Hierarchy Problem Research Articles

Dark matter and dark radiation from the early universe with a modulus coupled to the PQMSSM

The supersymmetrized DFSZ axion model is especially compelling in that it contains 1. the SUSY solution to the gauge hierarchy problem, 2. the Peccei-Quinn (PQ) solution to the strong CP problem and 3. the Kim-Nilles solution to the SUSY μ problem. In a string setting, where a discrete R-symmetry ( {textbf{Z}}_{24}^R for example) may emerge from the compactification process, a high-quality accidental axion (accion) can emerge from the accidental, approximate remnant global U(1)PQ symmetry where the decay constant fa is linked to the SUSY breaking scale, and is within the cosmological sweet zone. In this setup, one also expects the presence of stringy remnant moduli fields ϕi. Here, we consider the situation of a single light modulus ϕ coupled to the PQMSSM in the early universe, with mixed axion plus higgsino-like WIMP dark matter. We evaluate dark matter and dark radiation production via nine coupled Boltzmann equations and assess the severity of the cosmological moduli problem (CMP) along with dark matter and dark radiation production rates. We find that typically the light modulus mass should be mϕ ≳ 104 TeV to avoid the moduli-induced dark matter overproduction problem. If one is able to (anthropically) tune the modulus field amplitude, we find a value of ϕ0 ≲ 10–7mP would be required to solve the overall CMP.

Hierarchy problem in the Standard Model and extended Higgs potential with scale symmetry

Hierarchy problem in the Standard Model and extended Higgs potential with scale symmetry

Flexible extra dimensions

This paper discusses the origin of the small parameters with the aim of explaining the Hierarchy problem. The flexible extra dimensions are an essential tool in the process by which physical parameters are formed. The evolution of a multidimensional metric starts at the Planck scale and is completed with the static extra-dimensional metric and the 4-dim de Sitter space at high energies, where the exponential production of causally disconnected universes begins. Quantum fluctuations independently distort the metric within these universes, causing inflationary processes within them. Some of these universes tend asymptotically towards states characterised by small Hubble parameters. The effective parameter reduction applied to the Higgs sector of the Standard Model is explained by the presence of small-amplitude distributions of a scalar field in a fraction of these universes.

The coleman-weinberg potential and its application to the hierarchy problems

The Coleman-Weinberg Potential has and is still being applied in so many areas in modern physics which include analysis of Spontaneous Symmetry Breaking (SSB). In the SM, SSB is attained by introducing an ad-hoc kind of modification resulting in the mass term of the of the classical potential assuming a tachyon-like characteristics. By analyzing all the terms in the classical potential, it is vivid that only the mass term possesses a dimensional constant. Thus, we can trace the Hierarchy Problem to the ad-hoc modification via the squired mass term. This paper does not only focus on the study of the Coleman-Weinberg mechanism but also shows why application of the same is likely to unveil a clue that may lead scholars to resolving the Hierarchy Problem.

Simulating Software Evolution to Evaluate the Reliability of Early Decision-making among Design Alternatives toward Maintainability

Critical decisions among design altern seventh atives with regards to maintainability arise early in the software design cycle. Existing comparison models relayed on the structural evolution of the used design patterns are suitable to support such decisions. However, their effectiveness on predicting maintenance effort is usually verified on a limited number of case studies under heterogeneous metrics. In this article, a multi-variable simulation model for validating the decision-making reliability of the derived formal comparison models for the significant designing problem of recursive hierarchies of part-whole aggregations, proposed in our prior work, is introduced. In the absence of a strict validation, the simulation model has been thoroughly calibrated concerning its decision-making precision based on empirical distributions from time-series analysis, approximating the highly uncertain nature of actual maintenance process. The decision reliability of the formal models has been statistically validated on a sample of 1,000 instances of design attributes representing the entire design space of the problem. Despite the limited accuracy of measurements, the results show that the models demonstrate an increasing reliability in a long-term perspective, even under assumptions of high variability. Thus, the modeling theory discussed in our prior work delivers reliable models that significantly reduce decision-risk and relevant maintenance cost.

Risk Assessment Model of Chemical Process Based on Interval Type-2 Fuzzy Petri Nets

An interval type-2 fuzzy set and fuzzy Petri net combined risk assessment model for chemical production was proposed to solve the problems of disorganized hierarchy and poorly targeted measures, as well as the requirement for complex equipment associated with chemical production risk assessment. First, four different types of risk databases were established according to the production process of cyclohexane. Considering the intrinsic relationship between the risk factors in the fault database, the interval type-2 fuzzy set was used to improve the semantic transformation accuracy and calculate the confidence in the risk factors. The fuzzy Petri net model was used to simulate the dynamic development of accidents, and the parallel relationship between risk factors was intuitively described. Thereafter, the external relationship between risk factors was analyzed, and the net structure of each layer was divided to build a multilevel model. Finally, the catalyst activation process during cyclohexane production was taken as an example for risk assessment calculation, and the accident risk probability was calculated by multilevel fuzzy reasoning. The results demonstrate that the model is an improvement over traditional methods and can be used for precise prevention and control. Moreover, it can accurately analyze risk probability during chemical production, determine the risk associated with the reaction process, effectively prevent accidents, and provide a reference for risk evaluation and risk classification.

Higgs squared

We present a novel construction for a Higgs-VEV sensitive (HVS) operator, which can be used as a trigger operator in cosmic selection models for the electroweak hierarchy problem. Our operator does not contain any degrees of freedom charged under the SM gauge symmetries, leading to reduced tuning in the resulting models. Our construction is based on the extension of a two Higgs doublet model (2HDM) with a softly broken approximate global D8 symmetry (the symmetry group of a square). A cosmic crunching model based on our extended Higgs sector has only a percent level tuning corresponding to the usual little hierarchy problem. In large regions of parameter space the 2HDM is naturally pushed towards the alignment limit. A complete model requires the introduction of fermionic top partners to ensure the approximate D8 symmetry in the fermion sector. We also show that the same extended Higgs sector can be used for a novel implementation of the seesaw mechanism of neutrino masses.

A Concise Review on Some Higgs-Related New Physics Models in Light of Current Experiments

The Higgs boson may serve as a portal to new physics beyond the standard model (BSM), which is implied by the theoretical naturalness or experimental anomalies. This review aims to briefly survey some typical Higgs-related BSM models. First, for the theories to solve the hierarchy problem, the two exemplary theories, the low energy supersymmetry (focusing on the minimal supersymmetric model) and the little Higgs theory, are discussed. For the phenomenological models without addressing the hierarchy problem, we choose the two-Higgs-doublet models (2HDMs) to emphatically elucidate their phenomenological power in explaining current measurements of muon g−2, the W-boson mass and the dark matter (DM) data. For the singlet extensions, which are motivated by the cosmic phase transition and the DM issue, we illustrate the singlet-extended standard model (xSM) and the singlet-extended 2HDM (2HDM+S), emphasizing the vacuum stability. In the decade since the discovery of the Higgs boson, these theories have remained the typical candidates of new physics, which will be intensively studied in future theoretical and experimental research.

SU(6) gauge-Higgs grand unification: minimal viable models and flavor

Gauge-Higgs grand unification theories are models of gauge-Higgs unification that extend the electroweak group into a simple group that includes the color symmetry. The minimal option is a gauge-Higgs grand unification based on the SU(6) gauge group, mirroring SU(5) grand unification in 4D while providing a solution to the hierarchy problem. We explore different minimal and realistic novel incarnations of SU(6) gauge-Higgs grand unification. We submit the setup to the various flavor hierarchies observed in nature and, utilizing the power of the fifth dimension, identify an embedding that provides a compelling model of quarks and leptons that naturally explains the mass hierarchies and the CKM/PMNS structure. We perform a detailed study of quark- and lepton-flavor constraints (which are intimately related due to the GUT nature) together with an analysis of the Higgs potential which arises at the loop level. Electroweak precision constraints on the model are discussed and the rich scalar sector is analyzed. Future flavor constraints from upcoming experiments will provide a stringent test for this class of models, while a scalar singlet and leptoquark provide unique targets for current and future collider experiments to probe this solution to various open questions in nature.

Twin cogenesis

We investigate a cogenesis mechanism within the twin Higgs setup that can naturally explain the nature of dark matter, the cosmic coincidence puzzle, little hierarchy problem, leptogenesis, and the tiny neutrino masses. Three heavy Majorana neutrinos are introduced to the standard model sector and the twin sector respectively, which explain the tiny neutrino masses and generate the lepton asymmetry and the twin lepton asymmetry at the same time. The twin cogenesis mechanism applies to any viable twin Higgs model without an explicit breaking in the leptonic sector and evading the ΔN eff constraint. We illustrate the twin cogenesis mechanism using the neutrino-philic twin two Higgs doublet model, a newly proposed model to lift the twin neutrino masses with spontaneous breaking. The dark photon with a Stueckelberg mass MeV ensures the energy in the twin sector as well as the symmetric component of twin sector particles can be depleted. The lightest twin baryons are the dark matter candidates with masses of approximately 5.5 GeV, which explains naturally the amount of dark matter and visible matter in the Universe are of the same order. We also demonstrate twin cogenesis in the fraternal twin Higgs setup, in which the dark matter candidate is the twin bottom bound state .

QFT without infinities and hierarchy problem

The standard way to do computations in Quantum Field Theory (QFT) often results in the requirement of dramatic cancellations between contributions induced by a “heavy” sector into the physical observables of the “light” (or low energy) sector – the phenomenon known as “technical hierarchy problem”. This procedure uses divergent multi-loop Feynman diagrams, their regularisation to handle the UV divergences, and then renormalisation to remove them. At the same time, the ultimate outcome of the renormalisation is the mapping of several finite parameters defining the renormalisable field theory into different observables (e.g. all kinds of particle cross-sections). In this paper, we first demonstrate how to relate the parameters of the theory to observables without running into intermediate UV divergences. Then we go one step further: we show how in theories with different mass scales, all physics of the “light” sector can be computed in a way that does not require dramatic cancellations induced by the physics of the “heavy” sector. The existence of such a technique suggests that the “hierarchy problem” in renormalisable theories is not really physical, but rather an artefact of the conventional procedure to compute correlation functions. If the QFT is defined by the “divergencies-free” method all fine-tunings in theories with well-separated energy scales may be avoided.

A Portalino to the Twin Sector

Extensions of the Standard Model are often highly constrained by cosmology. New states in the theory can dramatically alter observed properties of the universe by the presence of additional matter or entropy. In particular, attempts to solve the hierarchy problem through naturalness invariably predict new particles near the weak scale which come into thermal equilibrium. Without a means to deposit this energy into the SM, these models are often excluded. Scenarios of “neutral naturalness” in particular, such as the Twin Higgs, frequently suffer from this. However, the Portalino, a singlet fermion that marries gauge neutral fermion operators, can naturally help provide a portal for entropy to return to the SM and to lift fermionic degrees of freedom in the Twin Sector. Together with spontaneous breaking of the Z2 SM ↔ Twin symmetry, there are new opportunities to confront the cosmological challenges of these models. Here, we attempt to develop such ideas. We shall show how one can lift many of the light fields by breaking Z2 with a U(1)Y scalar and its Twin partner. The introduction of Portalinos can lift the remaining degrees of freedom. We shall find that such models are highly constrained by precision SM measurements, motivating moderate extensions beyond this. We will discuss two, both of which include Z2 breaking, one with additional electroweak matter and another with additional colored matter. The electroweak model will involve simple dim-6 operators, which are easily UV completed. The strong model will involve the presence of new leptoquarks and diquarks. We will discuss the implications for the observed value of the muon anomalous magnetic moment, contributions to μ → eγ decay and possible colored signals even within these models of neutral naturalness, some of which might appear at the LHC or future colliders.

The dark universe: Primordial black hole ⇋ dark graviton gas connection

We study the possible correspondence between 5-dimensional primordial black holes and massive 5-dimensional KK gravitons as dark matter candidate within the recently proposed dark dimension scenario that addresses the cosmological hierarchy problem. First, we show that in the local universe a population of 5-dimensional black holes with MBH∼7×1013g would be practically indistinguishable from a KK tower of dark gravitons with mDM∼50keV. Second, we connect the mass increase of 5-dimensional black holes and the related temperature decrease with the cooling of the tower of massive spin-2 KK excitations of the graviton. The dark gravitons are produced at a mass ∼1−50GeV and the bulk of their mass shifts down to roughly 1−100keV today. The cooling of the system proceeds via decay to lighter gravitons without losing much total mass density, resembling the intra-tower decays that characterize the cosmological evolution of the dynamical dark matter framework. We associate the intra-tower decays of the graviton gas with the black hole growth through accretion. We also discuss that the primordial black hole ⇋ dark graviton gas connection can be nicely explained by the bound state picture of black holes in terms of gravitons.

Vacuum stability in the Standard Model with vectorlike fermions

The discovery of Standard-Model like Higgs at 125 GeV may raise more questions than the answers it provides. In particular, the hierarchy problem remains unsolved, and the Standard Model Higgs quartic self-coupling becomes negative below the Planck scale, necessitating new physics beyond the Standard Model. In this work we investigate a popular scenario, extensions of the Standard Model with vector-like fermion fields, such as the ones present in models with extra dimensions or in Higgs composite models, using a model independent approach. Since fermions decrease the Higgs quartic coupling at high energies, only exacerbating the self-coupling problem, we introduce first an additional scalar, which by itself is enough to overcome the vacuum stability limit, and then explore the effects of vector-like fermions in singlet, doublet and triplet representations. For each model, we identify the allowed fermion masses and mixing angles with the third family fermions required to satisfy the vacuum stability condition, and compare different representations. Allowed fermion masses emerge at around 1 TeV, raising hope that these will be found at the LHC. We also examine corrections to oblique parameters S and T from additional scalar and vector-like quarks which also impose constraints on mixing and mass splitting of both sectors., but these restrictions are relatively weak compared to the vacuum stability.

Неперевод и перевод у Хайдеггера, Лосева и Ортеги-и-Гассета

The article examines the ideas of Heidegger, Losev, and Ortega y Gasset regarding the possibility and necessity of translating philosophical texts. The concept of non-translation is an acknowledgment of the impossibility of adequately reproducing a philosophical text in another language while preserving its integrity. Particularly interesting for comparison are the concepts and practices of translation/non-translation found in works written during the same period (1920—1940s), which reveal numerous points of contact. All three philosophers reject conventional translation, proposing instead to consider ordinary words as philosophical terms. Despite the fact that such an approach may make the text appear contradictory to familiar norms, the philosophers insist on the necessity of violating convention. The opposition of translation vs non-translation is related to the multilingual nature of the text, as well as to the problem of language hierarchy and the attitude towards translating others' and one's own texts. Losev and Heidegger employ the technique of retrospective translation, which involves etymologizing or contextualizing texts that are older than the translated text. Etymologization (alongside commentary) is seen as a way to transfer ideas into a different cultural system, and Ortega y Gasset refers to humans as “etymological animals”. In Losev's interpretive translation, foreign translations or translations into other languages are viewed as interpretations and become objects of study. While Heidegger repeatedly criticizes the understanding of language as communication, and Ortega y Gasset takes a fundamentally anti-communicative position, Losev, on the contrary, emphasizes communication. Losev and Heidegger operate with the concept of clarity: the former consistently strives for maximum clarity by using apophatic techniques to eliminate irrelevant interpretations of meanings, but clarity is more of a propaedeutic task; the latter does not aim for clarity but utilizes the technique of infinite clarification. Both approaches raise the question of whether the criterion of scientificity is applicable to the translation of philosophical texts.

STUDENT’S MISTAKES IN SOLVING PROBLEM BASED ON WATSON’S CRITERIA AND LEARNING STYLE

This study aims to determine the types of errors students face when solving math problems. First, review the error types based on Watson's criteria and student learning styles. This study uses an explanatory sequential design model. Data analysis techniques include Quantitative data analysis techniques, descriptive statistics, and inferential statistics. At the same time, the qualitative data analysis techniques include; data reduction, data presentation, and conclusion. The results showed that the errors based on Watson's criteria and learning styles obtained were based on student responses, including; Inappropriate Data 40%, Omitted Conclusion 20%, Response Level Conflict 40%, and Above Other 40%. Furthermore, the types of errors obtained in classroom learning include Inappropriate Data 25%, Omitted Conclusion 50%, and Skill Hierarchy Problems 25%. In the visual learning pattern, there are five error classes: Inappropriate Data 9%, Omitted Conclusion 55%, Response Level Conflict 18%, Skill Hierarchy Problem 27%, and Above Other 18%. Several factors influence the error, including; the decline in students' motivation, interest, and thinking skills. Efforts can be made to minimize student errors, including increasing practice on story questions and eliminating students' negative mindset towards learning mathematics

Dark dimension, the swampland, and the origin of cosmic rays beyond the Greisen-Zatsepin-Kuzmin barrier

Very recently, it was pointed out that when basic ideas of the Swampland program are combined with the cosmological hierarchy problem (i.e. the smallness of the dark energy in Planck units) and together are confronted to experiment lead to the prediction of the existence of a single extra-dimension (dubbed the dark dimension) with characteristic length-scale in the micron range. We propose a feasible test procedure to probe the dark dimension using the highest energy cosmic rays.

A natural model of spontaneous CP violation

We examine the possibility of building a natural non-supersymmetric model of spontaneous CP violation equipped with the Nelson-Barr (NB) mechanism to address the strong CP problem. Our approach is to utilize a doubly composite dynamics where the first confinement of the CFT occurs at the scale of spontaneous CP violation (SCPV) and the second confinement at the TeV scale. A holographic dual description of this 4D set-up via a warped extra dimension with three 3-branes provides an explicit realization of this idea. In this model, radiative corrections to the strong CP phase are well under control, and the coincidence of mass scales, which we generally encounter in NB models, is addressed. Our model also provides an explanation to the quark Yukawa hierarchies, and a solution to the gauge hierarchy problem just as in the usual Randall-Sundrum model with the Higgs being localized on the TeV brane.

Moduli stabilization with bulk scalar in nested doubly warped braneworld model

We examine the modulus stabilization mechanism of a warped geometry model with nested warping. Such a model with multiple moduli is known to offer a possible resolution of the fermion mass hierarchy problem in the Standard Model. A six dimensional doubly warped braneworld model under consideration admits two distinct moduli, with the associated warp factors dynamically generating different physical mass scales on four 3-branes. In order to address the hierarchy problem related to the Higgs mass, both moduli need to be stabilized around their desired values without any extreme fine tuning of parameters. We show that it is possible to stabilize them simultaneously due to the appearence of an effective 4D moduli potential, which is generated by a single massive bulk scalar field having non-zero VEVs frozen on the 3-branes. This gives rise to two scalar radions, one of which has mass slightly below {mathcal {O}}(TeV) and couplings to SM fields proportional to the inverse of its {mathcal {O}}(TeV) VEV, and the other has nearly {mathcal {O}}(M_{Pl}) mass and interactions with SM fields suppressed by the Planck scale. We also discuss how the entire mechanism can possibly be understood from a purely gravitational point of view, with higher curvature f(R) contributions in the bulk automatically providing a scalar degree of freedom that can serve as the stabilizing field in the Einstein frame.

Precision early universe cosmology from stochastic gravitational waves

The causal tail of stochastic gravitational waves can be used to probe the energy density in free streaming relativistic species as well as measure g*(T) and beta functions β(T) as a function of temperature. In the event of the discovery of loud stochastic gravitational waves, we demonstrate that LISA can measure the free streaming fraction of the universe down to the the 10−3 level, 100 times more sensitive than current constraints. Additionally, it would be sensitive to mathcal{O} (1) deviations of g* and the QCD β function from their Standard Model value at temperatures ~ 105 GeV. In this case, many motivated models such as split SUSY and other solutions to the Electroweak Hierarchy problem would be tested. Future detectors, such as DECIGO, would be 100 times more sensitive than LISA to these effects and be capable of testing other motivated scenarios such as WIMPs and axions. The amazing prospect of using precision gravitational wave measurements to test such well motivated theories provides a benchmark to aim for when developing a precise understanding of the gravitational wave spectrum both experimentally and theoretically.