lee and Wick has been discussed. This theory is free of quadratic divergences and hence has a Higgs mass that is stable against radiative corrections. Here, we address the question of whether or not it is possible to couple very heavy particles, with masses much greater than the weak scale, to the Lee-Wick standard model degrees of freedom and still preserve the stability of the weak scale. We show that in the LW-standard model the familiar see-saw mechanism for generating neutrino masses preserves the solution to the hierarchy puz…
Grinstein, O'Connell and Wise have recently presented an extension of the Standard Model (SM), based on the ideas of Lee and Wick (LW), which demonstrates an interesting way to remove the quadratically divergent contributions to the Higgs mass induced by radiative corrections. This model predicts the existence of negative-norm copies of the usual SM fields at the TeV scale with ghost-like propagators and negative decay widths, but with otherwise SM-like couplings. In earlier work, it was demonstrated that the LW states in the gauge boson sector of these models, though easy to observe, cannot b…
The Lee-Wick (LW) formulation of higher-derivative theories can be extended from one in which the extra degrees of freedom are represented as a single heavy, negative-norm partner for each known particle (N=2), to one in which a second, positive-norm partner appears (N=3). We explore the extent to which the presence of these additional states in a LW Standard Model affect precision electroweak observables, and find that they tend either to have a marginal effect (e.g., quark partners on T), or a substantial beneficial effect (e.g., Higgs partners on the Zbb couplings). We find that precision c…
Inspired by the Lee-Wick higher-derivative approach to quantum field theory, Grinstein, O'Connell, and Wise have illustrated the utility of introducing into the Standard Model negative-norm states that cancel quadratic divergences in loop diagrams, thus posing a potential resolution of the hierarchy problem. Subsequent work has shown that consistency with electroweak precision parameters requires many of the partner states to be too massive to be detected at the LHC. We consider the phenomenology of a yet-higher derivative theory that exhibits three poles in its bare propagators (hence N=3), w…
We consider gauge coupling unification in Lee-Wick extensions of the Standard Model that include higher-derivative quadratic terms beyond the minimally required set. We determine how the beta functions are modified when some Standard Model particles have two Lee-Wick partners. We show that gauge coupling unification can be achieved in such models without requiring the introduction of additional fields in the higher-derivative theory and we comment on possible ultraviolet completions.
We perform an analysis of the electroweak precision observables in the Lee-Wick Standard Model. The most stringent restrictions come from the S and T parameters that receive important tree level and one loop contributions. In general the model predicts a large positive S and a negative T. To reproduce the electroweak data, if all the Lee-Wick masses are of the same order, the Lee-Wick scale is of order 5 TeV. We show that it is possible to find some regions in the parameter space with a fermionic state as light as 2.4-3.5 TeV, at the price of rising all the other masses to be larger than 5-8 T…
We study the Maxwell-Einstein theory in the framework of effective field theories. We show that the modified one-loop renormalizable Lagrangian due to quantum gravitational effects contains a Lee-Wick vector field as an extra degree of freedom in the theory. Thus gravity provides a natural mechanism for the emergence of this exotic particle.
We study the gravitational corrections to the Maxwell, Dirac and Klein-Gorden theories in the large extra dimension model in which the gravitons propagate in the (4+n)-dimensional bulk, while the gauge and matter fields are confined to the four-dimensional world. The corrections to the two-point Green's functions of the gauge and matter fields from the exchanges of virtual Kaluza-Klein gravitons are calculated in the gauge independent background field method. In the framework of effective field theory, we show that the modified one-loop renormalizable Lagrangian due to quantum gravitational ef…
It was pointed out some time ago that there can be two variations in which the divergences of a quantum field theory can be tamed using the ideas presented by Lee and Wick. In one variation the Lee-Wick partners of the normal fields live in an indefinite metric Hilbert space but have positive energy and in the other variation the Lee-Wick partners can live in a normal Hilbert space but carry negative energy. Quantum mechanically the two variations mainly differ in the way the fields are quantized. In this article the second variation of Lee and Wick's idea is discussed. Using statistical mecha…
An extension of the standard model, the Lee-Wick standard model, based on ideas of Lee and Wick was recently introduced. It does not contain quadratic divergences in the Higgs mass and hence solves the hierarchy puzzle. The Lee-Wick standard model contains new heavy Lee-Wick resonances at the TeV scale that decay to ordinary particles. In this paper we examine the behavior of Lee-Wick resonances at high temperature. We argue that they contribute negatively to the energy density rho and pressure p and at temperatures much greater than their mass M their O(T^4) contributions to rho and p cancel …
We revisit the previously unsolved problems of ensuring Lorentz invariance and non-perturbative unitarity in Lee-Wick theories. We base our discussion on an ultraviolet completion of QED by Lee-Wick ghost fields, which is argued to be asymptotically safe. We argue that as long as the state space is based upon a suitable choice of distributions of a type invented by Gel'fand and Shilov, the Lee-Wick ghosts can be eliminated while preserving Lorentz invariance to produce a unitary theory. The method for eliminating ghosts is in principle non-perturbatively well-defined, in contrast with some pre…
The present Thesis is dedicated to a formal and phenomenological investigation of extensions to two separate sectors of the Standard Model of particle physics (SM): the electroweak sector and the strong sector. The Thesis is divided into two main parts: Part I focuses on the Lee-Wick Standard Model (LW SM), which, by providing a solution to the Hierarchy problem, forms a natural extension of the electroweak sector, while Part II studies the coloron theory, arising from extending the strong sector gauge group. Providing a general introduction about the current state of the SM and the associated…
We investigate the electroweak precision constraints on the recently proposed Lee-Wick Standard Model at tree level. We analyze low energy, Z-pole (LEP1/SLC) and LEP2 data separately. We derive the exact tree level low energy and Z-pole effective Lagrangians from both the auxiliary field and higher derivative formulation of the theory. For the LEP2 data we use the fact that the Lee-Wick Standard Model belongs to the so-called 'universal class' which can be described by seven oblique parameters at leading order in m_W^2/M_{1,2}^2. At tree level we find that the only non-zero oblique parameters …
We investigate the gravitational one-loop divergences of the standard model in large extra dimensions, with gravitons propagating in the (4+delta)-dimensional bulk and gauge fields as well as scalar and fermionic multiplets confined to a three-brane. To determine the divergences we establish a cut-off regularization which allows us to extract gauge-invariant counterterms. In contrast to the claim of a recent paper [arXiv:0807.0132], we show that the fermionic and scalar higher derivative counterterms do not coincide with the higher derivative terms in the Lee-Wick standard model. We argue that…
The Lee-Wick theories require unusual Lee-Wick (LW) partners to the standard model (SM) particles. The excitations of the unusual fields may have indefinite norms in the Hilbert space. In the present talk the thermodynamic results of a toy LW (where each normal particle has only one LW partner and the standard massless gauge fields do not appear in the normal particle spectrum as their LW partners has the potential to produce negative energy density) as well as a realistic LW universe (where the above restrictions are not present) will be discussed.
The Lee-Wick Standard Model assumes a minimal set of higher-derivative quadratic terms that produce a negative-norm partner for each Standard Model particle. Here we introduce additional terms of one higher order in the derivative expansion that give each Standard Model particle two Lee-Wick partners: one with negative and one with positive norm. These states collectively cancel unwanted quadratic divergences and resolve the hierarchy problem as in the minimal theory. We show how this next-to-minimal higher-derivative theory may be reformulated via an auxiliary field approach and written as a …
The present article discusses about the effect of a Lee-Wick partner infested radiation phase of the early universe. As Lee-Wick partners can contribute negative energy density so it is always possible that at some early phase of the universe when the Lee-Wick partners were thermalized the total energy density of the universe became very small making the effective Hubble radius very big. This possibility gives rise to the probability of a bouncing universe. As will be shown in the article that a simple Lee-Wick radiation is not enough to produce a bounce. There can be two possibilities which c…
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.
We analyze the tension between naturalness and isospin violation in the Lee-Wick Standard Model (LW SM), by computing tree-level and fermionic one-loop contributions to the post-LEP electroweak parameters and the Zbb coupling. The model is most natural when the LW partners of the gauge bosons and fermions are light, but small partner masses can lead to large isospin violation. The post-LEP parameters yield a simple picture in the LW SM: the gauge sector contributes to Y and W only, with leading contributions arising at tree-level, while the fermion sector contributes to S-hat and T-hat only, w…
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 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 o…
In the present article the thermodynamic results of the Lee-Wick partner infested universe have been applied in a toy model where there is one Lee-Wick partner to each of the standard model particle and more over the longitudinal degrees of freedom of the massive partners of the standard massless gauge bosons are neglected at high temperatures. For practical purposes, the chiral fermionic sector of Lee-wick theories requires two Lee-Wick partners per fermion which opens up the possibility for a negative energy density of the early universe. A toy Lee-Wick model with one fermionic partner relax…
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 present article is about the statistical mechanics of non-trivial field configurations. The non-trivial fields arise from the negative sign of the commutators and the anticommutators of the bosonic and fermionic field excitations. These kinds of fields were previously studied by Pauli and Lee and Wick. The thermal distribution function of the above mentioned fields are calculated in the article and using the thermal distribution functions the energy density, pressure and entropy density of the non-trivial field configurations are found out. The results match exactly with a previous calcula…
We propose to search for wrong displaced vertices, where decay products of the secondary vertex move towards the primary vertex instead of away from it, as a signature for microscopic violation of causality. We analyze in detail the leptonic sector of the recently proposed Lee-Wick Standard Model, which provides a well motivated framework to study acausal effects. We find that, assuming Minimal Flavor Violation, the Lee-Wick partners of the electron, {\tilde l}^e and \tilde e, can produce measurable wrong vertices at the LHC, the most promising channel being q \bar{q} --> \bar{\tilde l}^e {\ti…
In this paper we discuss the global symmetries and the renormalizibility of Lee-Wick scalar QED. In particular, in the "auxiliary-field" formalism we identify softly broken SO(1,1) global symmetries of the theory. We introduce SO(1,1) invariant gauge-fixing conditions that allow us to show in the two-field formalism directly that the number of superficially divergent amplitudes in a LW Abelian gauge theory is finite. To illustrate the renormalizability of the theory, we explicitly carry out the one-loop renormalization program in LW scalar QED and demonstrate how the counterterms required are …
Solutions to the hierarchy problem that require partners for each standard model particle often require that these states live at or above the electroweak scale, to satisfy phenomenological bounds. Partners to possible dark sector particles may be significantly lighter, due to the assumed weakness of the couplings between the dark and visible sectors. Here we consider the possibility that a dark sector might include light Lee-Wick particles. We present the formulation of a theory in which a dark photon and its Lee-Wick partner have kinetic mixing with hypercharge. We point out that the Lee-Wic…
We consider the cosmological application of Lee-Wick theory where a field has a higher derivative kinetic operators. The higher derivative term can be eliminated by introducing a set of auxiliary fields. We investigate the cosmological evolutions of these fields as a candidate of dark energy. This model has the same structure as so called ``quintom' model except the form of potentials and the sign of the slope of the potentials. This model can give the stable late time phantom dominated scaling solution ($ω_{\DE} < -1$) or tracking attractors ($ω_{\DE} = 0$) depending on the choice of the slop…
It was recently realized that a model constructed from a Lee-Wick type scalar field theory yields, at the level of homogeneous and isotropic background cosmology, a bouncing cosmology. However, bouncing cosmologies induced by pressure-less matter are in general unstable to the addition of relativistic matter (i.e. radiation). Here we study the possibility of obtaining a bouncing cosmology if we add radiation coupled to the Lee-Wick scalar field. This coupling in principle would allow the energy to flow from radiation to matter, thus providing a drain for the radiation energy. However, we find …
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.
The Lee-Wick (LW) Standard Model (SM) offers a new solution to the hierarchy problem. We discuss, using effective potential techniques, its peculiar ultraviolet (UV) behaviour. We show how quadratic divergences in the Higgs mass Mh cancel as a result of the unusual dependence of LW fields on the Higgs background (in a manner reminiscent of Little Higgses). We then extract from the effective potential the renormalization group evolution of the Higgs quartic coupling lambda above the LW scale. After clarifying an apparent discrepancy with previous results for the LW Abelian Higgs model we focus …
In an extension of the Standard Model(SM) based on the ideas of Lee and Wick, Grinstein, O'Connell and Wise have found an interesting way to remove the usual quadratically divergent contributions to the Higgs mass induced by radiative corrections. Phenomenologically, the model predicts the existence of Terascale, negative-norm copies of the usual SM fields with rather unique properties: ghost-like propagators and negative decay widths, but with otherwise SM-like couplings. The model is both unitary and causal on macroscopic scales. In this paper we examine whether or not such states with these…
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…
We study the cosmology of a Lee-Wick type scalar field theory. First, we consider homogeneous and isotropic background solutions and find that they are nonsingular, leading to cosmological bounces. Next, we analyze the spectrum of cosmological perturbations which result from this model. Unless either the potential of the Lee-Wick theory or the initial conditions are finely tuned, it is impossible to obtain background solutions which have a sufficiently long period of inflation after the bounce. More interestingly, however, we find that in the generic non-inflationary bouncing cosmology, pertur…
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…
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 $gg \to h_0 h_0 \to \bar b b γγ$ 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 p…
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 …
We study a higher derivative (HD) field theory with an arbitrary order of derivative for a real scalar field. The degree of freedom for the HD field can be converted to multiple fields with canonical kinetic terms up to the overall sign. The Lagrangian describing the dynamics of the multiple fields is known as the Lee-Wick (LW) form. The first step to obtain the LW form for a given HD Lagrangian is to find an auxiliary field (AF) Lagrangian which is equivalent to the original HD Lagrangian up to the quantum level. Till now, the AF Lagrangian has been studied only for N=2 and 3 cases, where $N$…
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…
The Lee, Oehme and Yang (LOY) theory of time evolution in two state subspace of states of the complete system is discussed. Some inconsistencies in assumptions and approximations used in the standard derivation of the LOY effective Hamiltonian, H(LOY), governig this time evolution are found. Eliminating these inconsistecies and using the LOY method, approximate formulae for the effective Hamiltonian, H(eff), governing the time evolution in this subspace (improving those obtained by LOY) are derived. It is found, in contradistinction to the standard LOY result, that in the case of neutral kaons…
