Renormalizable Field Theory Research Articles

FlexibleDecay: An automated calculator of scalar decay widths

We present FlexibleDecay, a tool to calculate decays of scalars in a broad class of BSM models. The tool aims for high precision particularly in the case of Higgs boson decays. In the case of scalar and pseudoscalar Higgs boson decays the known higher order SM QED, QCD and EW effects are taken into account where possible. The program works in a modified MS‾ scheme that exhibits a decoupling property with respect to heavy BSM physics, with BSM parameters themselves treated in the MS‾/DR‾-scheme allowing for an easy connection to high scale tests for, e.g., perturbativity and vacuum stability, and the many observable calculations readily available in MS‾/DR‾ programs. Pure BSM effects are taken into account at the leading order, including all one-loop contributions to loop-induced processes. The program is implemented as an extension to FlexibleSUSY, which determines the mass spectrum for arbitrary BSM models, and does not require any extra configuration from the user. We compare our predictions for Higgs decays in the SM, singlet extended SM, type II THDM, CMSSM and MRSSM, as well as for squark decays in the CMSSM against a selection of publicly available tools. The numerical differences between our and other programs are explained. The release of FlexibleDecay officially deprecates the old effective couplings routines in FlexibleSUSY. Program summaryProgram Title:FlexibleDecayCPC Library link to program files:https://doi.org/10.17632/2c38hcpp5n.1Developer's repository link:https://github.com/FlexibleSUSY/FlexibleSUSYLicensing provisions: GPLv3Programming language: C++, Wolfram Language, Fortran, Bourne shellNature of problem: Calculation of decay widths of scalar bosons in extensions of the Standard Model of particle physics. For the calculation of Higgs boson decay widths known higher-order contributions are taken into account to achieve a high precision.Solution method: The decay widths of the scalar bosons are expressed in terms of Feynman diagrams in a general renormalizable quantum field theory and specialized to the considered model. The resulting expressions are numerically evaluated using special functions and numerical integration.Additional comments including restrictions and unusual features:FlexibleDecay is an addon to FlexibleSUSY [1, 2]. The decay widths can only be calculated in models that can be treated with FlexibleSUSY. Decay widths of fermions or vector bosons are not calculated. For non-Higgs scalar bosons the calculation is restricted to the leading order in the perturbation series.

Observational constraints on the fractal cosmology

In this paper, we explore a fractal model of the universe proposed by Calcagni (J High Energy Phys 03:120, 2010) for a power-counting renormalizable field theory living in a fractal spacetime. Considering a timelike fractal profile, we derived field equations in fractal cosmology, in order to explore the structure formation and the expansion history in fractal universe. Numerical investigations based on matter power spectra diagrams report higher structure growth in fractal cosmology, being in contrast to local galaxy surveys. Additionally, according to the evolution of Hubble parameter diagrams, it can be understood that Hubble constant would decrease in fractal cosmology, which is also incompatible with low redshift estimations of H_0. So, concerning primary numerical studies, it seems that fractal cosmology is not capable to alleviate the tensions between local and global observational probes. Then, in pursuance of more accurate results, we constrain the fractal cosmology by observational data, including Planck cosmic microwave background (CMB), weak lensing, supernovae, baryon acoustic oscillations (BAO), and redshift-space distortions (RSD) data. The derived constraints on fractal dimension beta indicate that there is no considerable deviation from standard model of cosmology.

Regularization in nonperturbative extensions of effective field theory

The process of renormalization in nonperturbative Hamiltonian effective field theory (HEFT) is examined in the $\mathrm{\ensuremath{\Delta}}$-resonance scattering channel. As an extension of effective field theory incorporating the L\"uscher formalism, HEFT provides a bridge between the infinite-volume scattering data of experiment and the finite-volume spectrum of energy eigenstates in lattice QCD. HEFT also provides phenomenological insight into the basis-state composition of the finite-volume eigenstates via the state eigenvectors. The Hamiltonian matrix is made finite through the introduction of finite-range regularization. The extent to which the established features of this regularization scheme survive in HEFT is examined. In a single-channel $\ensuremath{\pi}N$ analysis, fits to experimental phase shifts withstand large variations in the regularization parameter $\mathrm{\ensuremath{\Lambda}}$, providing an opportunity to explore the sensitivity of the finite-volume spectrum and state composition on the regulator. While the L\"uscher formalism ensures the eigenvalues are insensitive to $\mathrm{\ensuremath{\Lambda}}$ variation in the single-channel case, the eigenstate composition varies with $\mathrm{\ensuremath{\Lambda}}$; the admission of short-distance interactions diminishes single-particle contributions to the states. In the two-channel $\ensuremath{\pi}N$, $\ensuremath{\pi}\mathrm{\ensuremath{\Delta}}$ analysis, $\mathrm{\ensuremath{\Lambda}}$ is restricted to a small range by the experimental data. Here the inelasticity is particularly sensitive to variations in $\mathrm{\ensuremath{\Lambda}}$ and its associated parameter set. This sensitivity is also manifest in the finite-volume spectrum for states near the opening of the $\ensuremath{\pi}\mathrm{\ensuremath{\Delta}}$ scattering channel. Future high-quality lattice QCD results will be able to discriminate $\mathrm{\ensuremath{\Lambda}}$, describe the inelasticity, and constrain a description of the basis-state composition of the energy eigenstates. Finally, HEFT has the unique ability to describe the quark-mass dependence of the finite-volume eigenstates. The robust nature of this capability is presented and used to confront current state-of-the-art lattice QCD calculations.

Gravitational corrections to a non-Abelian gauge theory

This paper is part of a series of papers exploring the renormalization of field theories coupled to gravity using the effective field theory framework. In previous works, we studied the universality of the electric charge and the two-loops beta function in the Einstein-QED system. Now, we use this framework to study the non-Abelian gauge theory with fermions coupled to gravity. We show that even though some of the counterterms are dependent on the gravitational coupling, the renormalized coupling constant, and therefore the beta function, do not receive any gravitational correction at one-loop order. Also, we explicitly show that, at this order, the Slavnov-Taylor identities are respected. Finally, we end the paper by putting into perspective the results of the present and the past papers.

Higher-order $β$-functions in the Standard Model and beyond

In this contribution we consider the recent computation of the gauge coupling \betaβ-function at four loops and the Yukawa matrix \betaβ-function at three loops in the most general, renormalizable and four-dimensional quantum field theory. Furthermore, we discuss ambiguities and divergences arising in Yukawa matrix \betaβ-functions.

Renormalization in String-Localized Field Theories: A Microlocal Analysis

Using methods of microlocal analysis, we prove that the regularization of divergent amplitudes stays a pure ultraviolet problem in string-localized field theories, despite the weaker localization. Thus, power counting does not lose its significance as an indicator for renormalizability. It also follows that standard techniques can be used to regularize divergent amplitudes in string-localized field theories.

Gell-Mann-Low Criticality in Neural Networks.

Criticality is deeply related to optimal computational capacity. The lack of a renormalized theory of critical brain dynamics, however, so far limits insights into this form of biological information processing to mean-field results. These methods neglect a key feature of critical systems: the interaction between degrees of freedom across all length scales, required for complex nonlinear computation. We present a renormalized theory of a prototypical neural field theory, the stochastic Wilson-Cowan equation. We compute the flow of couplings, which parametrize interactions on increasing length scales. Despite similarities with the Kardar-Parisi-Zhang model, the theory is of a Gell-Mann-Low type, the archetypal form of a renormalizable quantum field theory. Here, nonlinear couplings vanish, flowing towards the Gaussian fixed point, but logarithmically slowly, thus remaining effective on most scales. We show this critical structure of interactions to implement a desirable trade-off between linearity, optimal for information storage, and nonlinearity, required for computation.

Scotogenic A5 → A4 Dirac neutrinos with freeze-in dark matter

Radiative Dirac neutrino masses and their mixing are linked to dark matter through the non-Abelian discrete symmetry A5 of the 4-dimensional pentatope, softly broken to A4 of the 3-dimensional tetrahedron. This unifying understanding of neutrino family structure from dark matter is made possible through the interplay of gauge symmetry, renormalizable Lagrangian field theory, and softly broken discrete symmetries. Dark neutral fermions are produced through Higgs decay.

Interfacial Entropy Profile in the One-loop Approximation

The near-critical interfacial entropy profile is calculated in the one-loop approximation of renormalized field theory. The shape of the profile is broadened by fluctuations and goes beyond the mean-field coupling between the entropy and the order parameter. The excess interfacial entropy and heat capacity are calculated by using the entropy profile. The interface creates corrections to the heat capacity and entropy of order χ/L, where $\xi$ is the correlation length, and L is a characteristic length of the system. These results are discussed in relation to finite-size scaling, surface critical phenomena, and the results of experiments and simulations.

Resonance-based schemes for dispersive equations via decorated trees

AbstractWe introduce a numerical framework for dispersive equations embedding their underlying resonance structure into the discretisation. This will allow us to resolve the nonlinear oscillations of the partial differential equation (PDE) and to approximate with high-order accuracy a large class of equations under lower regularity assumptions than classical techniques require. The key idea to control the nonlinear frequency interactions in the system up to arbitrary high order thereby lies in a tailored decorated tree formalism. Our algebraic structures are close to the ones developed for singular stochastic PDEs (SPDEs) with regularity structures. We adapt them to the context of dispersive PDEs by using a novel class of decorations which encode the dominant frequencies. The structure proposed in this article is new and gives a variant of the Butcher–Connes–Kreimer Hopf algebra on decorated trees. We observe a similar Birkhoff type factorisation as in SPDEs and perturbative quantum field theory. This factorisation allows us to single out oscillations and to optimise the local error by mapping it to the particular regularity of the solution. This use of the Birkhoff factorisation seems new in comparison to the literature. The field of singular SPDEs took advantage of numerical methods and renormalisation in perturbative quantum field theory by extending their structures via the adjunction of decorations and Taylor expansions. Now, through this work, numerical analysis is taking advantage of these extended structures and provides a new perspective on them.

Can we make sense out of "Tensor Field Theory"?

We continue the constructive program about tensor field theory through the next natural model, namely the rank five tensor theory with quartic melonic interactions and propagator inverse of the Laplacian on \mathbf{U(1)^5}𝐔(1)5. We make a first step towards its construction by establishing its power counting, identifying the divergent graphs and performing a careful study of (a slight modification of) its RG flow. Thus we give strong evidence that this just renormalizable tensor field theory is non perturbatively asymptotically free.

Symmetry and renormalisation in quantum field theory

Quantum systems governed by non-Hermitian Hamiltonians with symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We argue that symmetry may also be important and present at the level of Hermitian quantum field theories because of the process of renormalisation. In some quantum field theories renormalisation leads to -symmetric effective Lagrangians. We show how symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework. From the study of examples -symmetric interpretation is naturally built into a path integral formulation of quantum field theory; there is no requirement to calculate explicitly the norm that occurs in Hamiltonian quantum theory. We discuss examples where -symmetric field theories emerge from Hermitian field theories due to effects of renormalisation. We also consider the effects of renormalisation on field theories that are non-Hermitian but -symmetric from the start.

Renormalization in Combinatorially Non-Local Field Theories: The Hopf Algebra of 2-Graphs

Renormalization in perturbative quantum field theory is based on a Hopf algebra of Feynman diagrams. A precondition for this is locality. Therefore one might suspect that non-local field theories such as matrix or tensor field theories cannot benefit from a similar algebraic understanding. Here I show that, on the contrary, perturbative renormalization of a broad class of such field theories is based in the same way on a Hopf algebra. Their interaction vertices have the structure of graphs. This gives the necessary concept of locality and leads to Feynman diagrams defined as “2-graphs” which generate the Hopf algebra. These results set the stage for a systematic study of perturbative renormalization as well as non-perturbative aspects, e.g. Dyson-Schwinger equations, for a number of combinatorially non-local field theories with possible applications to random geometry and quantum gravity.

Renormalizability of Alternative Theories of Gravity: Differences between Power Counting and Entropy Argument

It is well known that General Relativity cannot be considered under the standard of a perturbatively renormalizable quantum field theory, but asymptotic safety is taken into account as a possibility for the formulation of gravity as a non-perturbative renormalizable theory. Recently, the entropy argument has however stepped into the discussion claiming for a “no-go” to the asymptotic safety argument. In this paper, we present simple counter-examples, considering alternative theories of gravity, to the entropy argument as further indications, among others, on the possible flows in the assumptions on which the latter is based. We considered different theories, namely curvature-based extensions of General Relativity as f(R), f(G), extensions of teleparallel gravity as f(T), and Horava–Lifshitz gravity, working out the explicit spherically symmetric solutions in order to make a comparison between power counting and the entropy argument. Even in these cases, inconsistencies were found.

ARGES – Advanced Renormalisation Group Equation Simplifier

We present the initial release of ARGES, a toolkit for obtaining renormalisation group equations in perturbation theory. As such, ARGES can handle any perturbatively renormalisable four-dimensional quantum field theory. Notable further features include a symbolic rather than numeric computation, input of unconventional scalar and Yukawa sectors, an interactive evaluation and disentanglement as well as capabilities to inject algebraic simplification rules. We provide a conceptual and practical introduction into ARGES, and highlight similarities and differences with complementary packages. Program summaryProgram Title: ARGESCPC Library link to program files:https://doi.org/10.17632/s2vhxgsk7s.1Licensing provisions: GPLv3Programming language: Wolfram Language (Mathematica)Nature of problem: Computation of renormalisation group equations of perturbatively renormalisable quantum field theories in four space-time dimensions to various orders in the loop expansion.Solution method: Automatize computation of RGEs from input of field content, representations, couplings and index contractions.Additional comments including restrictions and unusual features: Allows for variable generations, symmetry representations, and gauge groups. Advanced algebraic structures can be defined via simplification rules.

Braided Rota–Baxter algebras, quantum quasi-shuffle algebras and braided dendriform algebras

Rota–Baxter algebras and the closely related dendriform algebras have important physics applications, especially to renormalization of quantum field theory. Braided structures provide effective ways of quantization such as for quantum groups. Continuing recent study relating the two structures, this paper considers Rota–Baxter algebras and dendriform algebras in the braided contexts. Applying the quantum shuffle and quantum quasi-shuffle products, we construct free objects in the categories of braided Rota–Baxter algebras and braided dendriform algebras, under the commutativity condition. We further generalize the notion of dendriform Hopf algebra to the braided context and show that quantum shuffle algebra gives a braided dendriform Hopf algebra. Enveloping braided commutative Rota–Baxter algebras of braided commutative dendriform algebras are obtained.

Six-loop beta functions in general scalar theory

We consider general renormalizable scalar field theory and derive six-loop beta functions for all parameters in d = 4 dimensions within the overline{mathrm{MS}} -scheme. We do not explicitly compute relevant loop integrals but utilize O(n)-symmetric model counter-terms available in the literature. We consider dimensionless couplings and parameters with a mass scale, ranging from the trilinear self-coupling to the vacuum energy. We use obtained results to extend renormalization-group equations for several vector, matrix, and tensor models to the six-loop order. Also, we apply our general expressions to derive new contributions to beta functions and anomalous dimensions in the scalar sector of the Two-Higgs-Doublet Model.

Renormalization of Group Field Theories for Quantum Gravity: New Computations and Some Suggestions

We discuss motivation and goals of renormalization analyses of group field theory models of simplicial 4d quantum gravity, and review briefly the status of this research area. We present some new computations of perturbative Group field theories amplitudes, concerning in particular their scaling behavior, and the numerical techniques employed to obtain them. Finally, we suggest a number of research directions for further progress.

Positivity bounds and the massless spin-2 pole

The presence of a massless spin-2 field in an effective field theory results in a $t$-channel pole in the scattering amplitudes that precludes the application of standard positivity bounds. Despite this, recent arguments based on compactification to three dimensions have suggested that positivity bounds may be applied to the $t$-channel pole subtracted amplitude. If correct this would have deep implications for UV physics and the Weak Gravity Conjecture. Within the context of a simple renormalizable field theory coupled to gravity we find that applying these arguments would constrain the low-energy coupling constants in a way which is incompatible with their actual values. This contradiction persists on deforming the theory. Further enforcing the $t$-channel pole subtracted positivity bounds on such generic renormalizable effective theories coupled to gravity would imply new physics at a scale parametrically smaller than expected, with far reaching implications. This suggests that generically the standard positivity bounds are inapplicable with gravity and we highlight a number of issues that impinge on the formulation of a three-dimensional amplitude which simultaneously satisfies the required properties of analyticity, positivity and crossing symmetry. We conjecture instead a modified bound that ought to be satisfied independently of the precise details of the high energy completion.

Perturbative renormalization of the lattice regularized ϕ44 with flow equations

The flow equations of the renormalization group allow one to analyze the perturbative n-point functions of renormalizable quantum field theories. Rigorous bounds implying renormalizability permit one to control large momentum behavior, infrared singularities, and large order behavior in a number of loops and a number of arguments n. In this paper, we analyze the Euclidean four-dimensional massive ϕ4 theory using lattice regularization. We present a rigorous proof that this quantum field theory is renormalizable to all orders of the loop expansion based on the flow equations. The lattice regularization is known to break Euclidean symmetry. Our main result is the proof of the restoration of rotation and translation invariance in the renormalized theory using flow equations.