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Bulk Matters on a GRS-Inspired Braneworld
High Energy Physics - Theory · Submitted 10 Feb 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For spin 1/2 fermions coupled with the background scalar $\phi$ via $\eta\bar{\Psi}\phi^p\Psi$ with $p$ a positive odd integer, the zero mode of left-hand fermions can be localized on the thick brane for finite distance of the two thin branes, and there exist some massive bound modes and resonance modes.
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The abstract, sentence by sentence
In this paper we investigate the localization and mass spectra of bulk matter fields on a Gergory-Rubakov-Sibiryakov-inspired braneworld. In this braneworld model, there are one thick brane located at the origin of the extra dimension and two thin branes at two sides. For spin 1/2 fermions coupled with the background scalar $\phi$ via $\eta\bar{\Psi}\phi^p\Psi$ with $p$ a positive odd integer, the zero mode of left-hand fermions can be localized on the thick brane for finite distance of the two thin branes, and there exist some massive bound modes and resonance modes. The resonances correspond to the quasi-localized massive fermions. For free massless spin 0 scalars, the zero mode can not be localized on the thick brane when the two thin branes are located finitely. While for a massive scalar $\Phi$ coupled with itself and the background scalar field $\phi$, in order to get a localized zero mode on the thick brane, a fine-tuning relation should be introduced. Some massive bound modes and resonances also will appear. For spin 1 vectors, there is no bound KK mode because the effective potential felt by vectors vanishes outside the two thin branes. We also investigate the physics when the distance of the two thin branes tends to infinity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper we investigate the localization and mass spectra of bulk matter fields on a Gergory-Rubakov-Sibiryakov-inspired braneworld. | contribution 1.00 | 0.88 | 0.06 | asserted 0.75 |
| s1 | In this braneworld model, there are one thick brane located at the origin of the extra dimension and two thin branes at two sides. | method 0.59 | 0.29 | 0.03 | asserted 1.00 |
| s2 | For spin 1/2 fermions coupled with the background scalar $\phi$ via $\eta\bar{\Psi}\phi^p\Psi$ with $p$ a positive odd integer, the zero mode of left-hand fermions can be localized on the thick brane for finite distance of the two thin branes, and there exist some massive bound modes and resonance modes. | result 1.00 | 0.91 | 0.25 | asserted 1.00 |
| s3 | The resonances correspond to the quasi-localized massive fermions. | interpretation 0.94 | 0.71 | 0.06 | asserted 1.00 |
| s4 | For free massless spin 0 scalars, the zero mode can not be localized on the thick brane when the two thin branes are located finitely. | result 1.00 | 0.89 | 0.07 | asserted 1.00 |
| s5 | While for a massive scalar $\Phi$ coupled with itself and the background scalar field $\phi$, in order to get a localized zero mode on the thick brane, a fine-tuning relation should be introduced. | result 0.98 | 0.86 | 0.07 | asserted 0.96 |
| s6 | Some massive bound modes and resonances also will appear. | result 1.00 | 0.88 | 0.05 | asserted 0.83 |
| s7 | For spin 1 vectors, there is no bound KK mode because the effective potential felt by vectors vanishes outside the two thin branes. | result 1.00 | 0.89 | 0.07 | asserted 1.00 |
| s8 | We also investigate the physics when the distance of the two thin branes tends to infinity. | contribution 0.96 | 0.88 | 0.04 | asserted 0.74 |
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The paper
Original abstract
In this paper we investigate the localization and mass spectra of bulk matter fields on a Gergory-Rubakov-Sibiryakov-inspired braneworld. In this braneworld model, there are one thick brane located at the origin of the extra dimension and two thin branes at two sides. For spin 1/2 fermions coupled with the background scalar $\phi$ via $\eta\bar{\Psi}\phi^p\Psi$ with $p$ a positive odd integer, the zero mode of left-hand fermions can be localized on the thick brane for finite distance of the two thin branes, and there exist some massive bound modes and resonance modes. The resonances correspond to the quasi-localized massive fermions. For free massless spin 0 scalars, the zero mode can not be localized on the thick brane when the two thin branes are located finitely. While for a massive scalar $\Phi$ coupled with itself and the background scalar field $\phi$, in order to get a localized zero mode on the thick brane, a fine-tuning relation should be introduced. Some massive bound modes and resonances also will appear. For spin 1 vectors, there is no bound KK mode because the effective potential felt by vectors vanishes outside the two thin branes. We also investigate the physics when the distance of the two thin branes tends to infinity.
Human review
References
How the literature uses it
9 arXiv papers cite this in 12 sentences
Papers citing it · 7 sentences without a confident label
Cites it as background 5 papers
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For these thick branes generated by a kink scalar, in order to localize the 5D Dirac field, we usually introduce the coupling term $ηϕ^2n-1ψψ$ ($n$ is a positive integer), and when the coupling constant $η>η_0$ ($η_0$ is some constant parameter decided by the branes), then the left or right chiral Dirac fermion zero mode can be localized on these branes [ref] .
Localization of 5D Elko Spinors on Minkowski Branes · Conclusion and discussion · 0.85
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For recent developments see [ref] .
Domain wall brane in squared curvature gravity · Introduction · 0.97
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Symmetric and asymmetric single or multiple branes were investigated in [ref] .
Scalar-Kinetic Branes · Introduction · 0.96
What it cites · 44 sentences without a confident label
Uses the method or tool of 3 papers
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By decomposing $Φ(x,z)=∑_nϕ_n(x)χ_n(z)e^-3A/2$, we find the fifth part of the scalar field $χ_n(z)$ satisfies the following Schrödinger-like equation [equation] where we have assumed that the 4-dimensional massive Klein–Gordon equation [equation] is satisfied with $ĝ^μν=η^μν$ the 4-dimensional metric on the brane, and the effective potential is [equation] If we take the scalar potential as the form [ref] [equation] where $λ$ and $u$ are the coupling constants, then $U(ϕ)$ can be read as [equation] Furthermore, we need the following orthonormality condition to obtain the 4-dimensional effective action: [equation]
Fermions, scalars and Randall-Sundrum gravity on domain-wall branes · Spin 0 scalar fields · 0.81
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By decomposing $Φ(x,z)=∑_nϕ_n(x)χ_n(z)e^-3A/2$, we find the fifth part of the scalar field $χ_n(z)$ satisfies the following Schrödinger-like equation [equation] where we have assumed that the 4-dimensional massive Klein–Gordon equation [equation] is satisfied with $ĝ^μν=η^μν$ the 4-dimensional metric on the brane, and the effective potential is [equation] If we take the scalar potential as the form [ref] [equation] where $λ$ and $u$ are the coupling constants, then $U(ϕ)$ can be read as [equation] Furthermore, we need the following orthonormality condition to obtain the 4-dimensional effective action: [equation]
Localization of Matters on Anti-de Sitter Thick Branes · Spin 0 scalar fields · 0.81
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Then we use the following expression to define the relative probability of the KK mode within a narrow range $-z_b ≤z ≤z_b$ around the thick brane location [ref] [equation] where we choose $z_max=10 z_b$.
Fermion Localization and Resonances on A de Sitter Thick Brane · The resonance modes · 0.95
Compares with 7 papers
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However, for an infinite $z_0$, the integral $∫^z dze^Aϕ$ tends to: [equation] then the integrand $f_L0^2$ becomes [equation] so only when $η>k/2√(3)π$, the zero mode for the left chiral fermion can be localized on the brane, which is corresponding to that in Ref [ref] .
Localization and Mass Spectra of Fermions on Symmetric and Asymmetric Thick Branes · The zero mode · 0.83
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So there exist both bound KK modes and resonances, which are different with that for the potentials closer to the standard Pöschl-Teller potentials without the finite barriers in Refs. [ref] .
Effects of the variation of mass on fermion localization and resonances on thick branes · Discussions and conclusions · 1.00
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So there exist both bound KK modes and resonances, which are different with that for the potentials closer to the standard Pöschl-Teller potentials without the finite barriers in Refs. [ref] .
Localization and Mass Spectrum of Matters on Weyl Thick Branes · Discussions and conclusions · 1.00
Cites as background 22 papers
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On the base of the RS model, another model called the Gergory-Rubakov-Sibiryakov (GRS) model was proposed [ref] , in order to give some modifications of gravity at ultralarge scales.
Opening up extra dimensions at ultra-large scales · Introduction · 0.92
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If the central thin brane is replaced by a thick brane realized by a suitable configuration of a bulk scalar field [ref] , which is called the GRS-inspired brane [ref] , the action of this model is [equation] where $M$ is the basic Planck energy scale in the 5-dimensional space-time, $G_M N$ denotes the 5-dimensional metric and $g_μν$ the 4-dimensional one.
Synergistic Gravity and the Role of Resonances in GRS-Inspired Braneworlds · Review of the GRS-inspired model · 0.83
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If the central thin brane is replaced by a thick brane realized by a suitable configuration of a bulk scalar field [ref] , which is called the GRS-inspired brane [ref] , the action of this model is [equation] where $M$ is the basic Planck energy scale in the 5-dimensional space-time, $G_M N$ denotes the 5-dimensional metric and $g_μν$ the 4-dimensional one.
Localized Gravitons, Gauge Bosons and Chiral Fermions in Smooth Spaces Generated by a Bounce · Review of the GRS-inspired model · 0.83
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