Quadratic Divergences Research Articles

Proyecciones de población para áreas pequeñas: estimaciones a nivel de parroquia en cinco provincias del Noroeste de España

En este artículo se presenta un procedimiento sencillo para obtener proyecciones demográficas para áreas geográficas pequeñas. El método aquí presentado se basa en asumir que las tendencias de las zonas que se van a proyectar serán similares a las observadas en períodos anteriores, y en tomar las proyecciones para áreas geográficas más extensas como punto de referencia. En términos matemáticos, esta técnica pasa por un problema de minimización restringida de las divergencias cuadráticas entre las proyecciones obtenidas y las observadas en períodos pasados, donde las proyecciones demográficas agregadas se toman como restricción. Esta propuesta encaja adecuadamente con el escenario presente en el caso de las proyecciones demográficas que el Instituto Nacional de Estadística (INE) elabora para España, donde las previsiones se presentan a escala provincial pero no con más nivel de detalle. Aunque estas proyecciones provinciales son útiles de cara a la planificación de políticas y a la dotación de determinados servicios por parte del sector público, sería deseable disponer de ellas a una escala geográfica inferior al ámbito provincial. El procedimiento presentado en este trabajo se ilustra con el caso de cinco provincias de España, correspondientes a las comunidades autónomas de Asturias y Galicia, en las que las predicciones de población correspondientes para el año 2033 son desagregadas a una escala geográfica de parroquia.

Softly broken conformal symmetry with higher curvature terms

In a scalar-coupled-gravity model, the quadratically divergent counter term appearing in the mass renormalization of the scalar fields must inherit corrections arising out of gravitational interactions. In this work we have explicitly demonstrated that there are no such corrections of gravitational origin to the quadratic divergences in the mass counter terms. This statement holds true irrespective of the nature of the gravitational interaction, i.e., whether gravity is described by general relativity or f(R) theory. Interestingly, it also turns out that the one loop effective action of scalar-coupled-gravity system will be well-behaved \emph{if and only if} the $f(R)$ theory is free from ghosts. In particular, the results derived in the context of f(R) theory are shown to be in exact agreement with the corresponding results derived from the equivalent scalar-tensor representation. Our analysis suggests the tantalizing possibility that the masses of the scalar fields can be consistently kept smaller than some Ultra Violet (UV) cutoff scale and is independent of the nature of the gravity theory, which may involve higher curvature corrections. All these will be true provided the matter fields and the gravity theory can be embedded consistently into a UV complete theory at the Planck scale.

A twist on broken U(3) $$\times $$ U(3) supersymmetry

What symmetry breaking would be required for gauginos from a supersymmetric theory to behave like left-handed quarks of the Standard Model? Starting with a supersymmetric SU(3) $$\times $$ SU(3) $$\times $$ U(1) $$\times $$ U(1) gauge theory, the 18 adjoint-representation gauginos are replaced with 2 families of 9 gauginos in the (3,3*) representation of the group. After this explicit breaking of supersymmetry, two-loop quadratic divergences still cancel at a unification scale. Coupling constant unification is supported by deriving the theory from an SU(3) $$\times $$ SU(3) $$\times $$ SU(3) $$\times $$ SU(3) Grand Unified Theory (GUT). $${\hbox {Sin}}^2$$ of the Weinberg angle for the GUT is 1/4 rather than 3/8, leading to a lower unification scale than usually contemplated, $$\sim 10^9 \, \hbox {GeV}$$ . After spontaneous gauge symmetry breaking to SU(3) $$\times $$ SU(2) $$\times $$ U(1), the theory reproduces the main features of the Standard Model for two families of quarks and leptons, with gauginos playing the role of left-handed quarks and sleptons playing the role of the Higgs boson. An extension to the theory is sketched that incorporates the third family of quarks and leptons.

Correlation functions of Landau gauge Yang-Mills theory

Correlation functions of Yang-Mills theory in the Landau gauge are calculated from their equations of motion. The employed setup is completely parameter free and leads, within errors, to good quantitative agreement with corresponding lattice results for the ghost and gluon propagators as well as the ghost-gluon and three-gluon vertices. Also the four-gluon vertex is calculated. The present setup allows for the first time for a unique subtraction of quadratic divergences in the gluon propagator Dyson-Schwinger equation. Thus, there are no ambiguities which can arise due to the use of models or auxiliary workarounds. In addition, several self-tests of the results are described that allow assessing the truncation error in a self-consistent way. This enables a new perspective on how to identify limitations of the present setup and develop future improvements.

Minimal neutral naturalness model

We build a minimal neutral naturalness model in which the top partners are not charged under QCD, with a pseudo Goldstone Higgs arising from $SO(5)/SO(4)$ breaking. The color-neutral top partners generate the Higgs potential radiatively without quadratic divergence. The misalignment between the electroweak scale and global symmetry breaking scale is naturally obtained from suppression of the Higgs quadratic term, due to cancellation between singlet and doublet top partner contributions. This model can be embedded into ultraviolet holographic setup in composite Higgs framework, which even realizes finite Higgs potential.

Left-right symmetric composite Higgs model

We find the exchange symmetry between left and right handed top quark in composite Higgs model with partial compositeness is efficient to soften the Higgs potential and reduce fine tuning. This symmetry can keep the Higgs potential in top sector invariant under trigonometric parity $\sin (h/f) \leftrightarrow \cos (h/f)$ and thus the Higgs quadratic divergences can be completely cancelled, resulting a UV insensitive Higgs potential. We explicitly construct the minimal left-right symmetric model based on coset space $SO(6)/SO(5)$ which is locally isomorphic to $SU(4)/Sp(4)$ and thus has well defined fermionic UV completion. This UV completion can automatically keep Higgs potential in gauge sector finite even the gauge sector breaks this discrete symmetry. We find that the vector mesons can be very heavy while the colored top partners are relatively light ($>1.5$ TeV) to obtain a light Higgs.

Zero point energy of composite particles: The medium effects

We analyze the zero point energy of composite particles (or resonances) which are dynamically created from relativistic fermions. We compare the zero point energies in medium to the vacuum one, taking into account the medium modification of the constituent particles. Treating composite particles as if quasi-particles, their zero point energies contain the quadratic and logarithmic UV divergences even after the vacuum subtraction. The coefficients of these divergences come from the difference between the vacuum and in-medium fermion propagators. We argue that such apparent divergences can be cancelled by consistently using fermion propagators to compute the quasi-particle contributions as well as their interplay, provided that the self-energies of the constituents at large momenta approach to the vacuum ones sufficiently fast. In the case of quantum chromodynamics, mesons and baryons, which may be induced or destroyed by medium effects, yield the in-medium divergences in the zero point energies, but the divergences are assembled to cancel with those from the quark zero-point energy. This is particularly important for unified descriptions of hadronic and quark matter which may be smoothly connected by the quark-hadron continuity.

Fine-Tuned Spin-3/2 and the Hierarchy Problem

In the past, Kundu et al. and Chakraborty et al. used extra scalar fields to cancel the quadratic divergences in the Higgs mass squared and they determined the mass of the required scalar field. In this work, a spin-3/2 particle has been used in the same manner to nullify the power-law divergences, and it is determined that the mass of the spin-3/2 particle resides in the ball park of the GUT scale.

Fundamental limits on low-temperature quantum thermometry with finite resolution

While the ability to measure low temperatures accurately in quantum systems is important in a wide range of experiments, the possibilities and the fundamental limits of quantum thermometry are not yet fully understood theoretically. Here we develop a general approach to low-temperature quantum thermometry, taking into account restrictions arising not only from the sample but also from the measurement process. {We derive a fundamental bound on the minimal uncertainty for any temperature measurement that has a finite resolution. A similar bound can be obtained from the third law of thermodynamics. Moreover, we identify a mechanism enabling sub-exponential scaling, even in the regime of finite resolution. We illustrate this effect in the case of thermometry on a fermionic tight-binding chain with access to only two lattice sites, where we find a quadratic divergence of the uncertainty}. We also give illustrative examples of ideal quantum gases and a square-lattice Ising model, highlighting the role of phase transitions.

On strongly quasiconvex subgroups

We develop a theory of \emph{strongly quasiconvex subgroups} of an arbitrary finitely generated group. Strong quasiconvexity generalizes quasiconvexity in hyperbolic groups and is preserved under quasi-isometry. We show that strongly quasiconvex subgroups are also more reflexive of the ambient groups geometry than the stable subgroups defined by Durham-Taylor, while still having many analogous properties to those of quasiconvex subgroups of hyperbolic groups. We characterize strongly quasiconvex subgroups in terms of the lower relative divergence of ambient groups with respect to them. We also study strong quasiconvexity and stability in relatively hyperbolic groups, right-angled Coxeter groups, and right-angled Artin groups. We give complete descriptions of strong quasiconvexity and stability in relatively hyperbolic groups and we characterize strongly quasiconvex special subgroups and stable special subgroups of two dimensional right-angled Coxeter groups. In the case of right-angled Artin groups, we prove that two notions of strong quasiconvexity and stability are equivalent when the right-angled Artin group is one-ended and the subgroups have infinite index. We also characterize non-trivial strongly quasiconvex subgroups of infinite index (i.e. non-trivial stable subgroups) in right-angled Artin groups by quadratic lower relative divergence, expanding the work of Koberda-Mangahas-Taylor on characterizing purely loxodromic subgroups of right-angled Artin groups.

The Hierarchy Problem and the Cosmological Constant Problem Revisited

We argue that the Standard Model (SM) in the Higgs phase does not suffer from a "hierarchy problem" and that similarly the "cosmological constant problem" resolves itself if we understand the SM as a low energy effective theory emerging from a cutoff-medium at the Planck scale. We actually take serious Veltman's "The Infrared - Ultraviolet Connection" addressing the issue of quadratic divergences and the related huge radiative correction predicted by the SM in the relationship between the bare and the renormalized theory, usually called "the hierarchy problem" and claimed that this has to be cured. We discuss these issues under the condition of a stable Higgs vacuum, which allows to extend the SM up to the Planck cutoff. The bare Higgs boson mass then changes sign below the Planck scale, such that the SM in the early universe is in the symmetric phase. The cutoff enhanced Higgs mass term as well as the quartically enhanced cosmological constant term provide a large positive dark energy which triggers the inflation of the early universe. Reheating follows via the decays of the four unstable heavy Higgs particles, predominantly into top-antitop pairs, which at this stage are still massless. Preheating is suppressed in SM inflation since in the symmetric phase bosonic decay channels are absent at tree level. The coefficients of the shift between bare and renormalized Higgs mass as well as of the shift between bare and renormalized vacuum energy density exhibit close-by zeros at about $7.7 \times 10^{14}$ GeV and $3.1 \times 10^{15}$ GeV, respectively. The zero of of the Higgs mass counter term triggers the electroweak phase transition from the low energy Higgs phase and to the symmetric phase above the transition point. The scenario highly favors to understand the SM and its main properties as a natural structure emerging at long distance.

Naturalness sum rules and their collider tests

We present the most general sum rules reflecting the cancellation of ultraviolet divergences in the Higgs potential, which provide necessary conditions for any weakly-coupled extension of the Standard Model to be natural. There is a separate sum rule for the cancellation of the quadratic and logarithmic divergences, and their forms depend on whether the divergences are canceled by same-spin or opposite-spin partners. These sum rules can be applied to mass eigenstates and conveniently used for direct collider tests of naturalness. We study in detail the feasibility of testing these sum rules in the top sector at a future 100 TeV proton collider within two benchmark models, the Little Higgs (LH) and the Maximally Symmetric Composite Higgs (MSCH). We show how the two ingredients of the sum rules, the top partner masses and their Yukawa couplings to the Higgs, can be measured with sufficient accuracy to provide a highly non-trivial quantitative test of the sum rules. In particular, we study observables sensitive to the sign of the top partner Yukawa, which is crucial for verifying the sum rules but is notoriously difficult to measure. We demonstrate that in the benchmark models under study, a statistically significant discrimination between the two possible signs of each Yukawa will be feasible with a 30 ab−1 data set at 100 TeV.

Continuum naturalness

We present a novel class of composite Higgs models in which the top and gauge partners responsible for cutting off the Higgs quadratic divergences form a continuum. The continuum states are characterized by their spectral densities, which should have a finite gap for realistic models. We present a concrete example based on a warped extra dimension with a linear dilaton, where this finite gap appears naturally. We derive the spectral densities in this model and calculate the full Higgs potential for a phenomenologically viable benchmark point, with percent level tuning. The continuum top and gauge partners in this model evade all resonance searches at the LHC and yield qualitatively different collider signals.

Softly broken conformal symmetry with quantum gravitational corrections

We show that a previously proposed new mechanism to eliminate quadratic divergences for scalar masses is self-consistently compatible with corrections induced by perturbative quantum gravity, provided the theory embeds consistently into a UV completion at the Planck scale.

Indirect signs of the Peccei-Quinn mechanism

In the Standard Model, the renormalization of the QCD vacuum angle $\theta$ is extremely tiny, and small $\theta$ is technically natural. In the general Standard Model effective field theory (SMEFT), however, $\Delta\theta$ is quadratically divergent, reflecting the fact that new sources of hadronic CP-violation typically produce $\mathcal O(1)$ threshold corrections to $\theta$. The observation of such CP-violating interactions would therefore be in tension with solutions to the strong CP problem in which $\theta=0$ is an ultraviolet boundary condition, pointing to the Peccei-Quinn mechanism as the explanation for why $\theta$ is small in the infrared. We study the quadratic divergences in $\theta$ arising from dimension-6 SMEFT operators and discuss the discovery prospects for these operators at electric dipole moment experiments, the LHC, and future proton-proton colliders.

Discriminative Autoencoding Framework for Simple and Efficient Anomaly Detection

In this paper, a discriminative autoencoding framework is proposed for semi-supervised anomaly detection using reconstruction errors. The framework only consists of a generator and a discriminative encoder, and the output of the latter is a vector. In the training process, the framework is trained as a generative adversarial network based on quadratic potential divergence. An extra loss added in the objective function enforces the discriminative encoder to use the mean value of the output vector for discrimination, which also empowers it with encoding ability. In the testing process, the trained framework can be used as an autoencoder to reconstruct test samples, where the trained discriminative encoder works as an encoder, and samples with reconstruction errors above a predefined threshold are determined as anomalies. The properties of quadratic potential divergence ensure a simple training process with comparable performance, meanwhile the discriminative encoder with two functions makes full use of training resources and reduces required network structures. Comparisons on benchmark datasets also show the efficiency and superiorities of the proposed methods.

ANÁLISIS DE LOS DECAIMIENTOS DE UN BOSÓN ESCALAR EN EL MODELO BESTEST LITTLE HIGGS

The Bestest Little Higgs (BLH) model provides an interesting way to address the problem of hierarchy but also manages to overcome certain difficulties that arise in Little Higgs type models, for example, the mechanism to generate a Higgs quantum coupling frequently leads to great violations in custodial symmetry. The proposal in this work is to study the decays of a massive scalar Iƒ predicted in the BLH scenario to a pair of gluons and a pair of photons. It is of our interest, the decays that are induced at the one loop-level involving heavy quarks, since in this type of models the quadratic divergences due to the corrections of the Higgs boson mass can be canceled by the contribution of new heavy particles, with masses of the order of tera-electron volts (TeV). In this work, we determine the decay fractions corresponding to the processes Iƒ --> gg and Iƒ --> I³I³ at the one-loop level. We also present a study of the effective production section of the scalar Iƒ via fusion of gluons, these parameters are a function of the energy scale of the breakdown of the global symmetry of the model, denoted as f.

Trigonometric Parity for Composite Higgs Models.

We identify trigonometric parity as the key ingredient behind models of neutral naturalness for the Higgs potential and show how to construct the minimal model realizing trigonometric parity. We show that any symmetric coset space readily includes such a trigonometric parity, which is simply a combination of a π/2 rotation along a broken direction and a Higgs parity transformation. The top sector can be extended such that this Z_{2} remains intact, which ensures the cancelation of the quadratic divergences in the Higgs potential, yielding the simplest model of neutral naturalness.

Reducing the quadratic divergence in the Higgs boson mass squared without top partners

We examine a model with multiple scalar fields to see whether it is possible to reduce the fine- tuning of the SM Higgs mass without introducing low scale top partners. Our approach may be regarded as a generalization of the condition proposed by Veltman, who attempted to predict the Higgs mass using the criterion that the various low energy contributions to the quadratic divergence of the Higgs mass cancel. Although the Veltman condition predicts the wrong Higgs mass in the Standard Model, it can still be adapted to extended Higgs sectors. Furthermore, theories with additional Higgs bosons can lead to suppressed Yukawa couplings of the top quark to the 125 GeV Higgs, making the associated one-loop divergence smaller. Here, we review possible extensions of the Standard Model where the Veltman condition could be realized, and study in detail one minimal model with two extra scalar fields. For this model and for a cutoff of 5 TeV, we show that the overall fine-tuning can be considerably lowered without introducing low-scale Landau poles, albeit the Higgs sector will be strongly coupled at the cutoff. Models where the top Yukawa coupling is reduced, in particular, will be within the reach of the upcoming LHC searches.

High energy physics and cosmology at the unification frontier: Opportunities and challenges in the coming years

We give here an overview of recent developments in high energy physics and cosmology and their interconnections that relate to unification, and discuss prospects for the future. Thus there are currently three empirical data that point to supersymmetry as an underlying symmetry of particle physics: the unification of gauge couplings within supersymmetry, the fact that nature respects the supersymmetry prediction that the Higgs boson mass lie below 130 GeV, and vacuum stability up to the Planck scale with a Higgs boson mass at [Formula: see text][Formula: see text]125 GeV while the Standard Model does not do that. Coupled with the fact that supersymmetry solves the big hierarchy problem related to the quadratic divergence to the Higgs boson mass square along with the fact that there is no alternative paradigm that allows us to extrapolate physics from the electroweak scale to the grand unification scale consistent with experiment, supersymmetry remains a compelling framework for new physics beyond the Standard Model. The large loop correction to the Higgs boson mass in supersymmetry to lift the tree mass to the experimentally observable value, indicates a larger value of the scale of weak scale supersymmetry, making the observation of sparticles more challenging but still within reach at the LHC for the lightest ones. Recent analyses show that a high energy LHC (HE-LHC) operating at 27 TeV running at its optimal luminosity of [Formula: see text] can reduce the discovery period by several years relative to HL-LHC and significantly extend the reach in parameter space of models. In the coming years several experiments related to neutrino physics, searches for supersymmetry, on dark matter and dark energy will have direct impact on the unification frontier. Thus the discovery of sparticles will establish supersymmetry as a fundamental symmetry of nature and also lend direct support for strings. Further, discovery of sparticles associated with missing energy will constitute discovery of dark matter with LSP being the dark matter. On the cosmology front more accurate measurement of the equation of state, i.e. [Formula: see text], will shed light on the nature of dark energy. Specifically, [Formula: see text] will likely indicate the existence of a dynamical field, possibly quintessence, responsible for dark energy and [Formula: see text] would indicate an entirely new sector of physics. Further, more precise measurements of the ratio [Formula: see text] of tensor to scalar power spectrum, of the scalar and tensor spectral indices [Formula: see text] and [Formula: see text] and of non-Gaussianity will hopefully allow us to realize a Standard Model of inflation. These results will be a guide to further model building that incorporates unification of particle physics and cosmology.