5th Dimension Research Articles

The 5th Dimension

The 5th Dimension

Fermionic minimal dark matter in 5D gauge-Higgs unification

We propose a Minimal Dark Matter (MDM) scenario in the context of a simple gauge-Higgs Unification (GHU) model based on the gauge group SU(3) x U(1)' in 5-dimensional Minkowski space with a compactification of the 5th dimension on S^1/Z_2 orbifold. A pair of vector-like SU(3) multiplet fermions in a higher-dimensional representation is introduced in the bulk, and the DM particle is identified with the lightest mass eigenstate among the components in the multiplets. In the original model description, the DM particle communicates with the Standard Model (SM) particles only through the bulk gauge interaction, and hence our model is the GHU version of the MDM scenario. There are two typical realizations of the DM particle in 4-dimensional effective theory: (i) the DM particle is mostly composed of the SM SU(2)_L multiplets, or (ii) the DM is mostly composed of the SM SU(2)_L singlets. Since the case (i) is very similar to the original MDM scenario, we focus on the case (ii), which is a realization of the Higgs-portal DM scenario in the context of the GHU model. We identify an allowed parameter region to be consistent with the current experimental constraints, which will be fully covered by the direct dark matter detection experiments in the near future. In the presence of the bulk multiplet fermions in higher-dimensional $SU(3)$ representations, we reproduce the 125 GeV Higgs boson mass through the renormalization group evolution of Higgs quartic coupling with the compactification scale of 10-100 TeV.

Geometrical interpretation of electromagnetism in a 5-dimensional manifold

In this paper, Kaluza–Klein theory is revisited and its implications are elaborated. We show that electromagnetic 4-potential can be considered as a shearing-like deformation of a 5-dimensional (5D) manifold along the fifth (5th) axis. The charge-to-mass ratio has a physical meaning of the ratio between the movement along the direction of the 5th axis and the movement in the 4D space-time. In order to have a 5D matter which is consistent with the construction of the 5D manifold, a notion of particle-thread is suggested. Examinations on the compatibility of reference frames reveal a covariance breaking of the 5th dimension. The field equations which extend Einstein’s field equations give the total energy-momentum tensor as a sum of that of matter, electromagnetic field, and the interaction between electric current and electromagnetic potential. Finally, the experimental implications are calculated for the weak potential case.

Fermion dark matter in gauge-Higgs unification

We propose a Majorana fermion dark matter in the context of a simple gauge-Higgs Unification (GHU) scenario based on the gauge group SU(3)×U(1)′ in 5-dimensional Minkowski space with a compactification of the 5th dimension on S1/Z2 orbifold. The dark matter particle is identified with the lightest mode in SU(3) triplet fermions additionally introduced in the 5-dimensional bulk. We find an allowed parameter region for the dark matter mass around a half of the Standard Model Higgs boson mass, which is consistent with the observed dark matter density and the constraint from the LUX 2016 result for the direct dark matter search. The entire allowed region will be covered by, for example, the LUX-ZEPLIN dark matter experiment in the near future. We also show that in the presence of the bulk SU(3) triplet fermions the 125 GeV Higgs boson mass is reproduced through the renormalization group evolution of Higgs quartic coupling with the compactification scale of around 108 GeV.

Proton decay prediction from a gauge-Higgs unification scenario in five dimensions

The Higgs boson mass and top quark mass imply that the Higgs quartic coupling vanishes around the scale of $10^9 - 10^{13}$ GeV, depending on the precise value of the top quark mass. The vanishing quartic coupling can be naturally addressed if the Higgs field originates from a 5-dimensional gauge field and the 5th dimension is compactified at the scale of the vanishing Higgs quartic coupling, which is a scenario based on gauge-Higgs unification. We present a general prediction of the scenario on the proton decay process $p \to \pi^0 e^+$. In many gauge-Higgs unification models, the 1st generation fermions are localized towards an orbifold fixed point in order to realize the realistic Yukawa couplings. Hence, four-fermion operators responsible for the proton decay can appear with a suppression of the 5-dimensional Planck scale (not the 4-dimensional Planck scale). Since the 5-dimensional Planck scale is connected to the compactification scale, we have a correlation between the proton partial decay width and the top quark mass. We show that the future Hyper-Kamiokande experiment may discover the proton decay if the top quark pole mass is larger than about 172.5 GeV.

TECHNICAL ASPECTS FOR THE CREATION OF A MULTI-DIMENSIONAL LAND INFORMATION SYSTEM

Abstract. The complexity of modern urban environments and civil demands for fast, reliable and affordable decision-making requires not only a 3D Land Information System, which tends to replace traditional 2D LIS architectures, but also the need to address the time and scale parameters, that is, the 3D geometry of buildings in various time instances (4th dimension) at various levels of detail (LoDs - 5th dimension). This paper describes and proposes solutions for technical aspects that need to be addressed for the 5D modelling pipeline. Such solutions include the creation of a 3D model, the application of a selective modelling procedure between various time instances and at various LoDs, enriched with cadastral and other spatial data, and a procedural modelling approach for the representation of the inner parts of the buildings. The methodology is based on automatic change detection algorithms for spatial-temporal analysis of the changes that took place in subsequent time periods, using dense image matching and structure from motion algorithms. The selective modelling approach allows a detailed modelling only for the areas where spatial changes are detected. The procedural modelling techniques use programming languages for the textual semantic description of a building; they require the modeller to describe its part-to-whole relationships. Finally, a 5D viewer is developed, in order to tackle existing limitations that accompany the use of global systems, such as the Google Earth or the Google Maps, as visualization software. An application based on the proposed methodology in an urban area is presented and it provides satisfactory results.

Simple brane-world inflationary models — An update

In the light of the Planck 2015 results, we update simple inflationary models based on the quadratic, quartic, Higgs and Coleman–Weinberg potentials in the context of the Randall–Sundrum brane-world cosmology. Brane-world cosmological effect alters the inflationary predictions of the spectral index [Formula: see text] and the tensor-to-scalar ratio [Formula: see text] from those obtained in the standard cosmology. In particular, the tensor-to-scalar ratio is enhanced in the presence of the 5th dimension. In order to maintain the consistency with the Planck 2015 results for the inflationary predictions in the standard cosmology, we find a lower bound on the five-dimensional Planck mass [Formula: see text]. On the other hand, the inflationary predictions laying outside of the Planck allowed region can be pushed into the allowed region by the brane-world cosmological effect with a suitable choice of [Formula: see text].

Negative Λ induced by accelerated motion

A correlation between accelerated motion and a noncompact 5th dimension is proposed. The curvature invariants and the stress energy tensor in the bulk depend only on the 5th dimension w and vanish asymptotically while the proper acceleration of a static observer is proportional to 1/w. The brane (located at w = w0) metric is conformally flat (of AdS type) with Λ = −3/w02 and the invariant acceleration \(a = \sqrt {a^b a_b } = 1/w_0\). Therefore, we assume that a hyperbolic observer with the rest-system acceleration a is embedded in the 5th dimension at w0 = 1/a.

Telesonography - the 5th dimension of ultrasound examination.

Telesonography - the 5th dimension of ultrasound examination.

BIM & the 5D Project Cost Manager

This paper examines the global issues related to the role of project cost management professionals in the implementation and evolution of Building Information Modeling (BIM) in the construction industry. The paper is based on a review of current industry trends and issues with BIM implementation and detailed interviews with quantity surveying firms in Australia. BIM involves more than just 3D modelling and is also commonly defined in further dimensions such as 4D (time), 5D (cost) and even 6D (as-built operation). 4D links information and data in the 3D object model with project programming and scheduling data and facilitates the simulation analysis of construction activities. 5D integrates all of this information with cost data such as quantities, schedules and prices. 6D represents the as-built model that can then be used during the operational stages of the facility. This paper explores the importance for project cost management professionals to be integrally involved across all project phases and to embrace the 5th dimension to become key players in the BIM environment – the ‘5D Project Cost Manager’. The literature review and industry interviews will examine the issues associated with this and will identify leading edge best practices in the field by professional project cost management firms. The paper concludes with the findings that the greatest value with the modern day project cost manager lies in their ability to be 5D literate and to be able to utilise electronic models to provide detailed 5D estimates and living cost plans in real time.

The GEM Unification Theory of the Vacuum: Did Dimensional Collapse Trigger the Big Bang

The GEM (Gravity EM) unification theory builds on the Sakharov and Kaluza-Klein approaches to unify all four force fields of nature: Gravity, EM, Strong, and Weak using Feynman Path integral formalism. The model is rudimentary, and can be called a “Bohr Model” of unification. It is basically found that Gravity and the other forces can be understood as quantum electrodynamics. In particular the proton emerges as a fundamental particle despite being composed of quarks and is the principle interaction vertex of the Higgs boson, which is seen here as direct consequence of a hidden 5th dimension, where the Higgs mass is due to 5th dimensional compactification. Collapse and compactification of a 5th dimension is argued as the triggering event for the Big Bang. A particle mass formula based on Feynman Path Integrals including paths across the hidden 5th dimension gives the proton and electron masses to high accuracy and finds the charged bosons responsible for the short range nuclear forces. The masses calculated for the particles are as follows: the charged pion m = 2 me / 140.0 MeV and W boson: mw =2 mp = 80.4 GeV. The c meson m =2985 GeV is identified with the 5th dimension compactification force mediated by the Radion field. The Higgs boson associated with this mass inducing field is the most general EM+Radion scattering quanta off the hidden dimension size with a mass mp/α  127.7 GeV. This results in a structural resonance Higgs = rp where Higgs is the Compton radius of the Higgs boson and Higgs =c/mHiggsc2 the rp electro-dynamic length of the proton rp=e2/mpc2. Vacuum decay results from this value of the Higgs boson mass, which is a key parameter in a mass system that creates the proton-electron mass system and thus hydrogen in the Big Bang. The vacuum is found to decay into proton-electron pairs and to give an “eternally inflating” cosmos of Hubble Time TH  ( 9/ )1/3 /2 e2 /(4oGmemp ) re/c = 1.2 x1010 years. The predicted value of the CBR(Cosmic Background Radiation) temperature from this vacuum decay is TCBR  (4cGme2/(3Th2Stefan-Boltz.)1/3 = 2.65K Support for this consists of observation of the failure of the Sunaeyev-Zeldovich effect, where distant galaxies are not observed to cast shadows in the CBR indicating a source for the CBR in the vacuum itself in the line of sight to more distant galaxies.

Equivalence between Born–Infeld tachyon and effective real scalar field theories for brane structures in warped geometry

An equivalence between Born–Infeld and effective real scalar field theories for brane structures is built in some specific warped space–time scenarios. Once the equations of motion for tachyon fields related to the Born–Infeld action are written as first-order equations, a simple analytical connection with a particular class of real scalar field superpotentials can be found. This equivalence leads to the conclusion that, for a certain class of superpotentials, both systems can support identical thick brane solutions as well as brane structures described through localized energy densities, T00(y), in the 5th dimension, y. Our results indicate that thick brane solutions realized by the Born–Infeld cosmology can be connected to real scalar field brane scenarios which can be used to effectively map the tachyon condensation mechanism.

Recording Human Electrocorticographic (ECoG) Signals for Neuroscientific Research and Real-time Functional Cortical Mapping

Recording Human Electrocorticographic (ECoG) Signals for Neuroscientific Research and Real-time Functional Cortical Mapping

Recording Human Electrocorticographic (ECoG) Signals for Neuroscientific Research and Real-time Functional Cortical Mapping

Recording Human Electrocorticographic (ECoG) Signals for Neuroscientific Research and Real-time Functional Cortical Mapping

Continuum limit physics from2+1flavor domain wall QCD

We present physical results obtained from simulations using 2+1 flavors of domain wall quarks and the Iwasaki gauge action at two values of the lattice spacing a, [a−1=1.73(3) GeV and a−1=2.28(3) GeV]. On the coarser lattice, with 243×64×16 points (where the 16 corresponds to Ls, the extent of the 5th dimension inherent in the domain wall fermion formulation of QCD), the analysis of C. Allton et al. (RBC-UKQCD Collaboration), Phys. Rev. D 78 is extended to approximately twice the number of configurations. The ensembles on the finer 323×64×16 lattice are new. We explain in detail how we use lattice data obtained at several values of the lattice spacing and for a range of quark masses in combined continuum-chiral fits in order to obtain results in the continuum limit and at physical quark masses. We implement this procedure for our data at two lattice spacings and with unitary pion masses in the approximate range 290–420 MeV (225–420 MeV for partially quenched pions). We use the masses of the π and K mesons and the Ω baryon to determine the physical quark masses and the values of the lattice spacing. While our data in the mass ranges above are consistent with the predictions of next-to-leading order SU(2) chiral perturbation theory, they are also consistent with a simple analytic ansatz leading to an inherent uncertainty in how best to perform the chiral extrapolation that we are reluctant to reduce with model-dependent assumptions about higher order corrections. In some cases, particularly for fπ, the pion leptonic decay constant, the uncertainty in the chiral extrapolation dominates the systematic error. Our main results include fπ=124(2)stat(5)syst MeV, fK/fπ=1.204(7)(25) where fK is the kaon decay constant, msMS¯(2 GeV)=(96.2±2.7) MeV and mudMS¯(2 GeV)=(3.59±0.21) MeV (ms/mud=26.8±1.4) where ms and mud are the mass of the strange quark and the average of the up and down quark masses, respectively, [ΣMS¯(2 GeV)]1/3=256(6) MeV, where Σ is the chiral condensate, the Sommer scale r0=0.487(9) fm and r1=0.333(9) fm.52 MoreReceived 10 November 2010DOI:https://doi.org/10.1103/PhysRevD.83.074508© 2011 American Physical Society

Deep inelastic and dipole scattering on finite length hot [formula omitted] SYM matter

Deep inelastic scattering of R -currents and the scattering of a small dipole on finite length hot N = 4 SYM matter are discussed. In each case we find the scale when scattering becomes strong is determined by a saturation momentum Q s 2 ∼ L T 3 / x where L is the length of the matter. For R -currents we analyze the operator product expansion. For infinite length matter the series generated by the OPE is not Borel summable but we are able to determine the exponential part of the tunneling amplitude determining F 2 when Q 2 Q s 2 ≫ 1 from the position of the singularity closest to the origin on the real axis of the Borel plane. In finite length matter the OPE series is not convergent but it is Borel summable. When a small dipole, and the string connecting the ends of the dipole, pass through hot matter there is an induced motion of the string in the 5th dimension. When T 4 L cosh η , with the η the rapidity of the string, is large enough the string would normally break into several parts after leaving the medium, however, this cannot happen in the classical approximation in which we work.

S Parameter in the Holographic Walking/Conformal Technicolor

We explicitly calculate the S parameter in entire parameter space of the holographic walking/conformal technicolor (W/C TC), based on the deformation of the holographic QCD by varying the anomalous dimension from γm ≃ 0 through γm ≃ 1 continuously. The S parameter is given as a positive monotonic function of ξ which is fairly insensitive to γm and continuously vanishes as S ∼ ξ2 → 0 when ξ → 0, where ξ is the vacuum expectation value of the bulk scalar field at the infrared boundary of the 5th dimension z = zm and is related to the mass of (techni-) ρ meson (Mρ) and the decay constant (ƒπ) as ξ ∼ ƒπ zm ∼ ƒπ / Mρ for ξ ≪ 1. However, although ξ is related to the techni-fermion condensate 〈TT〉, we find no particular suppression of ξ and hence of S due to large γm, based on the correct identification of the renormalization-point dependence of 〈TT〉 in contrast to the literature. Then we argue possible behaviors of ƒπ/Mρ as 〈TT〉 → 0 near the conformal window characterized by the Banks-Zaks infrared fixed point in more explicit dynamics with γm ≃ 1. It is a curious coincidence that the result from ladder Schwinger-Dyson and Bethe-Salpeter equations well fits in the parameter space obtained in this paper. When ƒπ/Mρ → 0 is realized, the holography suggests a novel possibility that ƒπ vanishes much faster than the dynamical mass m does.

Archimedes in the 5th Dimension

Archimedes in the 5th Dimension

Casimir force in Randall-Sundrum models

We discuss and compare the effects of one extra dimension in the Randall-Sundrum models on the evaluation of the Casimir force between two parallel plates. We impose the condition that the result reproduce the experimental measurements within the known uncertainties in the force and the plate separation, and get an upper bound $kR\ensuremath{\lesssim}20$ if the curvature parameter $k$ of ${\mathrm{AdS}}_{5}$ is equal to the Planck scale. Although the upper bound decreases as $k$ decreases, $kR\ensuremath{\sim}12$, which is the required value for solving the hierarchy problem, is consistent with the Casimir force measurements. For the case where the 5th dimension is infinite, the correction to the Casimir force is very small and negligible.

Control of quantum fluctuations for a Yukawa interaction in the Kaluza–Klein picture

We study a system of fermions interacting with a scalar field, in 4+1 dimensions where the 5th dimension is compactified, using an exact functional method, where quantum fluctuations are controlled by the amplitude of the bare fermion mass. The integration of our equations leads to the properties of the dressed Yukawa coupling, that we study at one-loop so as to show the consistency of the approach. Beyond one loop, the non-perturbative aspect of the method gives us the possibility to derive the dynamical fermion mass. The result obtained is cutoff independent and this derivation proposes an alternative to the Schwinger–Dyson approach.