Symmetry Breaking Of Scale Invariance Research Articles

Conformal vector dark matter and strongly first-order electroweak phase transition

We study a conformal version of the Standard Model (SM), which apart from SM sector, containing a UD(1) dark sector with a vector dark matter candidate and a scalar field (scalon). In this model the dark sector couples to the SM sector via a Higgs portal. The theory is scale-invariant in lowest order, therefore the spontaneous symmetry breaking of scale invariance entails the existence of a scalar particle, scalon, with vanishing zeroth-order mass. However, one-loop corrections break scale invariance, so they give mass to the scalon. Because of the scale invariance, our model is subjected to constraints which remove many of the free parameters. We put constraints to the two remaining parameters from the Higgs searches at the LHC, dark matter relic density and dark matter direct detection limits by PandaX-II. The viable mass region for dark matter is about 1–2 TeV. We also obtain the finite temperature one-loop effective potential of the model and demonstrate that finite temperature effects, for the parameter space constrained by dark matter relic density, induce a strongly first-order electroweak phase transition.

Exorcising ghosts in induced gravity

Unitarity of the scale-invariant coupled theory of higher-derivative gravity and matter is investigated. A scalar field coupled with a Dirac fermion is taken as the matter sector. Following the idea of induced gravity the Einstein–Hilbert term is generated via dynamical symmetry breaking of scale invariance. The renormalisation group flows are computed and one-loop RG improved effective potential of scalar is calculated. The scalar field develops a new minimum via the Coleman–Weinberg procedure inducing the Newton constant and masses in the matter sector. The spin-2 problematic ghost and the spin-0 mode of the metric fluctuation get a mass in the broken phase of the theory. The energy dependence of the vacuum expectation value in the RG improved scenario implies a running for the induced parameters. This sets up platform to ask whether it is possible to evade the spin-2 ghost by keeping its mass always above the running energy scale? In broken phase this question is satisfactorily answered for a large domain of coupling parameter space where the ghost is evaded. The spin-0 mode can be made physically realisable or not depending upon the choice of the initial parameters. The induced Newton constant is seen to vanish in the ultraviolet case. By properly choosing parameters it is possible to make the matter fields physically unrealisable.

Spontaneous breaking of non-relativistic scale symmetry

We analyze the mechanism of spontaneous symmetry breaking of scale invariance in Galilean invariant field theories. We show that the existence of a dynamic gapless dilaton mode depends on whether the U(1) particle number or the Galilean boost symmetry are spontaneously broken. When both scale and particle number symmetries are spontaneously broken there is one propagating gapless Nambu-Goldstone mode. Its dispersion relation is linear if the chemical potential is nonzero and quadratic otherwise. We discuss the reversibility of RG flows in such theories.

Scale symmetry breaking from total derivative densities and the cosmological constant problem

The use in the action integral of totally divergent densities in generally coordinate invariant theories can lead to interesting mechanisms of spontaneous symmetry breaking of scale invariance. With dependence in the action on a metric independent density Φ, in 4D, we can define Φ=εμναβ∂μAναβ that gives a new interesting mechanism for breaking scale symmetry in 4D theories of gravity plus matter fields, through the Aναβ equations of motion which lead to an integration constant the breaks the scale symmetry, while introducing terms of the form eGlnK, e being the determinant of the vierbein, G being the Gauss–Bonnet scalar and K being scalar functions of the fields transforming like K→cK (where c is a constant) under a scale transformation. Such a term is invariant only up to a total divergence and therefore leads to breaking of scale invariance due to gravitational instantons. The topological density constructed out of gauge field strengths εμναβFμνaFαβa can be coupled to the dilaton field linearly to produce a scale invariant term up to a total divergence. The scale symmetry can be broken by Yang–Mills instantons which lead to a very small vacuum energy for our Universe.

Can the nearly conformal sextet gauge model hide the Higgs impostor?

New results are reported from large scale lattice simulations of a frequently discussed strongly interacting gauge theory with a fermion flavor doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group. We find that the chiral condensate and the mass spectrum of the sextet model are consistent with chiral symmetry breaking in the limit of vanishing fermion mass. In contrast, sextet fermion mass deformations of spectral properties are not consistent with leading conformal scaling behavior near the critical surface of a conformal theory. A recent paper could not resolve the conformal fixed point of the gauge coupling from the slowly walking scenario of a very small nearly vanishing β-function (DeGrand et al. [3]). It is argued that overall consistency with our new results is resolved if the sextet model is close to the conformal window, staying outside with a very small non-vanishing β-function. The model would exhibit then the simplest composite Higgs mechanism leaving open the possibility of a light scalar state with quantum numbers of the Higgs impostor. It would emerge as the pseudo-Goldstone dilaton state from spontaneous symmetry breaking of scale invariance. We will argue that even without association with the dilaton, the scalar Higgs-like state can be light very close to the conformal window. A new Higgs project of sextet lattice simulations is outlined to resolve these important questions.

Higgs–Dilaton cosmology: Are there extra relativistic species?

Recent analyses of cosmological data suggest the presence of an extra relativistic component beyond the Standard Model content. The Higgs–Dilaton cosmological model predicts the existence of a massless particle – the dilaton – associated with the spontaneous symmetry breaking of scale invariance and undetectable by any accelerator experiment. Its ultrarelativistic character makes it a suitable candidate for contributing to the effective number of light degrees of freedom in the Universe. In this Letter we analyze the dilaton production at the (p)reheating stage right after inflation and conclude that no extra relativistic degrees of freedom beyond those already present in the Standard Model are expected within the simplest Higgs–Dilaton scenario. The elusive dilaton remains thus essentially undetectable by any particle physics experiment or cosmological observation.

NONSINGULAR ORIGIN OF THE UNIVERSE AND ITS PRESENT VACUUM ENERGY DENSITY

We consider a nonsingular origin for the universe starting from an Einstein static universe, the so-called "emergent universe" scenario, in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field ϕ are considered in the action. The first-order formalism is applied. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking of scale invariance. After spontaneous symmetry breaking of scale invariance it is found that a nontrivial potential for the dilaton is generated. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe, followed by an inflationary phase and ϕ → - ∞, describing our present universe. The dynamics of the scalar field becomes nonlinear and these nonlinearities are instrumental in the stability of some of the emergent universe solutions, which exists for a parameter range of values of the vacuum energy in ϕ → - ∞, which must be positive but not very big, avoiding the extreme fine tuning required to keep the vacuum energy density of the present universe small. Zero vacuum energy density for the present universe defines the threshold for the creation of the universe.

CONFINEMENT EFFECT AS A RESULT OF SPONTANEOUS BREAKING OF SCALE INVARIANCE

In this paper the consequences of introducing spontaneous symmetry breaking of scale invariance through a scale that is obtained from the integration of the equations of motion of four index field strengths are studied. Confinement is obtained for all values of this constant of integration. For negative values two point charges have a potential energy that grows linearly with distance, but they can be arbitrarily far apart (although this is costly from the point of view of energy). For positive values of the integration constant, there is no possibility of separating charges too far apart; at a certain point a new charge of opposite sign has to be added to form a neutral system that cannot be bigger that a critical size. We discuss this using different methods, including some developed by Adler and Piran. In addition, we discuss a few alternative effective actions that are similar and that also give confinement.

STRONG INTERACTION DYNAMICS FROM SPONTANEOUS SYMMETRY BREAKING OF SCALE INVARIANCE

Using the mechanism of spontaneous symmetry breaking of scale invariance obtained from the dynamics of maximal rank field strengths, it is possible to spontaneously generate confining behavior. Introducing a dilaton field, the study of nontrivial confining and de-confining transitions appears possible. This is manifest in two ways at least: One can consider bags which contain an unconfined phase in the internal region and a confined phase outside and also one obtains a simple model for deconfinement at high temperature from the finite temperature dynamics of the dilaton field.

Static potential from spontaneous breaking of scale symmetry

We determine the static potential for a heavy quark–antiquark pair from the spontaneous symmetry breaking of scale invariance in a non-Abelian gauge theory. Our calculation is done within the framework of the gauge-invariant, path-dependent, variables formalism. The result satisfies the 't Hooft basic criterion for achieving confinement.

Confinement from spontaneous breaking of scale symmetry

Abstract We show that one can obtain naturally the confinement of static charges from the spontaneous symmetry breaking of scale invariance in a gauge theory. At the classical level a confining force is obtained and at the quantum level, using a gauge invariant but path-dependent variables formalism, the Cornell confining potential is explicitly obtained. Our procedure answers completely to the requirements by 't Hooft for “perturbative confinement”.

SCALE SYMMETRY BREAKING FROM THE DYNAMICS OF MAXIMAL RANK GAUGE FIELD STRENGTHS

Scale invariant theories which contain maximal rank gauge field strengths (of D indices in D dimensions) are studied. The integration of the equations of motion of these gauge fields leads to the scale symmetry breaking of scale invariance. The cases in study are (i) the spontaneous generation of r-1 potentials in particle mechanics in a theory that contains only r-2 potentials in the scale invariant phase, (ii) mass generation in scalar field theories, (iii) generation of nontrivial dilaton potentials in generally covariant theories, and (iv) spontaneous generation of confining behavior in gauge theories. The possible origin of these models is discussed.