Spontaneous Breaking Of Scale Invariance Research Articles

Exploring the conformal transition from above and below

We consider conformal transitions arising from the merging of IR and UV fixed points, expected to occur in QCD with a large enough number of flavors. We study the smoothness of physical quantities across this transition, being mostly determined by the logarithmic breaking of conformal invariance. We investigate this explicitly using holography where approaching the conformal transition either from outside or inside the conformal window (perturbed by a mass term) is characterized by the same dynamics. The mass of spin-1 mesons and Fπ are shown to be continuous across the transition, as well as the dilaton mass. This implies that the lightness of the dilaton cannot be a consequence of the spontaneous breaking of scale invariance when leaving the conformal window. Our analysis suggests that the light scalar observed in QCD lattice simulations is a qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q} $$\\end{document} meson that becomes light since the qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q} $$\\end{document}-operator dimension reaches its minimal value.

Electroweak symmetry breaking by gravity

We consider a simple scale-invariant action coupling the Higgs field to the metric scalar curvature R and containing an R2 term that exhibits spontaneous breaking of scale invariance and electroweak symmetry. The coefficient of the R2 term in this case determines the self-coupling of the Higgs boson in the Einstein frame, and the scalaron becomes a dilaton weakly coupled to the Higgs boson. Majorana mass terms for right-handed neutrinos can be generated in a scale-invariant manner by using the Higgs-field invariant; in this case, the existing experimental limits on the Higgs-boson total width rule out Majorana mass values in a certain range. The model inherits the naturalness issues of general relativity connected with the smallness of the gravitational and cosmological constants.

Light dilaton in rare meson decays and extraction of its CP property

The dilaton ϕ is a pseudo-Nambu-Goldstone boson associated with the spontaneous breaking of scale invariance in a nearly conformal theory, and couples to the trace of the stress-energy tensor. We analyze experimental constraints on a light dilaton with mass in the MeV–GeV range from rare meson decays. New model-independent inclusive bounds for the b → sϕ transition largely exclude the parameter space of a light dilaton that could explain the muon g − 2 anomaly. Despite similarities between a dilaton and a Higgs-portal scalar, the dilaton-photon coupling is enhanced compared to the Higgs-portal scalar due to contributions from loops of the conformal sector. Consequently, the shortened lifetime of the dilaton relaxes bounds from K → π + invisible searches at the NA62 experiment and constraints from the Big Bang Nucleosynthesis. We utilize this fact to search for the dilaton signature at a lepton collider such as the ongoing Belle II experiment. Further, we demonstrate how to extract the CP property of the dilaton using the variation of the differential cross-section of e+e− → e+e−ϕ with the azimuthal angle between the outgoing leptons.

Unifying inflation with early and late dark energy with multiple fields: Spontaneously broken scale invariant two measures theory

A unified multi scalar field model with three flat regions is discussed. The three flat regions are the inflation, early and late dark energy epochs. The potential is obtained by a spontaneous breaking of scale invariance generated by Non Riemannian Measures of integration (or Two Measures Theories (TMT)).We define the scale invariant couplings of the scalar fields to the different measures through exponential potentials. Spontaneous breaking of scale invariance takes place when integrating the fields that define the measures. When going to the Einstein frame we obtain: (i) An effective potential for the scalar fields with three flat regions which allows for a unified description of both early universe inflation (in the higher energy density flat region) as well as of present dark energy epoch which can be realized with a double phase, i.e., in two flat regions. (ii) In the slow roll inflation, only one field combination the ``dilaton", which transforms under scale transformations, has non trivial dynamics, the orthogonal one, which is scale invariant remains constant. (iv) In the late universe we define scale invariant couplings of Dark Matter to the dilaton. These couplings define a matter induced potential for the dilaton and extremizing this potential determines the scale invariant scalar field, while all exotic non canonical behavior of the Dark Matter as well as any possible $5^{th}$ force disappear. (v) We calculate the evolution of the late universe under these conditions with the realization of two different possible realizations of $\Lambda$CDM type scenarios depending of the flat region in the late universe. These two phases could appear at different times in the history of the universe.(vi) From the Planck data, we find the constraints on the parameters during the inflationary epoch and these values are used to obtain constraints relevant to the present epoch.

Unified emergence of energy scales and cosmic inflation

In the quest for unification of the Standard Model with gravity, classical scale invariance can be utilized to dynamically generate the Planck mass MPl. However, the relation of Planck scale physics to the scale of electroweak symmetry breaking μH requires further explanation. In this paper, we propose a model that uses the spontaneous breaking of scale invariance in the scalar sector as a unified origin for dynamical generation of both scales. Using the Gildener-Weinberg approximation, only one scalar acquires a vacuum expectation value of υS ∼ (1016−17) GeV, thus radiatively generating {M}_{mathrm{P}1}approx {beta}_S^{1/2}{upsilon}_S and μH via the neutrino option with right handed neutrino masses mN = yMυS ∼ 107 GeV. Consequently, active SM neutrinos are given a mass with the inclusion of a type-I seesaw mechanism. Furthermore, we adopt an unbroken Z2 symmetry and a Z2-odd set of right-handed Majorana neutrinos χ that do not take part in the neutrino option and are able to produce the correct dark matter relic abundance (dominantly) via inflaton decay. The model also describes cosmic inflation and the inflationary CMB observables are predicted to interpolate between those of R2 and linear chaotic inflationary model and are thus well within the strongest experimental constraints.

Multifractal Model of Atmospheric Turbulence Applied to Elastic Lidar Data

This paper shall present a multifractal interpretation of turbulent atmospheric entities, considering them a complex system whose dynamics are manifested on continuous yet non-differentiable multifractal curves. By bringing forth theoretical considerations regarding multifractal structures through non-differentiable functions in the form of an adaptation of scale relativity theory, the minimal vortex of an instance of turbulent flow is considered. In this manner, the spontaneous breaking of scale invariance becomes a mechanism for atmospheric turbulence generation. This then leads to a general equation for the non-differentiable vortex itself, with its component velocity fields, and to a vortex turbulent energy dissipation—all of which are plotted and studied. Once the structure of the non-differentiable multifractal structure is mathematically described, an improved phenomenological turbulence model and relations between turbulent energy dissipation and the minimal vortex are employed together, exemplifying the codependency of such models. Using turbulent medium wave propagation theory, certain relations are then extrapolated which allow the obtaining of the inner and outer length scales of the turbulent flow using lidar data. Finally, these altitude profiles are compiled and assembled into timeseries to exemplify the theory and to compare the results with known literature. This model is a generalization of our recent results published under the title “On a Multifractal Approach of Turbulent Atmosphere Dynamics”.

Phase transition and vacuum stability in the classically conformal B\u2013L model

Within classically conformal models, the spontaneous breaking of scale invariance is usually associated to a strong first order phase transition that results in a gravitational wave background within the reach of future space-based interferometers. In this paper we study the case of the classically conformal gauged B–L model, analysing the impact of this minimal extension of the Standard Model on the dynamics of the electroweak symmetry breaking and derive its gravitational wave signature. Particular attention is paid to the problem of vacuum stability and to the role of the QCD phase transition, which we prove responsible for concluding the symmetry breaking transition in part of the considered parameter space. Finally, we calculate the gravitational wave signal emitted in the process, finding that a large part of the parameter space of the model can be probed by LISA.

Conformal realization of the neutrino option

It was recently proposed that the electroweak hierarchy problem is absent if the generation of the Higgs potential stems exclusively from quantum effects of heavy right-handed neutrinos which can also generate active neutrino masses via the type-I seesaw mechanism. Hence, in this framework dubbed the "neutrino option", the tree-level scalar potential is assumed to vanish at high energies. Such a scenario therefore lends itself particularly well to be embedded in a classically scale-invariant theory. In this paper we perform a survey of models featuring conformal symmetry at the high scale. We find that the minimal framework compatible with the "neutrino option" requires the Standard Model to be extended by two real scalar singlet fields in addition to right-handed neutrinos. The spontaneous breaking of scale invariance, which induces the dynamical generation of Majorana masses for the right-handed neutrinos, is triggered by renormalization group effects. We identify the parameter space of the model for which a phenomenologically viable Higgs potential and neutrino masses are generated, and for which all coupling constants remain in the perturbative regime up to the Planck scale.

Local scale-invariance breaking in the standard model by two-measure theory

We introduce Weyl's scale invariance as additional local symmetry in the standard model of electroweak interactions. Under this, the gauge symmetry of the standard model now is $SU(3)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0ex}{0ex}}U(1)\ifmmode\times\else\texttimes\fi{}\stackrel{\texttildelow{}}{U}(1)$, where $\stackrel{\texttildelow{}}{U}(1)$ is for local scale invariance, and its gauge boson is called the Weylon. Also introduced are two new scalars ${\ensuremath{\sigma}}_{1}$ and ${\ensuremath{\sigma}}_{2}$ with the common scaling weight $\ensuremath{-}1$. The mechanism for spontaneous breaking of scale invariance is invoked by coupling ${\ensuremath{\sigma}}_{2}$ to a metric-independent measure defined in terms of an additional four scalars ${\ensuremath{\phi}}^{I}(I=1,2,3,4)$. Weyl's scale invariance is now implemented by combining it with internal diffeomorphisms of the four scalars ${\ensuremath{\phi}}^{i}$. We show that once local scale invariance is broken, the phenomenon (a) generates Newton's gravitational constant ${G}_{N}$ and (b) triggers spontaneous symmetry breaking in the conventional manner resulting in masses for the conventional fermions and bosons. The scale at which Weyl's scale symmetry breaks is of order Planck mass. If right-handed neutrinos are also introduced, their absence at present energy scales is attributed to their mass being tied to the scale at which scale invariance breaks. New $C$- and $CP$-violating effects can also be induced by mixing the Weylon with the hypercharge gauge boson of the standard model.

The radion as a dark matter candidate

I study a class of Randall–Sundrum (RS) models with Spontaneous Breaking of Scale Invariance (SBSI). This class of models implements the Contino–Pomarol–Rattazzi (CPR) mechanism to achieve SBSI through the small running of an external close-to-marginal scale-breaking operator that leads to a light dilaton/radion with couplings to matter suppressed by the small running. I show that for radion masses [Formula: see text] KeV, it can serve as a dark matter (DM) candidate, with a lifetime longer than the age of the universe, and show that the experimental bounds from LHC, non-Newtonian gravity and Axion-Like Particle (ALP) searches allow for the existence of such a radion. In spite of the small relic abundance of the light radion produced in this model, we show that it could be possible to obtain the required abundance through additional assumptions, an issue we postpone to the future.

A minimal scale invariant axion solution to the strong CP-problem

We present a scale-invariant extension of the Standard model allowing for the Kim-Shifman-Vainstein-Zakharov (KSVZ) axion solution of the strong CP problem in QCD. We add the minimal number of new particles and show that the Peccei-Quinn scalar might be identified with the complex dilaton field. Scale invariance, together with the Peccei-Quinn symmetry, is broken spontaneously near the Planck scale before inflation, which is driven by the Standard Model Higgs field. We present a set of general conditions which makes this scenario viable and an explicit example of an effective theory possessing spontaneous breaking of scale invariance. We show that this description works both for inflation and low-energy physics in the electroweak vacuum. This scenario can provide a self-consistent inflationary stage and, at the same time, successfully avoid the cosmological bounds on the axion. Our general predictions are the existence of colored TeV mass fermion and the QCD axion. The latter has all the properties of the KSVZ axion but does not contribute to dark matter. This axion can be searched via its mixing to a photon in an external magnetic field.

A first-order approach to conformal gravity

We investigate whether a spontaneously-broken gauge theory of the group may be a viable alternative to general relativity. The basic ingredients of the theory are an gauge field and a Higgs field W in the adjoint representation of the group with the Higgs field producing the symmetry breaking . The action for gravity is polynomial in and the field equations are first-order in derivatives of these fields. The new symmetry in the gravitational sector is interpreted in terms of an emergent local scale symmetry and the existence of ‘conformalized’ general relativity and fourth-order Weyl conformal gravity as limits of the theory is demonstrated. Maximally symmetric spacetime solutions to the full theory are found and stability of the theory around these solutions is investigated; it is shown that regions of the theory’s parameter space describe perturbations identical to that of general relativity coupled to a massive scalar field and a massless one-form field. The coupling of gravity to matter is considered and it is shown that Lagrangians for all fields are naturally gauge-invariant, polynomial in fields and yield first-order field equations; no auxiliary fields are introduced. Familiar Yang–Mills and Klein–Gordon type Lagrangians are recovered on-shell in the general-relativistic limit of the theory. In this formalism, the general-relativistic limit coincides with a spontaneous breaking of scale invariance and it is shown that this generates mass terms for Higgs and spinor fields.

Fixed points and the spontaneous breaking of scale invariance

We investigate critical $N$-component scalar field theories and the spontaneous breaking of scale invariance in three dimensions using functional renormalisation. Global and local renormalisation group flows are solved analytically in the infinite $N$ limit to establish the phase diagram including the Wilson-Fisher fixed point and a line of asymptotically safe UV fixed points characterised by an exactly marginal sextic coupling. We also study the Bardeen-Moshe-Bander phenomenon of spontaneously broken scale invariance and the stability of the vacuum for general regularisation. Our findings clarify a long-standing puzzle about the apparent unboundedness of the effective potential. Implications for other theories are indicated.

Dilatonlike Higgs boson with scalar singlet dark matter

We study a model with a Higgs-like dilaton and a Standard Model gauge-singlet scalar dark matter candidate. We begin by updating the status of identifying the observed 125 GeV Higgs-like boson with the pseudo Nambu-Goldstone boson that arises from the spontaneous breaking of scale invariance using recent Higgs boson signal strength measurements by the ATLAS and CMS collaborations. We then constrain the extended model with recent constraints on the Higgs invisible width, the observed dark matter relic abundance and the latest dark matter direct detection limits. We found that the magnitude of the dilaton-$\gamma\gamma$ and dilaton-glue-glue coupling is constrained to be close to the standard model values. The mass of the dark matter candidate is contrained to be greater than half the dilaton mass by relic abundance limits and Higgs invisible width limits. Dark matter direct detection limits allow only small mass regions which will be further constrained by upcoming DEAP measurements.

Accidental dark matter: Case in the scale invariant localB−Lmodel

We explore the idea of accidental dark matter (aDM) stability in the scale invariant local $U(1)_{B-L}$ model, which is a theory for neutrino and at the same time radiatively breaks scale invariance via quantum mechanical dynamics in the $U(1)_{B-L}$ sector. A real singlet scalar can be accidental DM with an accidental $Z_2$, by virtue of both extended symmetries. A $U(1)_{B-L}$ charged complex scalar can also be a viable accidental DM due to an accidental (or remanent) $Z_3$. They can reproduce correct relic density via the annihilations through the conventional Higgs portal or dark Higgs portal. The dark Higgs portal scenario is in tension with the LHC bound on $Z_{B-L}$, and only heavy DM of a few TeVs can have correct relic density. In particular, DM may trigger spontaneous breaking of scale Invariance (SISB). The situation is relaxed significantly in the $Z_3$ case due to the effective semi-annihilation mode and then light DM can be accommodated easily. In addition, the $Z_3$ model can accommodate the GeV scale $\gamma-$ray excess from the galactic center (GC) via semi-annihilation into pseudo Goldstone boson (PGSB). The best fit is achieved at a DM about 52 GeV, with annihilation cross section consistent with the thermal relic density. The invisible Higgs branching ratio is negligible because the Higgs portal quartic coupling is very small $\lambda_{h\phi} \lesssim 10^{-3}$.

Spontaneous breaking of scale invariance in a D = 3 U(N ) model with Chern-Simons gauge fields

We study spontaneous breaking of scale invariance in the large N limit of three dimensional $U(N)_\kappa$ Chern-Simons theories coupled to a scalar field in the fundamental representation. When a $\lambda_6(\phi^\dagger\cdot\phi)^3$ self interaction term is added to the action we find a massive phase at a certain critical value for a combination of the $\lambda_6$ and 't Hooft's $\lambda=N/\kappa$ couplings. This model attracted recent attention since at finite $\kappa$ it contains a singlet sector which is conjectured to be dual to Vasiliev's higher spin gravity on $AdS_4$. Our paper concentrates on the massive phase of the 3d boundary theory. We discuss the advantage of introducing masses in the boundary theory through spontaneous breaking of scale invariance.

A higgs-like dilaton: viability and implications

We re-examine the feasibility of the higgs-like particle discovered at the LHC being a dilaton: the Goldstone boson of spontaneous breaking of scale invariance. We review the expected phenomenological deviations from the SM higgs and compare with other Goldstone higgs scenarios, with particular emphasis on double higgs production.

Scale-invariant alternatives to general relativity

We study the general class of gravitational field theories constructed on the basis of scale invariance (and therefore absence of any mass parameters) and invariance under transverse diffeomorphisms (TDiff), which are the 4-volume conserving coordinate transformations. We show that these theories are equivalent to a specific type of scalar-tensor theories of gravity (invariant under all diffeomorphisms) with a number of properties, making them phenomenologically interesting. They contain, in addition to the dimensionless coupling constants of the original theory, an arbitrary dimensionful parameter $\Lambda_0$. This parameter is associated with an integration constant of the equations of motion, similar to the arbitrary cosmological constant appearing in unimodular gravity. We focus on the theories where Newton's constant and the electroweak scale emerge from the spontaneous breaking of scale invariance and are unrelated to $\Lambda_0$. The massless particle spectrum of these theories contains the graviton and a new particle -- dilaton. For $\Lambda_0=0$, the massless dilaton has only derivative couplings to matter fields and the bounds on the existence of a 5th force are easily satisfied. As for the matter fields, we determine the conditions leading to a renormalizable low-energy theory. If $\Lambda_0\neq 0$, scale invariance is broken. The arbitrary constant $\Lambda_0$ produces a "run-away" potential for the dilaton. As a consequence, the dilaton can act as a dynamical dark energy component. We elucidate the origin of the cosmological constant in the class of theories under consideration and formulate the condition leading to its absence. If this condition is satisfied, dark energy is purely dynamical and associated to the dilaton.

Attractive holographic baryons

We propose a holographic model of baryon interactions based on non-supersymmetric D7-anti-D7 flavor branes embedded in the Klebanov-Strassler background. The baryons are D3-branes wrapping the 3-sphere of the conifold with M strings connecting the D3 and the flavor branes. Depending on the location of the latter there are two possibilities: the D3 either remains separate from the flavor branes or dissolves in them and becomes a flavor instanton. The leading order interaction between the baryons is a competition between the attraction and the repulsion due to the sigma and omega mesons. The lightest 0++ particle sigma is a pseudo-Goldstone boson associated with the spontaneous breaking of scale invariance. In a certain range of parameters it is parametrically lighter than any other massive state. As a result at large distances baryons attract each other. At short distances the potential admits a repulsive core due to an exchange of the omega vector meson. We discuss baryon coupling to glueballs, massive mesons and pions and point out the condition for the model to have a small binding energy.

THE CONFINEMENT TERM

Motivated by arguments based on spontaneous breaking of scale invariance, a term of the form [Formula: see text] is introduced in the action of the gauge fields. For N<0 this leads to linear confinement, while for N>0, after appropriate regularization, this leads to the vanishing of the gauge fields beyond a critical length, i.e. to a different realization of confinement. A mechanism where two values of N can be connected is discussed.