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Analytical Green's Functions for Continuum Spectra
High Energy Physics - Phenomenology · Submitted 17 Jun 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This simplified metric, which can be considered as an approximation of a more complicated (and smooth) one, leads to analytical Green's functions (with a mass gap $m_g \sim \textrm{TeV}$ and a continuum for $s > m_g^2$) which could then be easily incorporated in the experimental codes.
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The abstract, sentence by sentence
Green's functions with continuum spectra are a way of avoiding the strong bounds on new physics from the absence of new narrow resonances in experimental data. We model such a situation with a five-dimensional model with two branes along the extra dimension $z$, the ultraviolet (UV) and the infrared (IR) one, such that the metric between the UV and the IR brane is AdS$_5$, thus solving the hierarchy problem, and beyond the IR brane the metric is that of a linear dilaton model, which extends to $z\to\infty$. This simplified metric, which can be considered as an approximation of a more complicated (and smooth) one, leads to analytical Green's functions (with a mass gap $m_g \sim \textrm{TeV}$ and a continuum for $s > m_g^2$) which could then be easily incorporated in the experimental codes. The theory contains Standard Model gauge bosons in the bulk with Neumann boundary conditions in the UV brane. To cope with electroweak observables the theory is also endowed with an extra custodial gauge symmetry in the bulk, with gauge bosons with Dirichlet boundary conditions in the UV brane, and without zero (massless) modes. All Green's functions have analytical expressions and exhibit poles in the second Riemann sheet of the complex plane at $s=M_n^2-i M_n\Gamma_n$, denoting a discrete (infinite) set of broad resonances with masses ($M_n$) and widths ($\Gamma_n$). For gauge bosons with Neumann or Dirichlet boundary conditions, the masses and widths of resonances satisfy the (approximate) equation $s= - 4 m_g^2 \mathcal W_n^2[\pm (1+i)/4]$, where $\mathcal W_n$ is the $n$-th branch of the Lambert function.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Green's functions with continuum spectra are a way of avoiding the strong bounds on new physics from the absence of new narrow resonances in experimental data. | background 0.99 | 0.07 | 0.18 | asserted 1.00 |
| s1 | We model such a situation with a five-dimensional model with two branes along the extra dimension $z$, the ultraviolet (UV) and the infrared (IR) one, such that the metric between the UV and the IR brane is AdS$_5$, thus solving the hierarchy problem, and beyond the IR brane the metric is that of a linear dilaton model, which extends to $z\to\infty$. | method 0.95 | 0.70 | 0.05 | asserted 0.98 |
| s2 | This simplified metric, which can be considered as an approximation of a more complicated (and smooth) one, leads to analytical Green's functions (with a mass gap $m_g \sim \textrm{TeV}$ and a continuum for $s > m_g^2$) which could then be easily incorporated in the experimental codes. | result 0.40 | 0.85 | 0.32 | hedged possibility 0.87 |
| s3 | The theory contains Standard Model gauge bosons in the bulk with Neumann boundary conditions in the UV brane. | method 0.97 | 0.49 | 0.03 | asserted 1.00 |
| s4 | To cope with electroweak observables the theory is also endowed with an extra custodial gauge symmetry in the bulk, with gauge bosons with Dirichlet boundary conditions in the UV brane, and without zero (massless) modes. | method 0.91 | 0.63 | 0.04 | asserted 1.00 |
| s5 | All Green's functions have analytical expressions and exhibit poles in the second Riemann sheet of the complex plane at $s=M_n^2-i M_n\Gamma_n$, denoting a discrete (infinite) set of broad resonances with masses ($M_n$) and widths ($\Gamma_n$). | result 1.00 | 0.87 | 0.32 | asserted 1.00 |
| s6 | For gauge bosons with Neumann or Dirichlet boundary conditions, the masses and widths of resonances satisfy the (approximate) equation $s= - 4 m_g^2 \mathcal W_n^2[\pm (1+i)/4]$, where $\mathcal W_n$ is the $n$-th branch of the Lambert function. | result 1.00 | 0.88 | 0.24 | asserted 0.93 |
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The paper
Original abstract
Green's functions with continuum spectra are a way of avoiding the strong bounds on new physics from the absence of new narrow resonances in experimental data. We model such a situation with a five-dimensional model with two branes along the extra dimension $z$, the ultraviolet (UV) and the infrared (IR) one, such that the metric between the UV and the IR brane is AdS$_5$, thus solving the hierarchy problem, and beyond the IR brane the metric is that of a linear dilaton model, which extends to $z\to\infty$. This simplified metric, which can be considered as an approximation of a more complicated (and smooth) one, leads to analytical Green's functions (with a mass gap $m_g \sim \textrm{TeV}$ and a continuum for $s > m_g^2$) which could then be easily incorporated in the experimental codes. The theory contains Standard Model gauge bosons in the bulk with Neumann boundary conditions in the UV brane. To cope with electroweak observables the theory is also endowed with an extra custodial gauge symmetry in the bulk, with gauge bosons with Dirichlet boundary conditions in the UV brane, and without zero (massless) modes. All Green's functions have analytical expressions and exhibit poles in the second Riemann sheet of the complex plane at $s=M_n^2-i M_n\Gamma_n$, denoting a discrete (infinite) set of broad resonances with masses ($M_n$) and widths ($\Gamma_n$). For gauge bosons with Neumann or Dirichlet boundary conditions, the masses and widths of resonances satisfy the (approximate) equation $s= - 4 m_g^2 \mathcal W_n^2[\pm (1+i)/4]$, where $\mathcal W_n$ is the $n$-th branch of the Lambert function.
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References
How the literature uses it
7 arXiv papers cite this in 13 sentences
Papers citing it · 6 sentences without a confident label
Uses its method or tool 1 paper
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Using this procedure, the zeros of this function turn out to be [ref]
Continuum spectra from warped dimensions · Resonances · 0.85
Cites it as background 4 papers
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This model with $ν= 1$ has been applied for particle physics in Refs. [ref] , and for cosmology including its thermodynamics and braneworld cosmology properties in Refs. [ref] .
Linear Dilaton in Cosmology and Particle Physics · Solutions in the AdS-$ν$ model · 0.91
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[ See [ref] for LST reviews, [ref] for formal holographic aspects of the linear dilaton background, and [ref] for field theoretical studies of the LD background and related phenomenological developments.] More generally it is widely accepted that a (less predictive) holographic principle formulated in terms of information content applies to any spacetime [ref] .
Entanglement Entropy and Thermal Phase Transitions from Curvature Singularities · Introduction · 0.90
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This model is known to have peculiar thermodynamic [ref] and field theoretical properties [ref] .
Cosmological Dark Matter from a Bulk Black Hole · Introduction · 0.87
What it cites · 39 sentences without a confident label
Compares with 5 papers
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Notice that while the RS model leads to a discrete KK spectrum with zero widths [ref] , the linear dilaton model has a purely continuous spectrum above the mass gap, apart from the possible existence of isolated zero modes [ref] (see also [ref] ).
A Large Mass Hierarchy from a Small Extra Dimension · Conclusions and outlook · 0.93
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Notice that while the RS model leads to a discrete KK spectrum with zero widths [ref] , the linear dilaton model has a purely continuous spectrum above the mass gap, apart from the possible existence of isolated zero modes [ref] (see also [ref] ).
On gapped continuum resonance spectra · Conclusions and outlook · 0.93
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Notice that while the RS model leads to a discrete KK spectrum with zero widths [ref] , the linear dilaton model has a purely continuous spectrum above the mass gap, apart from the possible existence of isolated zero modes [ref] (see also [ref] ).
The Continuum Linear Dilaton · Conclusions and outlook · 0.93
Cites as background 22 papers
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One of the most successful BSM models is the Randall-Sundrum (RS) model, proposed in 1999 [ref] , where the hierarchy between the four-dimensional (4D) Planck scale $M_Pl$ and the $$ scale is solved by means of a warped fifth dimension and two branes, the UV brane and the infrared (IR) brane.
A Large Mass Hierarchy from a Small Extra Dimension · Introduction · 1.00
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Some other exploring scenarios include the clockwork models, as well as their 5D continuum limit [ref] , the linear dilaton models (LDM) [ref] and the Little String theories [ref] , which predict discrete spectra with a TeV mass gap and a mass separation between modes $∼30$.
Little String Theory at a TeV · Introduction · 0.94
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Some other exploring scenarios include the clockwork models, as well as their 5D continuum limit [ref] , the linear dilaton models (LDM) [ref] and the Little String theories [ref] , which predict discrete spectra with a TeV mass gap and a mass separation between modes $∼30$.
Phenomenology of TeV Little String Theory from Holography · Introduction · 0.94
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