Nonrenormalizable Models Research Articles

The influence of quark anomalous magnetic moment in the Nambu–Jona‐Lasinio model with different regularizations

AbstractThe Nambu–Jona‐Lasinio model is known for its simplicity and capacity to reproduce some of the basic characteristics of the quantum chromodynamics phase diagram. However, since it is a nonrenormalizable model, there are regularization issues that should be treated conveniently. This is the case when considering the quark anomalous magnetic moment (AMM) when external constant magnetic fields are present. Regularization procedures based on entangled functions between the magnetic field and the cutoff of the model can predict first‐order phase transitions for chiral symmetry restoration at finite values of magnetic fields and inverse magnetic catalysis. The strengths of magnetic fields explored in NJL model and lattice QCD do not show first‐order phase transition. In the present work, we show that some of the previous results are regularization‐dependent effects and how to handle the divergences using the vacuum magnetic regularization scheme.

A non-renormalizable neutrino mass model with S3 ⊗ Z2 symmetry

The lepton sector is studied within a flavored non-renormalizable model where the S3 ⊗ Z2 flavor symmetry controls the masses and mixings. In this work, the effective neutrino as well as the charged lepton mass matrices are hierarchical and these have (under a benchmark in the charged sector) a kind of Fritzsch textures that accommodate the mixing angles in good agreement with the last experimental data. The model favors the normal hierarchy, this also predicts consistent values for the CP-violating phase and the |mee| effective Majorana neutrino mass rate. Along with this, the branching ratio for the lepton flavor violation process, µ → eγ, is below the current bound.

Gravitational self-regularization of quantum fields at Planck scales

Loop diagrams with near-Planck energies create a strong external gravitational field, which slows down local processes for distant observers up to their freezing. Since Planck length is the gravitational radius of the system of quanta, the events of this and smaller scale cannot occur in finite world time t and do not contribute to the S-matrix. Consequently, gravitational time dilation, leading to a strong redshift of local frequencies, provides gravitational self-regularization of the loop diagrams. The loop corrections without gravity effects, cut off at Planck energy, give upper bounds for the corrections with gravity effects and this fact leads to simple rules of gravitational regularization. The corrections with quanta of gauge fields and gravitons are small, and the perturbation theory series converge. At pre-Planck energies, one-loop graviton contributions are sufficient, since the multi-loop ones are damped by high degrees of the relation “energy/Planck energy”. Scalar field with power-law growing corrections should be effective field. Non-linearity of fields enhances gravity and get faster freezing, which suppresses the high energy terms. Nonrenormalizable models are finite, but become consistent only when their loop corrections remain small on Planck scale and this occurs in quantum gravity. Gravitationally regularized Extended Standard Model (ESM), including gravitons and Standard Model with effective scalars, is renormalizable and finite, which simplifies its further generalization.

Do we need to use regularization for the thermal part in the NJL model? * *Supported by the Natural Science Foundation of Jiangsu Province (BK20140523), the start-up funding of Jiangsu University (15JDG042, 4111190010), the National Natural Science Foundation of China (11735007)

The Nambu–Jona-Lasinio (NJL) model is one of the most useful tools for studying non-perturbative strong interactions in matter. Because it is a nonrenormalizable model, the choice of regularization is a subtle issue. In this paper, we discuss one of the general issues regarding regularization in the NJL model, which is whether we need to use regularization for the thermal part by evaluating the quark chiral condensate and thermal properties in the two-flavor NJL model. The calculations in this work include three regularization schemes that contain both gauge covariant and invariant schemes. We found that, regardless of the regularization scheme we choose, it is necessary to use regularization for the thermal part when calculating physical quantities related to the chiral condensate and to not use regularization for the thermal part when calculating physical quantities related to the grand potential.

What is the scale of new physics behind the muon g−2 ?

We study the constraints imposed by perturbative unitarity on the new physics interpretation of the muon $g-2$ anomaly. Within a Standard Model Effective Field Theory (SMEFT) approach, we find that scattering amplitudes sourced by effective operators saturate perturbative unitarity at about 1 PeV. This corresponds to the highest energy scale that needs to be probed in order to resolve the new physics origin of the muon $g-2$ anomaly. On the other hand, simplified models (e.g.~scalar-fermion Yukawa theories) in which renormalizable couplings are pushed to the boundary of perturbativity still imply new on-shell states below 200 TeV. We finally suggest that the highest new physics scale responsible for the anomalous effect can be reached in non-renormalizable models at the PeV scale.

QCD phase diagram in a magnetized medium from the chiral symmetry perspective: the linear sigma model with quarks and the Nambu–Jona-Lasinio model effective descriptions

We review the main features of the QCD phase diagram description, at finite temperature, baryon density and in the presence of a magnetic field, from the point of view of effective models, whose main ingredient is chiral symmetry. We concentrate our attention on two of these models: The linear sigma model with quarks and the Nambu--Jona-Lasinio model. We show that a main ingredient to understand the characteristics of the phase transitions is the inclusion of plasma screening effects that capture the physics of collective, long-wave modes, and thus describe a prime property of plasmas near transition lines, namely, long distance correlations. Inclusion of plasma screening makes possible to understand the inverse magnetic catalysis phenomenon even without the need to consider magnetic field-dependent coupling constants. Screening is also responsible for the emergence of a critical end point in the phase diagram even for small magnetic field strengths. Although versatile, the NJL model is also a more limited approach since, being a non-renormalizable model, a clear separation between pure vacuum and medium effects is not always possible. The model cannot describe inverse magnetic catalysis unless a magnetic field dependent coupling is included. The location of the critical end point strongly depends on the choice of the type of interaction and on the magnetic field dependence of the corresponding coupling. Overall, both models provide sensible tools to explore the properties of magnetized, strongly interacting matter. However, a cross talk among them as well as a consistent physical approach to determine the model parameters is much needed.

Building a Genuine Quantum Gravity

An affine quantization approach leads to a genuine quantum theory of general relativity by extracting insights from a short list of increasingly more complex, soluble, perturbably nonrenormalizable models.

Vanishing trace anomaly in flat spacetime

Quantum scale invariant regularization is a variant of dimensional regularization where the renormalization scale is treated as a dynamical field. But, rather than be regarded as a novel regularization method on par with dimensional regularization, momentum cutoff, Pauli-Villars etc., it should be understood as a way to define a subset in the infinite space of nonrenormalizable models of certain type. The subset realizes the demand that renormalization scale, along with any other dimensionful parameters, should be interpreted as a dynamical field's homogeneous background. This restriction is most straightforwardly implemented using dimensional regularization but it can hypothetically be imposed with any regularization method. Theories that satisfy it offer a new perspective on the radiative violation of global scale symmetry associated with RGE functions. As a result of the quantum scale invariant regularization being implemented, the scale symmetry is preserved at the quantum level despite the RGE functions being non-zero, as can be inspected at the level of composite quantum operators that govern dilatation of Green functions. We analyze these statements in explicit detail using a specific but easily generalized toy model with scalar fields.

Recursion relations for tree-level amplitudes in theSU(N)nonlinear sigma model

It is well-known that the standard BCFW construction cannot be used for on-shell amplitudes in effective field theories due to bad behavior for large shifts. We show how to solve this problem in the case of the SU(N) non-linear sigma model, i.e. non-renormalizable model with infinite number of interaction vertices, using scaling properties of the semi-on-shell currents, and we present new on-shell recursion relations for all on-shell tree-level amplitudes in this theory.

New Affine Coherent States Based on Elements of Nonrenormalizable Scalar Field Models

Recent proposals for a nontrivial quantization of covariant, nonrenormalizable, self‐interacting, scalar quantum fields have emphasized the importance of quantum fields that obey affine commutation relations rather than canonical commutation relations. When formulated on a spacetime lattice, such models have a lattice version of the associated ground state, and this vector is used as the fiducial vector for the definition of the associated affine coherent states, thus ensuring that in the continuum limit, the affine field operators are compatible with the system Hamiltonian. In this article, we define and analyze the associated affine coherent states as well as briefly review the author′s approach to nontrivial formulations of such nonrenormalizable models.

Taming nonrenormalizability

Nonrenormalizable scalar fields, such as φ4n, n ⩾ 5, require infinitely many distinct counterterms when perturbed about the free theory, and lead to free theories when defined as the continuum limit of a lattice regularized theory restricted only to arbitrary mass and coupling constant renormalization. Based on the proposal that functional integrals for interacting nonrenormalizable models do not reduce to the expression for the free field functional integral as the coupling constant vanishes—a proposal supported by the fact that even the set of classical solutions for such models does not reduce to the set of free field solutions as the coupling constant vanishes—it has been conjectured that for nonrenormalizable models the interaction term acts partially as a hard core eliminating certain fields otherwise allowed by the free theory. As a consequence, interacting models are continuously connected to a pseudofree theory that takes into account the hard core as the coupling constant vanishes, and this general view is supported by simple quantum mechanical examples as well as soluble but nonrelativistic nonrenormalizable models. This paper proposes a pseudofree model for relativistic nonrenormalizable models about which it is argued that a perturbation expansion of the interaction is term-by-term divergence free.

A new approach to nonrenormalizable models

Nonrenormalizable quantum field theories require counter-terms; and based on the hard-core interpretation of such interactions, it is initially argued, contrary to the standard view, that counter-terms suggested by renormalized perturbation theory are in fact inappropriate for this purpose. Guided by the potential underlying causes of triviality of such models, as obtained by alternative analyses, we focus attention on the ground-state distribution function, and suggest a formulation of such distributions that exhibits nontriviality from the start. Primary discussion is focused on self-interacting scalar fields. Conditions for bounds on general correlation functions are derived, and there is some discussion of the issues involved with the continuum limit.

Some properties of meta-stable supersymmetry-breaking vacua in Wess–Zumino models

Abstract As a contribution to the current efforts to understand supersymmetry-breaking by meta-stable vacua, we study general properties of supersymmetry-breaking vacua in Wess–Zumino models: we show that tree-level degeneracy is generic, explore some constraints on the couplings and present a simple model with a long-lived meta-stable vacuum, ending with some generalizations to non-renormalizable models.

One-loop determinant of Dirac operator in non-renormalizable models

We use proper-time regularizations to define the one-loop fermion determinant in the form suggested by Gasser and Leutwyler some years ago. We show how to obtain the polynomial by which this definition of ln detD needs to be modified in order to arrive at the fermion determinant whose modulus is invariant under chiral transformations. As an example it is shown how the fundamental symmetries associated with the NJL model are preserved in a consistent way.

New models of gauge mediated dynamical supersymmetry breaking

We propose a simple class of nonrenormalizable models of gauge mediated dynamical supersymmetry breaking. The models do not have gauge singlet fields. The Standard Model gauge group is embedded in the global symmetry of the SUSY breaking sector. At the renormalizable level the models possess a set of classical flat directions. Only one of those flat directions is unlifted by quantum effects, and requires nonrenormalizable term to stabilize the potential for the corresponding modulus. Large vacuum expectation value of this modulus at the minimum of the potential generates mass terms for the messenger fields. There are no light messengers, thus this class of models evades difficulties encountered in earlier constructions using nonrenormalizable models.

TOP CONDENSATES AS HIGGS SUBSTITUTE

We review developments in top condensation starting from the first example which was a simple effective Nambu–Jona-Lasinio (NJL) model. The connection between the underlying four-fermion interaction and the structure of the composite Higgs sector is generalized to obtain the scalar sectors of a number of Standard Model extensions dynamically from some NJL model, as well as to include possible radial and spin excitations of the Higgs sector. In all these NJL models the symmetries do not forbid further higher dimensional four-fermion operators. If such operators could have arbitrary strength then this would result in arbitrary Higgs and top mass predictions. The nonrenormalizable NJL model is however thought to be only an effective description of some fully consistent theory where higher dimensional operators are not free parameters so that the corresponding four-fermion operators are restricted. We discuss renormalizable gauge theories of top condensation where this is the case. These models are therefore predictive and do not lead to arbitrary predictions.

Cutoff quantization and the Skyrmion.

The putative classical soliton in the minimal nonlinear \ensuremath{\sigma} model (no Skyrme term) is known to be unstable to collapse. We note that the imposition of a short-distance cutoff (which is anyway physically reasonable for a nonrenormalizable model) yields a stable classical soliton. We further suggest that this cutoff, carrying as it does some implicit dynamical information, be treated as a quantized dynamical variable. The resulting one- (experimentally fixed) parameter model agrees with experiment roughly as well as the simple \ensuremath{\sigma} model with the Skyrme term. We interpret this feature as an indication of the robustness of the description of the nucleon as being dominated by a hedgehog-type meson cloud. It is suggested that the same approach might be useful in some other situations where the long-distance description of the physics is more precisely known than is the short-distance description.

Completeness and nontriviality of the solutions of the consistency conditions

For the case of a compact gauge group we determine all solutions to the consistency conditions. In particular, our results imply that the known list of anomalies is complete also for nonrenormalizable models.

Nonlinear parabolic stochastic differential equations with additive colored noise onR d �R +: A regulated stochastic quantization

We prove the existence of solutions to the nonlinear parabolic stochastic differential equation $$({\partial \mathord{\left/ {\vphantom {\partial {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}} - \Delta )\varphi = - V'(\varphi ) + \eta _c $$ for polynomialsV of even degree with positive leading coefficient and ν c a gaussian colored noise process onR d ×R +. When ν c is colored enough that the gaussian solution to the linear problem has Holder continuous covariance, the nongaussian processes are almost surely realized by continuous functions. Uniqueness, regularity properties, asymptotic perturbation expansions and nonperturbative fluctuation bounds are obtained for the infinite volume processes. These equations are a cutoff version of the Parisi-Wu stochastic quantization procedure forP(ϕ) d models, and the results of this paper rigorously establish the nonperturbative nature of regularization via modification of the noise process. In the limit ν c → gaussian white noise we find that the asymptotic expansion and the rigorous bounds agree for processes corresponding to the (regulated) stochastic quantization of super-renormalizable and small coupling, strictly renormalizable scalar field theories and disagree for nonrenormalizable models.

A bound on the structure of vacua divergences in quantum field theory

An estimate from above for the nonrenormalizable density of vacuum energy in quantum field theory is obtained. It is shown that if we use the dimensional regularization for the model of neutral scalar field with the interaction Lagrangian L I=-ɡϕ 4 the nonrenormalizable vacuum energy density contains at most a quadratic singularity in 1/ε. A bound on the structure of the vacuum divergences in some nonrenormalizable models of quantum field theory is found.