Approximate Scale Symmetry Research Articles

Dilaton in a multicritical 3+epsilon-D parity violating field theory

The multi-critical behavior of an approximately scale and conformal invariant quantum field theory, which can be regarded as the deformation of the critical Gross-Neveu model in 3+epsilon dimensions by a nearly marginal parity violating operator, is studied using a large N expansion. When epsilon is greater than a number of order 1/N, the deformation is marginally relevant and it is found to exhibit spontaneous breaking of the approximate scale symmetry accompanied by the appearance of a light scalar in its spectrum. The scalar mass is parametrically small, of order epsilon times the fermion mass and it can be identified with a light dilaton. When the dimension is reduced to 3 the deformation of the Gross-Neveu model becomes marginally irrelevant, what was a minimum of the potential becomes a maximum and the theory has a non-perturbative global instability. There is a metastable perturbative phase where the scalar does not condense and the fermions are massless separated by an energy barrier with height of order one (rather than N) from an energetically favored phase with a runaway condensate.

Higgs-dilaton model revisited: Can a dilaton act as a QCD axion?

The Standard Model Lagrangian has an approximate scale symmetry in the high-energy limit. This observation can be included in the fundamental principle of the ultimate theory of Nature as the requirement of the exact quantum scale invariance. In this setup, all low-energy particle phenomenology can be obtained as a result of the spontaneous breaking of scale symmetry leading to the presence of the extra massless scalar field -- the dilaton. We explore the scenario in which this field is capable of solving the strong CP-problem in QCD in a similar way as in QCD axion models. The dilaton, playing the role of the axion, is coupled to the QCD sector and acquires a mass term due to non-perturbative breaking of scale symmetry. We show that the dilaton can form dark matter after the low-scale inflation. As a proof of concept, we construct a model of Higgs-driven inflation consistently realising the axion-like dilaton dark matter production compatible with the CMB data.

Approximate Nonlocal Symmetries for a Perturbed Schrödinger Equation with a Weak Infinite Power-Law Memory

A nonlocally perturbed linear Schrödinger equation with a small parameter was derived under the assumption of low-level fractionality by using one of the known general nonlocal wave equations with an infinite power-law memory. The problem of finding approximate symmetries for the equation is studied here. It has been shown that the perturbed Schrödinger equation inherits all symmetries of the classical linear equation. It has also been proven that approximate symmetries corresponding to Galilean transformations and projective transformations of the unperturbed equation are nonlocal. In addition, a special class of nonlinear, nonlocally perturbed Schrödinger equations that admits an approximate nonlocal extension of the Galilei group is derived. An example of constructing an approximately invariant solution for the linear equation using approximate scaling symmetry is presented.

Supercool composite Dark Matter beyond 100 TeV

Dark Matter could be a composite state of a confining sector with an approximate scale symmetry. We consider the case where the associated pseudo-Goldstone boson, the dilaton, mediates its interactions with the Standard Model. When the confining phase transition in the early universe is supercooled, its dynamics allows for Dark Matter masses up to 106 TeV. We derive the precise parameter space compatible with all experimental constraints, finding that this scenario can be tested partly by telescopes and entirely by gravitational waves.

Primordial flat frame: A new view on inflation

Models of inflationary cosmology admit a choice of the metric for which the geometry of homogeneous isotropic solutions becomes flat Minkowski space in the infinite past. In this primordial flat frame all mass scales vanish in the infinite past and quantum scale symmetry is realized. The cosmological evolution is dominantly described by the slow increase of a scalar field which sets the scale of all masses. We construct the primordial flat frame for standard models of inflation as Starobinsky inflation or chaotic inflation. In particular, we discuss the evolution of inhomogeneous solutions in the neighborhood of the homogeneous isotropic background solution and their relation to the observable primordial fluctuation spectrum. If the propagators for the graviton and scalar field remain regular, our observed inhomogeneous Universe can be extrapolated back to the infinite past in physical time. In this case there is no physical big-bang singularity -- the latter reflects only a singular choice of ``field coordinates". Independently of the issue of singularity the primordial flat frame offers a new view on the physical properties of the inflationary universe, which can be characterized as a very slowly evolving almost empty vacuum state with approximate scale symmetry.

Dimensional transmutation in gravity and cosmology

We review (and extend) the analysis of general theories of all interactions (gravity included) where the mass scales are due to dimensional transmutation. Quantum consistency requires the presence of terms in the action with four derivatives of the metric. It is shown, nevertheless, how unitary is achieved and the classical Ostrogradsky instabilities can be avoided. The four-derivative terms also allow us to have a UV complete framework and a naturally small ratio between the Higgs mass and the Planck scale. Moreover, black holes of Einstein gravity with horizons smaller than a certain (microscopic) scale are replaced by horizonless ultracompact objects that are free from any singularity and have interesting phenomenological applications. We also discuss the predictions that can be compared with observations of the microwave background radiation anisotropies and find that this scenario is viable and can be tested with future data. Finally, how strong phase transitions can emerge in models of this type with approximate scale symmetry and how to test them with GW detectors is reviewed and explained.

Weyl scaling invariant R2 gravity for inflation and dark matter

Inflation in the early universe can generate the nearly conformal invariant fluctuation that leads to the structures we observe at the present. The simple viable Starobinsky R2 inflation has an approximate global scale symmetry. We study the conformal symmetric Weyl Rˆ2 and general F(Rˆ) theories and demonstrate their equivalence to Einstein gravity coupled with a scalar and a Weyl gauge field. The scalar field in Weyl Rˆ2 gravity can be responsible for inflation with Starobinsky model as the attractor, potentially distinguishable from the latter by future experiments. The intrinsic Weyl gauge boson becomes massive once the Einstein frame is fixed, and constitutes as a dark matter candidate with mass up to ∼5×1016GeV.

Phenomenology of the new light Higgs bosons in Gildener-Weinberg models

Gildener-Weinberg (GW) models of electroweak symmetry breaking are especially interesting because the low mass and nearly Standard Model couplings of the 125 GeV Higgs boson $H$ are protected by approximate scale symmetry. Another important but so far underappreciated feature of these models is that a sum rule bounds the masses of the new charged and neutral Higgs bosons appearing in all these models to be below about 500 GeV. Therefore, they are within reach of LHC data currently or soon to be in hand. Also so far unnoticed of these models, certain cubic and quartic Higgs scalar couplings vanish at the classical level. This is due to spontaneous breaking of the scale symmetry. These couplings become nonzero from explicit scale breaking in the Coleman-Weinberg loop expansion of the effective potential. In a two-Higgs doublet GW model, we calculate ${\ensuremath{\lambda}}_{HHH}\ensuremath{\simeq}2({\ensuremath{\lambda}}_{HHH}{)}_{\mathrm{SM}}=64\text{ }\text{ }\mathrm{GeV}$. This corresponds to $\ensuremath{\sigma}(pp\ensuremath{\rightarrow}HH)\ensuremath{\cong}15--20\text{ }\text{ }\mathrm{fb}$, its minimum value for $\sqrt{s}=13--14\text{ }\text{ }\mathrm{TeV}$ at the LHC. It will require at least the 27 TeV HE-LHC to observe this cross section. We also find ${\ensuremath{\lambda}}_{HHHH}\ensuremath{\simeq}4({\ensuremath{\lambda}}_{HHHH}{)}_{\mathrm{SM}}=0.129$, whose observation in $pp\ensuremath{\rightarrow}HHH$ requires a 100 TeV collider. Because of the above-mentioned sum rule, these results apply to all GW models. In view of this unpromising forecast, we stress that LHC searches for the new relatively light Higgs bosons of GW models are by far the surest way to test them in this decade.

Dynamical Violation of Scale Invariance and the Dilaton in a Cold Fermi Gas.

We use the large-N approximation to find an exotic phase of a cold, two-dimensional, N-component Fermi gas which exhibits dynamically broken approximate scale symmetry. We identify a particular weakly damped collective excitation as the dilaton, the pseudo-Goldstone boson associated with the broken approximate scale symmetry. We argue that the symmetry breaking phase is stable for a range of parameters of the theory and there is a fluctuation induced first order quantum phase transition between the normal and the scale symmetry breaking phases which can be driven by tuning the chemical potential. We find that the compressibility of the gas at its lower critical density is anomalously large, 2N times that of a perfect gas at the same density.

Introducing Causality Violation for Improved DPOAE Component Unmixing.

The DPOAE response consists of the linear superposition of two components, a nonlinear distortion component generated in the overlap region, and a reflection component generated by roughness in the DP resonant region. Due to approximate scaling symmetry, the DPOAE distortion component has approximately constant phase. As the reflection component may be considered as a SFOAE generated by the forward DP traveling wave, it has rapidly rotating phase, relative to that of its source, which is also equal to the phase of the DPOAE distortion component. This different phase behavior permits effective separation of the DPOAE components (unmixing), using time-domain or time-frequency domain filtering. Departures from scaling symmetry imply fluctuations around zero delay of the distortion component, which may seriously jeopardize the accuracy of these filtering techniques. The differential phase-gradient delay of the reflection component obeys causality requirements, i.e., the delay is positive only, and the fine-structure oscillations of amplitude and phase are correlated to each other, as happens for TEOAEs and SFOAEs relative to their stimulus phase. Performing the inverse Fourier (or wavelet) transform of a modified DPOAE complex spectrum, in which a constant phase function is substituted for the measured one, the time (or time-frequency) distribution shows a peak at (exactly) zero delay and long-latency specular symmetric components, with a modified (positive and negative) delay, which is that relative to that of the distortion component in the original response. Component separation, applied to this symmetrized distribution, becomes insensitive to systematic errors associated with violation of the scaling symmetry in specific frequency ranges.

Classically scale invariant inflation, supermassive WIMPs, and adimensional gravity

We introduce a minimal and yet comprehensive framework with $CP$ and classical scale symmetries in order to simultaneously address the hierarchy problem, neutrino masses, dark matter, and inflation. One complex gauge singlet scalar and three flavors of the right-handed Majorana neutrinos are added to the standard model content, facilitating the see-saw mechanism, among others. An adimensional theory of gravity (Agravity) is employed, allowing for the trans-Planckian field excursions. The weak and Planck scales are induced by the Higgs portal and the scalar nonminimal couplings, respectively, once a Coleman-Weinberg dynamically generated vacuum expectation value for the singlet scalar is obtained. All scales are free from any mutual quadratic destabilization. The $CP$ symmetry prevents a decay of the pseudoscalar singlet, rendering it a suitable WIMPzilla dark matter candidate with the correct observational relic abundance. Identifying the pseudo-Nambu-Goldstone boson of the (approximate) scale symmetry with the inflaton field, the model accommodates successful slow-roll inflation, compatible with the observational data. We reach the conclusion that a pseudo-Nambu-Goldstone inflaton, within a classically scale-symmetric framework, yields lighter WIMPzillas.

Classically Scale Invariant Inflation and (A)gravity

In this talk, I present the minimal classically scale-invariant and [Formula: see text]-symmetric extension of the standard model, containing one additional complex gauge singlet and three flavors of right-handed Majorana neutrinos, incorporated within a renormalizable framework of gravity, consistent with these symmetries; the Agravity. I particularly focus on the slow-roll inflationary paradigm within this framework, by identifying the pseudo-Nambu-Goldstone boson of the (approximate) scale symmetry with the inflaton field, constructing its one-loop effective potential, computing the slow-roll parameters and the inflationary observables, and demonstrating the compatibility of the small field inflation scenario with the latest Planck collaboration data sets. a

Lattice Studies on 8-Flavor QCD in The Light of Physics Beyond The Standard Model

We report the latest results of the LatKMI collaboration on 8-flavor QCD using Monte Carlo simulations of the lattice gauge theory. The subject receives growing interest with regards to physics beyond the Standard Model (BSM). We show that a flavor-singlet scalar meson (σ) emerges as one of the lightest bound states and can be a composite Higgs boson with mass 125 GeV. The light σ may be a technidilaton, a pseudo Nambu-Goldstone boson of the approximate scale symmetry, which results from a slowly running (walking) coupling constant associated with an infra-red fixed point. Consistently to this reasoning, a mass anomalous dimension γ is found to be large γ∼1. We discuss the applicability of 8-flavor QCD to the BSM model building.

Walking on the ladder: 125 GeV technidilaton, or Conformal Higgs

The walking technicolor based on the ladder Schwinger-Dyson gap equation is studied, with the scale-invariant coupling being an idealization of the Caswell-Banks-Zaks infrared fixed point in the "anti-Veneziano limit", such that $N_C \rightarrow \infty$ with $N_C \cdot \alpha(\mu^2)=$ fixed and $N_F/N_C=$ fixed ($\gg 1$), of the $SU(N_C)$ gauge theory with massless $N_F$ flavors near criticality. We show that the 125 GeV Higgs can be naturally identified with the technidilaton (TD) predicted in the walking technicolor, a pseudo Nambu-Goldstone (NG) boson of the spontaneous symmetry breaking of the approximate scale symmetry. Ladder calculations yield the TD mass $M_\phi$ from the trace anomaly as $M_\phi^2 F_\phi^2= -4 \langle \theta_\mu^\mu \rangle = - \frac{\beta(\alpha (\mu^2))}{\alpha(\mu^2)}\, \langle G_{\lambda \nu}^2(\mu^2)\rangle \simeq N_C N_F\frac{16}{\pi^4} m_F^4$, independently of the renormalization point $\mu$, where $m_F$ is the dynamical mass of the technifermion, and $F_\phi={\cal O} (\sqrt{N_F N_C}\, m_F)$ the TD decay constant. It reads $M_\phi^2\simeq (\frac{v_{\rm EW}}{2} \cdot \frac{5 v_{\rm EW}}{F_\phi})^2 \cdot [\frac{8}{N_F}\frac{4}{N_C}]$, ($v_{\rm EW}=246$ GeV), which implies $F_\phi\simeq 5 \,v_{\rm EW} $ for $M_\phi \simeq 125\, {\rm GeV}\simeq \frac{1}{2} v_{\rm EW}$ in the one-family model ($N_C=4, N_F=8$), in good agreement with the current LHC Higgs data. The result reflects a generic scaling $ M_\phi^2/v_{\rm EW}^2\sim M_\phi^2/F_\phi^2 \sim m_F^2 /F_\phi^2 \sim 1/(N_F N_C) \rightarrow 0 $ as a vanishing trace anomaly, namely the TD has a mass vanishing in the anti-Veneziano limit, similarly to $\eta^\prime$ meson as a pseudo-NG boson of the ordinary QCD with vanishing $U(1)_A$ anomaly in the Veneziano limit ($N_F/N_C \ll 1$).

Prospects for discovering the Higgs-like pseudo-Nambu-Goldstone boson of the classical scale symmetry

We examine the impact of the expected reach of the LHC and the XENON1T experiments on the parameter space of the minimal classically scale invariant extension of the standard model (SM), where all the mass scales are induced dynamically by means of the Coleman-Weinberg mechanism. In this framework, the SM content is enlarged by the addition of one complex gauge singlet scalar with a scale invariant and $CP$-symmetric potential. The massive pseudoscalar component, protected by the $CP$-symmetry, forms a viable dark matter candidate, and three flavors of the right-handed Majorana neutrinos are included to account for the nonzero masses of the SM neutrinos via the see-saw mechanism. The projected constraints on the parameter space arise by applying the ATLAS heavy Higgs discovery prospects, with an integrated luminosity of 300 and 3000~fb$^{-1}$ at $\sqrt s = 14$~TeV, to the pseudo-Nambu-Goldstone boson of the (approximate) scale symmetry, as well as by utilizing the expected reach of the XENON1T direct detection experiment for the discovery of the pseudoscalar dark matter candidate. A null-signal discovery by these future experiments implies that vast regions of the model's parameter space can be thoroughly explored; the combined projections are expected to confine a mixing between the SM and the singlet sector to very small values, while probing the viability of the TeV~scale pseudoscalar's thermal relic abundance as the dominant dark matter component in the Universe. Furthermore, the vacuum stability and triviality requirements of the framework up to the Planck scale are studied and the viable region of the parameter space is identified. The results are summarized in extensive exclusion plots, incorporating additionally the prior theoretical and experimental bounds for comparison.

2 TeV walking technirho at LHC?

The ATLAS collaboration has recently reported an excess of about 2.5 σ global significance at around 2 TeV in the diboson channel with the boson-tagged fat dijets, which may imply a new resonance beyond the standard model. We provide a possible explanation of the excess as the isospin-triplet technivector mesons (technirhos, denoted as ρΠ±,3) of the walking technicolor in the case of the one-family model as a benchmark. As the effective theory for the walking technicolor at the scales relevant to the LHC experiment, we take a scale-invariant version of the hidden local symmetry model so constructed as to accommodate technipions, technivector mesons, and the technidilaton in such a way that the model respects spontaneously broken chiral and scale symmetries of the underlying walking technicolor. In particular, the technidilaton, a (pseudo) Nambu–Goldstone boson of the (approximate) scale symmetry predicted in the walking technicolor, has been shown to be successfully identified with the 125 GeV Higgs. Currently available LHC limits on those technihadrons are used to fix the couplings of technivector mesons to the standard-model fermions and weak gauge bosons. We find that the technirhos are mainly produced through the Drell–Yan process and predominantly decay to the dibosons, which accounts for the currently reported excess at around 2 TeV. The consistency with the electroweak precision test and other possible discovery channels of the 2 TeV technirhos are also addressed.

New solutions with accelerated expansion in string theory

We present concrete solutions with accelerated expansion in string theory, requiring a small, tractable list of stress energy sources. We explain how this construction (and others in progress) evades previous no go theorems for simple accelerating solutions. Our solutions respect an approximate scaling symmetry and realize discrete sequences of values for the equation of state, including one with an accumulation point at w=-1 and another accumulating near w=-1/3 from below. In another class of models, a density of defects generates scaling solutions with accelerated expansion. We briefly discuss potential applications to dark energy phenomenology, and to holography for cosmology.

Light composite scalar in eight-flavor QCD on the lattice

We present the first observation of a flavor-singlet scalar meson as light as the pion in $N_f=8$ QCD on the lattice, using the Highly Improved Staggered Quark action. Such a light scalar meson can be regarded as a composite Higgs with mass 125 GeV. In accord with our previous lattice results showing that the theory exhibits walking behavior, the light scalar may be a technidilaton, a pseudo Nambu-Goldstone boson of the approximate scale symmetry in walking technicolor.

Gluonic effects ong−2: Holographic view

We study "gluonic effects" (gluon condensation effects) on the hadronic leading order (HLO) contributions to the anomalous magnetic moment (g-2) of leptons, based on a holographic model having explicit gluonic mode introduced for consistency with the operator product expansion of QCD. We find gluonic enhancement of HLO contributions to the muon g-2 by about 6%, which nicely fills in the gap between the holographic estimate without gluonic effects and the phenomenological one using the experimental data as inputs. Similar calculations including the gluonic effects for the electron and the tau lepton g-2 are also carried out in good agreement with the phenomenological estimates. We then apply our holographic estimate to the Walking Technicolor (WTC) where large techni-gluonic effects were shown to be vital for the Technidilaton, (pseudo) Nambu-Goldstone boson of the (approximate) scale symmetry of WTC, to be naturally as light as 125 GeV. It is shown that the value of the techni-HLO contributions to the muon g-2 is 10-100 times enhanced by inclusion of the same amount of the gluonic effects as that realizing the 125 GeV Technidilaton, although such an enhanced techni-HLO contribution is still negligibly small compared with the current deviation of the Standard Model prediction of the muon g-2 from the experiments. The techni-HLO contributions to the tau lepton g-2 is also discussed, suggesting a possible phenomenological relevance to be tested by the future experiments.

Cyclic cosmology, conformal symmetry and the metastability of the Higgs

Recent measurements at the LHC suggest that the current Higgs vacuum could be metastable with a modest barrier (height (1010–12 GeV)4) separating it from a ground state with negative vacuum density of order the Planck scale. We note that metastability is problematic for standard bang cosmology but is essential for cyclic cosmology in order to end one cycle, bounce, and begin the next. In this Letter, motivated by the approximate scaling symmetry of the standard model of particle physics and the primordial large-scale structure of the universe, we use our recent formulation of the Weyl-invariant version of the standard model coupled to gravity to track the evolution of the Higgs in a regularly bouncing cosmology. We find a band of solutions in which the Higgs field escapes from the metastable phase during each big crunch, passes through the bang into an expanding phase, and returns to the metastable vacuum, cycle after cycle after cycle. We show that, due to the effect of the Higgs, the infinitely cycling universe is geodesically complete, in contrast to inflation.