Broken Scale Invariance Research Articles

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.

Estimating cochlear tuning dependence on stimulus level and frequency from the delay of otoacoustic emissions

An objective technique based on the time-frequency analysis of otoacoustic emissions is proposed to get fast and stable estimates of cochlear tuning. Time-frequency analysis allows one to get stable measurements of the delay/frequency function, which is theoretically expected to be a function of cochlear tuning. Theoretical considerations and numerical solutions of a nonlinear cochlear model suggest that the average phase-gradient delay of the otoacoustic emission single-reflection components, weighted, for each frequency, by the amplitude of the corresponding wavelet coefficients, approximately scales as the square root of the cochlear quality factor. The application of the method to human stimulus-frequency and transient-evoked otoacoustic emissions shows that tuning decreases approximately by a factor of 2, as the stimulus level increases by 30 dB in a moderate stimulus level range. The results also show a steady increase of tuning with increasing frequency, by a factor of 2 between 1 and 5 kHz. This last result is model-dependent, because it relies on the assumption that cochlear scale-invariance breaking is only due to the frequency dependence of tuning. The application of the method to the reflection component of distortion product otoacoustic emissions, separated using time-frequency filtering, is complicated by the necessity of effectively canceling the distortion component.

Tuning the cosmological constant, broken scale invariance, unitarity

We study gravity coupled to a cosmological constant and a scale but not conformally invariant sector. In Minkowski vacuum, scale invariance is spontaneously broken. We consider small fluctuations around the Minkowski vacuum. At the linearised level we find that the trace of metric perturbations receives a positive or negative mass squared contribution. However, only for the Fierz-Pauli combination the theory is free of ghosts. The mass term for the trace of metric perturbations can be cancelled by explicitly breaking scale invariance. This reintroduces fine-tuning. Models based on four form field strength show similarities with explicit scale symmetry breaking due to quantisation conditions.

Fine-tuning with brane-localized flux in 6D supergravity

There are claims in the literature that the cosmological constant problem could be solved in a braneworld model with two large (micron-sized) supersymmetric extra dimensions. The mechanism relies on two basic ingredients: First, the cosmological constant only curves the compact bulk geometry into a rugby shape while the 4D curvature stays flat. Second, a brane-localized flux term is introduced in order to circumvent Weinberg's fine-tuning argument, which otherwise enters here through a backdoor via the flux quantization condition. In this paper, we show that the latter mechanism does not work in the way it was designed: The only localized flux coupling that guarantees a flat on-brane geometry is one which preserves the scale invariance of the bulk theory. Consequently, Weinberg's argument applies, making a fine-tuning necessary again. The only remaining window of opportunity lies within scale invariance breaking brane couplings, for which the tuning could be avoided. Whether the corresponding 4D curvature could be kept under control and in agreement with the observed value will be answered in our companion paper [arXiv:1512.03800].

Late time behavior of non-conformal plasmas

We determine analytically the dependence of the approach to thermal equilibrium of strongly coupled plasmas on the breaking of scale invariance. The theories we consider are the holographic duals to Einstein gravity coupled to a scalar with an exponential potential. The coefficient in the exponent, $X$, is the parameter that controls the deviation from the conformally invariant case. For these models we obtain analytic solutions for the plasma expansion in the late-time limit, under the assumption of boost-invariance, and we determine the scaling behaviour of the energy density, pressure, and temperature as a function of time. We find that the temperature decays as a function of proper time as $T\sim \tau^{-s/4}$ with $s$ determined in terms of the non-conformality parameter $X$ as $s=4(1-4X^2)/3$. This agrees with the result of Janik and Peschanski, $s=4/3$, for the conformal plasmas and generalizes it to non-conformal plasmas with $X\neq 0$. We also consider more realistic potentials where the exponential is supplemented by power-law terms. Even though in this case we cannot have exact solutions, we are able under certain assumptions to determine the scaling of the energy, that receives logarithmic corrections.

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 $\lambda_{h\phi} \lesssim 10^{-3}$.

Covariant non-commutative space–time

We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation introduces a short-distance scale ℓp, and thus breaks scale invariance, but preserves all space–time isometries. The non-commutative algebra is defined on space–times with non-zero constant curvature, i.e. dS4 or AdS4. The construction makes essential use of the representation of CFT tensor operators as polynomials in an auxiliary polarization tensor. The polarization tensor takes active part in the non-commutative algebra, which for dS4 takes the form of so(5,1), while for AdS4 it assembles into so(4,2). The structure of the non-commutative correlation functions hints that the deformed theory contains gravitational interactions and a Regge-like trajectory of higher spin excitations.

Predictions of a model of weak scale from dynamical breaking of scale invariance

We consider a model where the weak and the DM scale arise at one loop from the Coleman–Weinberg mechanism. We perform a precision computation of the model predictions for the production cross section of a new Higgs-like scalar and for the direct-detection cross section of the DM particle candidate.

Softened gravity and the extension of the standard model up to infinite energy

Attempts to solve naturalness by having the weak scale as the only breaking of classical scale invariance have to deal with two severe difficulties: gravity and the absence of Landau poles. We show that solutions to the first problem require premature modifications of gravity at scales no larger than 1011 GeV, while the second problem calls for many new particles at the weak scale. To build models that fulfill these properties, we classify 4- dimensional Quantum Field Theories that satisfy Total Asymptotic Freedom (TAF): the theory holds up to infinite energy, where all coupling constants flow to zero. We develop a technique to identify such theories and determine their low-energy predictions. Since the Standard Model turns out to be asymptotically free only under the unphysical conditions g 1 = 0, M t = 186 GeV, M τ = 0, M h = 163 GeV, we explore some of its weak-scale extensions that satisfy the requirements for TAF.

Inflation from broken scale invariance.

We construct a model of inflation based on a low-energy effective theory of spontaneously broken global scale invariance. This provides a shift symmetry that protects the inflaton potential from quantum corrections. Since the underlying scale invariance is noncompact, arbitrarily large inflaton field displacements are readily allowed in the low-energy effective theory. A weak breaking of scale invariance by almost marginal operators provides a nontrivial inflaton minimum, which sets and stabilizes the final low-energy value of the Planck scale. The underlying scale invariance ensures that the slow-roll approximation remains valid over large inflaton displacements, and yields a scale invariant spectrum of perturbations, as required by the cosmic microwave background observations.

Ultra-weak sector, Higgs boson mass, and the dilaton

The Higgs boson mass may arise from a portal coupling to a singlet field σ which has a very large VEV f≫mHiggs. This requires a sector of “ultra-weak” couplings ζi, where ζi≲mHiggs2/f2. Ultra-weak couplings are technically naturally small due to a custodial shift symmetry of σ in the ζi→0 limit. The singlet field σ has properties similar to a pseudo-dilaton. We engineer explicit breaking of scale invariance in the ultra-weak sector via a Coleman–Weinberg potential, which requires hierarchies amongst the ultra-weak couplings.

Cosmological signatures of a UV-conformal standard model.

Quantum scale invariance in the UV has been recently advocated as an attractive way of solving the gauge hierarchy problem arising in the standard model. We explore the cosmological signatures at the electroweak scale when the breaking of scale invariance originates from a hidden sector and is mediated to the standard model by gauge interactions (gauge mediation). These scenarios, while being hard to distinguish from the standard model at LHC, can give rise to a strong electroweak phase transition leading to the generation of a large stochastic gravitational wave signal in possible reach of future space-based detectors such as eLISA and BBO. This relic would be the cosmological imprint of the breaking of scale invariance in nature.

Universal quench dynamics of interacting quantum impurity systems

The equilibrium physics of quantum impurities frequently involves a universal crossover from weak to strong reservoir-impurity coupling, characterized by single-parameter scaling and an energy scale $T_K$ (Kondo temperature) that breaks scale invariance. For the non-interacting resonant level model, the non-equilibrium time evolution of the Loschmidt echo after a local quantum quench was recently computed explicitely [R. Vasseur, K. Trinh, S. Haas, and H. Saleur, Phys. Rev. Lett. 110, 240601 (2013)]. It shows single-parameter scaling with variable $T_K t$. Here, we scrutinize whether similar universal dynamics can be observed in various interacting quantum impurity systems. Using density matrix and functional renormalization group approaches, we analyze the time evolution resulting from abruptly coupling two non-interacting Fermi or interacting Luttinger liquid leads via a quantum dot or a direct link. We also consider the case of a single Luttinger liquid lead suddenly coupled to a quantum dot. We investigate whether the field theory predictions for the universal scaling as well as for the large time behavior successfully describe the time evolution of the Loschmidt echo and the entanglement entropy of microscopic models.

Dynamical string tension in string theory with spacetime Weyl invariance

AbstractThe fundamental string length, which is an essential part of string theory, explicitly breaks scale invariance. However, in field theory we demonstrated recently that the gravitational constant, which is directly related to the string length, can be promoted to a dynamical field if the standard model coupled to gravity (SM+GR) is lifted to a locally scale (Weyl) invariant theory. The higher gauge symmetry reveals previously unknown field patches whose inclusion turn the classically conformally invariant SM+GR into a geodesically complete theory with new cosmological and possibly further physical consequences. In this paper this concept is extended to string theory by showing how it can be “Weyl lifted” with a local scale symmetry acting on target space background fields. In this process the string tension (fundamental string length) is promoted to a dynamical field, in agreement with the parallel developments in field theory. We then propose a string theory in a geodesically complete cosmological stringy background which suggests previously unimagined directions in the stringy exploration of the very early universe.

Relic gravity waves and 7 keV dark matter from a GeV scale inflaton

We study the mechanism of generation of 7 keV sterile neutrino Dark Matter (DM) in the model with light inflaton χ, which serves as a messenger of scale invariance breaking. In this model the inflaton, in addition to providing reheating to the Standard Model (SM) particles, decays directly into sterile neutrinos. The latter are responsible for the active neutrino oscillations via seesaw type I mechanism. While the two sterile neutrinos may also produce the lepton asymmetry in the primordial plasma and hence explain the baryon asymmetry of the Universe, the third one being the lightest may be of 7 keV and serve as DM. For this mechanism to work, the mass of the inflaton is bound to be light (0.1–1 GeV) and uniquely determines its properties, which allows to test the model. For particle physics experiments these are: inflaton lifetime (10−5–10−12 s), branching ratio of B-meson to kaon and inflaton (10−6–10−4) and inflaton branching ratios into light SM particles like it would be for the SM Higgs boson of the same mass. For cosmological experiments these are: spectral index of scalar perturbations (ns≃0.957–0.967), and amount of tensor perturbations produced at inflation (tensor-to-scalar ratio r≃0.15–0.005).

The Knotted Sky II: does BICEP2 require a nontrivial primordial power spectrum?

An inflationary gravitational wave background consistent with BICEP2 is difficult to reconcile with a simple power-law spectrum of primordial scalar perturbations. Tensor modes contribute to the temperature anisotropies at multipoles with l≲ 100, and this effect — together with a prior on the form of the scalar perturbations — was the source of previous bounds on the tensor-to-scalar ratio. We compute Bayesian evidence for combined fits to BICEP2 and Planck for three nontrivial primordial spectra: a) a running spectral index, b) a cutoff at fixed wavenumber, and c) a spectrum described by a linear spline with a single internal knot. We find no evidence for a cutoff, weak evidence for a running index, and significant evidence for a ``broken'' spectrum. Taken at face-value, the BICEP2 results require two new inflationary parameters in order to describe both the broken scale invariance in the perturbation spectrum and the observed tensor-to-scalar ratio. Alternatively, this tension may be resolved by additional data and more detailed analyses.

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.

Physical naturalness and dynamical breaking of classical scale invariance

We propose a model of a confining dark sector, dark technicolor, that communicates with the Standard Model (SM) through the Higgs portal. In this model electroweak (EW) symmetry breaking and dark matter (DM) share a common origin, and the EW scale is generated dynamically. Our motivation to suggest this model is the absence of evidence for new physics from recent Large Hadron Collider (LHC) data. Although the conclusion is far from certain at this point, this lack of evidence may suggest that no mechanism exists at the EW scale to stabilize the Higgs mass against radiative corrections from ultraviolet (UV) physics. The usual reaction to this puzzling situation is to conclude that the stabilizing new physics is either hidden from us by accident, or that it appears at energies that are currently inaccessible, such that nature is indeed fine-tuned. In order to re-examine the arguments that have led to this dichotomy, we review the concept of naturalness in effective field theories, discussing in particular the role of quadratic divergences in relation to different energy scales. This leads us to suggest classical scale invariance as a guideline for model building, implying that explicit mass scales are absent in the underlying theory.

Conformal inflation coupled to matter

We formulate new conformal models of inflation and dark energy which generalise the Higgs-Dilaton scenario. We embed these models in unimodular gravity whose effect is to break scale invariance in the late time Universe. In the early Universe, inflation occurs close to a maximum of both the scalar potential and the scalar coupling to the Ricci scalar in the Jordan frame. At late times, the dilaton, which decouples from the dynamics during inflation, receives a potential term from unimodular gravity and leads to the acceleration of the Universe. We address two central issues in this scenario. First we show that the Damour-Polyalov mechanism, when non-relativistic matter is present prior to thestart of inflation, sets the initial conditions for inflation at the maximum of the scalar potential. We then show that conformal invariance implies that matter particles are not coupled to the dilaton in the late Universe at the classical level. When fermions acquire masses at low energy, scale invariance is broken and quantum corrections induce a coupling between the dilaton and matter which is still small enough to evade the gravitational constraints in the solar system.

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.