Scale-invariant Model Research Articles

Scale invariant scotogenic model: CDF-II W -boson mass and the 95 GeV excesses

The anomalies observed in the W mass measurements at the CDF-II experiments and the excesses seen around 95 GeV at the Large Hadron Collider (LHC) motivate this work, in which we investigate and constrain the parameter space of the Scale Invariant Scotogenic Model with a Majorana dark matter candidate. The scanned parameters are chosen to be consistent with the dark matter relic density and the observed excesses at ∼95 GeV signal strength rates in different channels. We found that significant part of the viable space addresses the excess in the channel γγ, while a tight part can address the excess in both γγ and bb¯ channels. Furthermore, the model’s viable parameters can be probed in both the LHC and future e+e− colliders for di-Higgs production. Published by the American Physical Society 2024

Testing scale-invariant inflation against cosmological data

There is solid theoretical and observational motivation behind the idea of scale-invariance as a fundamental symmetry of Nature. We consider a recently proposed classically scale-invariant inflationary model, quadratic in curvature and featuring a scalar field non-minimally coupled to gravity. We go beyond earlier analytical studies, which showed that the model predicts inflationary observables in qualitative agreement with data, by solving the full two-field dynamics of the system — this allows us to corroborate previous analytical findings and set robust constraints on the model's parameters using the latest Cosmic Microwave Background (CMB) data from Planck and BICEP/Keck. We demonstrate that scale-invariance constrains the two-field trajectory such that the effective dynamics are that of a single field, resulting in vanishing entropy perturbations and protecting the model from destabilization effects. We derive tight upper limits on the non-minimal coupling strength, excluding conformal coupling at high significance. By explicitly sampling over them, we demonstrate an overall insensitivity to initial conditions. We argue that the model predicts a minimal level of primordial tensor modes set by r ≳ 0.003, well within the reach of next-generation CMB experiments. These will therefore provide a litmus test of scale-invariant inflation, and we comment on the possibility of distinguishing the model from Starobinsky and α-attractor inflation. Overall, we argue that scale-invariant inflation is in excellent health, and possesses features which make it an interesting benchmark for tests of inflation from future CMB data.

Scale invariant extension of the Standard Model: a nightmare scenario in cosmology

Inflationary observables of a classically scale invariant model, in which the origin of the Planck mass and the electroweak scale including the right-handed neutrino mass is chiral symmetry breaking in a QCD-like hidden sector, are studied. Despite a three-field inflation the initial-value-dependence is strongly suppressed thanks to a river-valley like potential. The model predicts the tensor-to-scalar ratio r of cosmological perturbations smaller than that of the R 2 inflation, i.e., 0.0044 ≳ r ≳ 0.0017 for e-foldings between 50 and 60: the model will be consistent even with a null detection at LiteBird/CMB-S4. We find that the non-Gaussianity parameter f NL is O(10-2), the same size as that of single-field inflation. The dark matter particles are the lightest Nambu-Goldstone bosons associated with chiral symmetry breaking, which are decay products of one of the inflatons and are heavier than 109 GeV with a strongly suppressed coupling with the standard model, implying that the dark matter will be unobservable in direct as well as indirect measurements.

A discrete probabilistic model yielding multidimensional q − Gaussians in the thermodynamic limit for specific parameter values

We show that the N → ∞ limiting probability distributions (with N being the number of random variables to be summed) of a particular case belonging to a family of d − dimensional scale-invariant probabilistic models based on Leibniz-like (d + 1) − dimensional hyperpyramids (introduced in Rodríguez and Tsallis, J. Math. Phys 2012) are given, after an appropriate change o variables, by d − dimensional q − Gaussian distributions ( fq,β(x)∝eq−βxTΣ−1x , with x taking values in a subset of Rd , q and β real parameters, Σ a positive definite matrix, and eqx=[1+1(1−q)x]+11−q , with [u]+=max{u,0} ), for the particular parameter values q = 3 and β < 0. Some features of these distributions, which arise in the context of Nonextensive Statistical Mechanics, as well as a connection between Dirichlet distributions and q − Gaussian distributions, which generalizes the one given for dimension 1 by Rodríguez et al, are also exposed.

Resonant graviton-photon transitions with cosmological stochastic magnetic field

We explore the possibility of detecting resonant conversions of high frequency gravitational waves to radio-signals. We show how the graviton-photon transitions, from Gertsenshtein effect, can be resonantly amplified in a cosmological stochastic magnetic background. In particular, we found parametric resonances for both the monochromatic and scale invariant power spectrum models of magnetic field fluctuations. Our results substantially departs from those predicted in resonance-less magnetic domain-like models in a large region of magnetic and oscillation wavelength scales. Resonances can be tested by radio telescopes such as ARCADE 2 and EDGES as a probe of high frequency gravitational wave sources and new physics models for magnetogenesis. Analysis are performed with a robust perturbative approach in discrete scheme for including cosmological decoherence in graviton-photon oscillations.

Dynamic effects of tourism shocks on innovation in an open-economy Schumpeterian growth model

International travel restrictions during the COVID-19 pandemic drastically reduced the number of tourists. This study explores the dynamic effects of tourism shocks in an open-economy Schumpeterian model with endogenous market structure. A tourism shock affects the economy via a reallocation effect and an employment effect. A positive tourism shock increases employment, which raises production and innovation in the short run. However, a positive tourism shock also reallocates labor from production to service for tourists, which reduces production and innovation. If leisure preference is weak, the reallocation effect dominates, and the short-run effect of positive tourism shocks on innovation is monotonically negative. If leisure preference is strong, the employment effect dominates initially, and the short-run effect of tourism shocks on innovation becomes inverted-U, which is consistent with the stylized facts that we document using cross-country data. Finally, permanent tourism shocks do not affect the steady-state innovation rate in our scale-invariant model.

Gravitational waves from phase transitions in scale invariant models

We investigate the properties of the gravitational waves (GW) generated during a strongly first order electroweak phase transition (EWPT) in models with the classical scale invariance (CSI). Here, we distinguish two parameter space regions that correspond to the cases of (1) light dilaton and (2) purely radiative Higgs mass (PRHM). In the CSI models, the dilaton mass, or the Higgs mass in the PRHM case, in addition to some triple scalar couplings are fully triggered by the radiative corrections (RCs). In order to probe the RC effects on the EWPT strength and on the GW spectrum, we extend the standard model by a real singlet to assist the electroweak symmetry breaking and an additional scalar field Q with multiplicity NQ and mass mQ. After imposing all theoretical and experimental constraints, we show that a strongly first order EWPT with detectable GW spectra can be realized for the two cases of light dilaton and PRHM. We also show the corresponding values of the relative enhancement of the cross section for the di-Higgs production process, which is related to the triple Higgs boson coupling. We obtain the region in which the GW spectrum can be observed by different future experiments such as LISA and DECIGO. We also show that the scenarios (1) and (2) can be discriminated by future GW observations and measurements of the di-Higgs productions at future colliders.

Pseudo-Goldstone dark matter in a radiative inverse seesaw scenario

We consider a scale-invariant inverse seesaw model with dynamical breaking of gauge symmetry and lepton number. In some regions of the parameter space, the Majoron — the pseudo-Goldstone of lepton number breaking — is a viable dark matter candidate. The bound on the Majoron decay rate implies a very large dilaton vacuum expectation value, which also results in a suppression of other dark matter couplings. Because of that, the observed dark matter relic abundance can only be matched via the freeze-in mechanism. The scalar field which gives mass to heavy neutrinos can play the role of the inflaton, resulting in a tensor-to-scalar ratio r ≲ 0.01 for metric inflation and r ≲ 0.21 for Palatini gravity.

Inflation and primordial gravitational waves in scale-invariant quadratic gravity with Higgs

In scale-invariant models of fundamental physics all mass scales are generated via spontaneous symmetry breaking. In this work, we study inflation in scale-invariant quadratic gravity, in which the Planck mass is generated classically by a scalar field, which evolves from an unstable fixed point to a stable one thus breaking scale-invariance. We investigate the dynamics by means of dynamical system standard techniques. By computing the spectral indices and comparing them with data, we put some constraints on the three dimensionless parameters of the theory. We show that certain regions of the parameter space will be within the range of future CMB missions like CMB-S4, LiteBIRD and STPol. The second half of the paper is dedicated to the analysis of inflationary first-order tensor perturbations and the calculation of the power spectrum of the gravitational waves. We comment on our results and compare them with the ones of mixed Starobinsky-Higgs inflation.

Scale-invariant semilinear damped wave models with mass term and integrable in time speed of propagation

In this paper, we consider the Cauchy problem for scale-invariant semilinear wave models with time-dependent mass, dissipation and integrable time-dependent propagation speed. The goal is to study the interplay between the coefficients appearing in the mass and dissipation term and the exponent in the speed of propagation to prove global (in time) existence of small data Sobolev solutions and blow-up results.

Sci-Net: scale-invariant model for buildings segmentation from aerial imagery

Buildings’ segmentation is a fundamental task in the field of earth observation and aerial imagery analysis. Most existing deep learning-based methods in the literature can be applied to a fixed or narrow-range spatial resolution imagery. In practical scenarios, users deal with a broad spectrum of image resolutions. Thus, a given aerial image often needs to be re-sampled to match the spatial resolution of the dataset used to train the deep learning model, which results in a degradation in segmentation performance. To overcome this challenge, we propose, in this manuscript, scale-invariant neural network (Sci-Net) architecture that segments buildings from wide-range spatial resolution aerial images. Specifically, our approach leverages UNet hierarchical representation and dense atrous spatial pyramid pooling to extract fine-grained multi-scale representations. Sci-Net significantly outperforms state-of-the-art models on the open cities AI and the multi-scale building datasets with a steady improvement margin across different spatial resolutions.

Large eddy simulation of atmospheric boundary layer flow over complex terrain in comparison with RANS simulation and on-site measurements under neutral stability condition

Large eddy simulation (LES) of the atmospheric boundary layer (ABL) flow over complex terrain is presented with a validation using meteorological tower (met-tower) data through an improved neutral stability sampling approach. The proposed stability sampling procedure includes a condition based on the most-likely occurrence time-periods of the neutral ABL and reduces the variabilities of the conditional wind statistics calculated at the met-towers in comparison to our previous work. The ABL flow simulations are carried out over a potential wind site with a prominent hill based using the OpenFOAM-based simulator for on/off-shore wind farm applications by applying the Lagrangian-averaged scale-invariant dynamic sub-grid scale turbulence model. A low-dissipative scale-selective discretization scheme for the non-linear convection term in the LES governing equation is adopted implicitly to ensure both the second-order accuracy and bounded solution. The LES inflow is generated through a precursor method with a “tiling” approach based on the flow driving parameters obtained from a corresponding Reynolds-averaged Navier–Stokes (RANS) simulation. Overall, the averaged wind velocity profiles predicted by the LES approach at all met-tower locations show a similar tendency as the RANS results, which are also in reasonable agreement with the met-tower data. An obvious difference in wind speed standard deviation profiles is seen between LES and RANS, especially at regions downstream of the hill edge, where the LES shows under-predicted results at the highest measurement levels in comparison to the tower data. The computational costs of the LES are found to be about 20 times higher than the RANS simulations.

Conformal model for gravitational waves and dark matter: a status update

We present an updated analysis of the first-order phase transition associated with symmetry breaking in the early Universe in a classically scale-invariant model extended with a new SU(2) gauge group. Including recent developments in understanding supercooled phase transitions, we compute all of its characteristics and significantly constrain the parameter space. We then predict gravitational wave spectra generated during this phase transition and by computing the signal-to-noise ratio we conclude that this model is well-testable (and falsifiable) with LISA. We also provide predictions for the relic dark matter abundance. It is consistent with observations in a rather narrow part of the parameter space. We strongly constrain the so-called supercool dark matter scenario based on an improved description of percolation and reheating after the phase transition as well as the inclusion of the running of couplings. Finally, we devote attention to the renormalisation-scale dependence of the results. Even though our main results are obtained with the use of renormalisation-group improved effective potential, we also perform a fixed-scale analysis which proves that the dependence on the scale is not only qualitative but also quantitative.

Scale-invariant 3-3-1-1 model with B−L symmetry

Motivated by a possible interplay between the mechanism of dynamical symmetry breaking and the seesaw mechanism for generating fermion masses, we present a scale-invariant model that extends the gauge symmetry of the Standard Model electroweak sector to SU(3)$_L\otimes$U(1)$_X\otimes$U(1)$_N$, with a built-in $B-L$ symmetry. The model is based on the symmetry structure of the known 3-3-1 models and, thus, it relates the number of the three observed fermion generations with the cancellation of gauge anomalies. Symmetry breaking is triggered via the Coleman-Weinberg mechanism taking into account a minimal set of scalar field multiplets. We establish the stability conditions for the tree-level scalar potential imposing the copositivity criteria and use the method of Gildener-Weinberg for computing the one-loop effective potential when one has multiple scalar fields. With the addition of vectorial fermions, getting their mass mainly through the vacuum expectation value of scalar singlets at $10^3$ TeV, the $B-L$ symmetry leads to textures for the fermion mass matrices, allowing seesaw mechanisms for neutrinos and quarks to take place. In particular, these mechanisms could partly explain the mass hierarchies of the quarks. Once the breakdown of the SU(3)$_L$ symmetry is supposed to occur around 10 TeV, the model also predicts new particles with TeV-scale masses, such as a neutral scalar, $H_{1}$, a charged scalar, $H^\pm$, and the gauge bosons $Z^{\prime}$, $W^{\prime\pm}$ and $Y^0$, that could be searched with the high-luminosity LHC.

Scaling solution for field-dependent gauge couplings in quantum gravity

Quantum gravity can determine the dependence of gauge couplings in a scalar field, which is related to possible fifth forces and time varying fundamental “constants”. This prediction is based on the scaling solution of functional flow equations. For momenta below the field-dependent Planck mass the quantum scale invariant standard model emerges as an effective low energy theory. For a small non-zero value of the infrared cutoff scale the time-variation of couplings or apparent violations of the equivalence principle turn out to be negligibly small for the present cosmological epoch, unless some further quantum scale symmetry violation beyond the standard model comes into play. More sizable effects of quantum scale symmetry violation are expected during nucleosynthesis or before. Scaling solutions relate field dependence and dependence on the renormalization scale. We find asymptotically free gauge couplings for the standard model coupled to gravity, while for grand unified models the gauge couplings are asymptotically safe with non-zero values at the ultraviolet fixed point. The scaling solution of asymptotically safe metric quantum gravity yields restrictions for model building, as limiting the number of scalars in grand unified theories.

Vacuum stability of conformally invariant scalar dark matter models

We discuss vacuum structure and vacuum stability in classically scale-invariant renormalizable models with a scalar dark matter multiplet of global O(N) symmetry together with an electroweak singlet scalar mediator. Our conformally invariant scalar potential generates the electroweak symmetry breaking via the Coleman-Weinberg mechanism, and the new scalar singlet mediator acquires its mass through radiative corrections of the scalar dark matters as well as of the standard model particles. Taking into account the present collider bounds, we find the region of parameter space where the scalar potential is stable and all the massless couplings are perturbative up to the Planck scale. With the obtained parameter sets satisfying the vacuum stability condition, we present the allowed region of new physics parameters satisfying the recent measurement of relic abundance, and predict the elastic scattering cross section of the new scalar multiplet into target nuclei for a direct detection of the dark matter. We also discuss the collider signatures and future discovery potentials of the new scalars.

BPS skyrmions of generalized Skyrme model in higher dimensions

In this work we consider the higher dimensional Skyrme model, with spatial dimension d > 3, focusing on its BPS submodels and their corresponding features. To accommodate the cases with a higher topological degree, B ≥ 1, a modified generalized hedgehog ansatz is used where we assign an integer ni for each rotational plane, resulting in a topological degree that proportional to product of these integers. It is found via BPS Lagrangian method that there are only two possible BPS submodels for this spherically symmetric ansatz which shall be called as BPS Skyrme model and scale-invariant model. The properties of the higher dimensional version of both submodels are studied and it is found that the BPS Skyrmions with B ≥ 1 exist in the first submodel but there is only B = 1 BPS Skyrmion in the second submodel. We also study the higher dimensional version of self-duality conditions in terms of strain tensor eigenvalues and find that, in general, the scale-invariant model has a stronger self-duality condition than the BPS Skyrme model.

Purely radiative Higgs mass in scale invariant models

In this work, we investigate the possibility of having scale invariant (SI) standard model (SM) extensions, where the light CP-even scalar matches the SM-like Higgs instead of being a light dilaton. After deriving the required conditions for this scenario, we show that the radiative corrections that give rise to the Higgs mass can trigger the scalar mixing to the experimentally allowed values. In addition, we discuss the constraints on the parameters space that makes the CP-even scalars properties in a good agreement with all the recent ATLAS and CMS measurements. We illustrate this scenario by considering the SI-scotogenic model as an example, while imposing all the theoretical and experimental constraints. We show that the model is viable and leads to possible modifications of the di-Higgs signatures at current/future with respect to the SM.

Dark matter-induced multi-phase dynamical symmetry breaking

We consider the classically scale invariant Higgs-dilaton model of dynamical symmetry breaking extended with an extra scalar field that plays the role of dark matter. The Higgs boson is light near a critical boundary between different symmetry breaking phases, where quantum corrections beyond the usual Gildener-Weinberg approximation become relevant. This implies a tighter connection between dark matter and Higgs phenomenology. The model has only three free parameters, yet it allows for the observed relic abundance of dark matter while respecting all constraints. The direct detection cross section mediated by the Higgs boson is determined by the dark matter mass alone and is testable at future experiments.

Dark matter and muon g − 2 anomaly via scale symmetry breaking

The Standard Model (SM) without the Higgs mass term is scale invariant. Gildener and Weinberg generalized the scale invariant standard model (SISM) by including the multiplication of scalars in quartic forms. They pointed out that along the flat direction only one scalar -called the scalon- is classically massless and all other scalars are massive. Here we choose a SISM with one scalon and one heavy scalar and extend that further respecting the scale invariance by a vector-like lepton (VLL). By an appropriate choice of the flat direction, the heavy scalar enjoys the ℤ2 symmetry and is assumed as DM particle. The scalon connects the visible and dark sector via the Higgs-portal and by interacting with both the muon lepton and the VLL. The VLL is charged under U(1)Y and interacts with γ/Z bosons. We show that the model correctly accounts for the observed dark matter (DM) relic abundance in the universe, while naturally evading the current and future bounds from direct detection (DD) experiments. Moreover, the model is capable to explain the (g − 2)μ anomaly observed in Fermilab. We also show a feature in SISM scenarios which is not present in other Higgs-portal models; despite having the Higgs-portal term |H|2s2 (s being the scalon) in SISM, the effective potential after the electroweak symmetry breaking lacks an important expected vertex hs2. This property immediately forbids the tree-level invisible Higgs decay h → ss and the one-loop Higgs decay h → μ+μ−.