REVIEW
Phenomenology, Astrophysics and Cosmology of Theories with Sub-Millimeter Dimensions and TeV Scale Quantum Gravity
High Energy Physics - Phenomenology · Submitted 12 Jul 1998 · 20 references
Pith's verdict: The constraint roadmap that decided the sub-millimeter extra-dimension idea survives — and it has held up — with one abstract-level overclaim about the n = 2 string escape hatch.
T0 · AI review
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Referee report
The paper
The paper claims
The authors argue that a world with millimeter-sized extra dimensions and quantum gravity at the TeV scale is not ruled out by any experiment, star, or cosmological observation they can check.
The reading
What carries the argument
The load-bearing object is the relation between the two Planck scales, $M_{(4)}^2 = M_{(4+n)}^{n+2} r_n^n$, derived three ways: by Gauss's law in the compactified space, by dimensional reduction of the Einstein-Hilbert action, and by summing the Kaluza-Klein tower of the graviton. Everything follows from it. The wall-localized Standard Model couples to the bulk graviton through $T^{/mu/nu} H_{/mu/nu}/M_{(4+n)}^{(n+2)/2}$ evaluated at the brane position, so extra-dimensional momentum need not be conserved while energy is, and the brane can recoil without absorbing energy. The second piece of machinery is the dictionary the authors use to convert known axion bounds into graviton bounds: replace $1/f_a^2$ by $T^{n}/M_{(4+n)}^{n+2}$, where $T$ is the temperature of the stellar or cosmological system. That replacement encodes the whole infrared-softness argument in one line, and the paper is candid that it is a rough mapping rather than a computation. A third element, used to argue that emitted gravitons do not come back, is the escape width $/Gamma /sim E^3/M_{(4)}^2$, which gives lifetimes exceeding the age of the universe for gravitons below about 100 MeV.
Extended reading notes
Core claim
The central claim is that the sub-millimeter extra-dimension scenario survives every phenomenological, astrophysical, and cosmological constraint the authors can construct, except for a real but tolerable squeeze in the two-extra-dimension case. The argument runs through a single class of process: emission of massless $(4+n)$-dimensional gravitons into the bulk. Because each Kaluza-Klein mode couples only as $1/M_{(4)}$ but there are of order $(E r_n)^n$ modes below energy $E$, the summed rate scales as $E^{n}/M_{(4+n)}^{n+2}$ rather than as $1/M_{(4)}^2$. That scaling is soft in the infrared, and softness is what saves the theory: for $n>2$ the resulting bounds from kaon and $Z$ decays, from solar and red-giant cooling, from supernova energy loss, and from graviton over-closure and late decays all sit below $M_{(4+n)} = 1$ TeV. For $n=2$ the same logic bites harder, and nucleon-nucleon bremsstrahlung in SN1987A together with distortions of the diffuse photon background push the six-dimensional Planck scale above roughly 30 TeV. The authors note that even this is not fatal, because in the type-I string embedding the string scale can stay near 1 TeV while $M_{(6)}$ sits an order of magnitude higher.
Load-bearing premise
The headline numbers come from order-of-magnitude dimensional analysis with every unknown coefficient set to one, most consequentially the 30 millibarn nucleon-nucleon bremsstrahlung cross-section and the diffuse photon flux bound, and the authors themselves call the axion-to-graviton replacement a rough dictionary.
Editorial extensions
If this is right
- If the argument holds, the hierarchy problem has a solution that requires no low-energy supersymmetry and no technicolor, only $n \geq 2$ extra dimensions of sub-millimeter size with the Standard Model confined to a three-brane.
- For $n>2$, the fundamental Planck scale can sit at 1 TeV, so quantum gravitational effects and graviton emission become collider physics at the LHC, visible as missing-energy signals.
- For $n=2$, the six-dimensional Planck scale must exceed roughly 30 TeV, which shrinks the extra dimensions to tens of microns and makes a direct sub-millimeter test of the $1/r^2 \to 1/r^4$ transition correspondingly harder.
- A Peccei-Quinn axion placed in the bulk solves strong CP with a decay constant near the weak scale, evading the astrophysical axion bounds that exclude an ordinary 1 TeV axion.
- A gauge field propagating in the bulk acquires a minuscule four-dimensional coupling $g_4 \sim 10^{-16}$ and a mass of order $(\text{mm})^{-1}$ when the symmetry breaks on the brane, producing repulsive forces $10^6$ to $10^8$ times gravity at sub-millimeter distances if it couples to baryon or lepton number.
- Gravitons emitted from our brane and captured on a higher-dimensional 'fat' brane can decay there into non-relativistic products, giving a dark matter candidate that is dark to us only because it shines on another brane.
Reading between the lines
- The paper's safety argument is really a statement about the density of states: the same large multiplicity that makes gravity strong at a TeV also makes each individual mode so weakly coupled that no single mode can do much damage, so the theory becomes safer as $n$ grows and the Kaluza-Klein spacing approaches the cutoff.
- The 30 TeV bound for $n=2$ is the natural target for the next generation of sub-millimeter force experiments, but it also predicts that the $1/r^4$ turn-on sits at tens of microns rather than at a millimeter, which is a harder measurement than the original proposal implied.
- Because the bulk gauge coupling is fixed to $g_{4+n}^2 \sim M_{(4+n)}^{-n}$ by the cutoff, the tiny $10^{-16}$ four-dimensional coupling is not a tuning but a prediction; this makes bulk gauge fields a more sharply testable sector of the scenario than the graviton itself.
- The cosmological discussion is explicitly conditional on a reheating temperature $T_*$ and on an unknown radius-stabilizing potential, so the graviton over-closure and diffuse-photon bounds should be read as constraints on that early history rather than on the extra-dimensional geometry itself.
Original abstract
We recently proposed a solution to the hierarchy problem not relying on low-energy supersymmetry or technicolor. Instead, the problem is nullified by bringing quantum gravity down to the TeV scale. This is accomplished by the presence of $n \geq 2$ new dimensions of sub-millimeter size, with the SM fields localised on a 3-brane in the higher dimensional space. In this paper we systematically study the experimental viability of this scenario. Constraints arise both from strong quantum gravitational effects at the TeV scale, and more importantly from the production of massless higher dimensional gravitons with TeV suppressed couplings. Theories with $n>2$ are safe due mainly to the infrared softness of higher dimensional gravity. For $n=2$, the six dimensional Planck scale must be pushed above $\sim 30$ TeV to avoid cooling SN1987A and distortions of the diffuse photon background. Nevertheless, the particular implementation of our framework within type I string theory can evade all constraints, for any $n \geq 2$, with string scale $m_s \sim 1$ TeV. We also explore novel phenomena resulting from the existence of new states propagating in the higher dimensional space. The Peccei-Quinn solution to the strong CP problem is revived with a weak scale axion in the bulk. Gauge fields in the bulk can mediate repulsive forces $\sim 10^6 - 10^8$ times stronger than gravity at sub-mm distances, and may help stabilize the proton. Higher-dimensional gravitons produced on our brane and captured on a different "fat" brane can provide a natural dark matter candidate.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We recently proposed a solution to the hierarchy problem not relying on low-energy supersymmetry or technicolor. Instead, the problem is nullified by bringing quantum gravity down to the TeV scale. This is accomplished by the presence of $n \geq 2$ new dimensions of sub-millimeter size, with the SM fields localised on a 3-brane in the higher dimensional space. In this paper we systematically study the experimental viability of this scenario. Constraints arise both from strong quantum gravitational effects at the TeV scale, and more importantly from the production of massless higher dimensional gravitons with TeV suppressed couplings. Theories with $n>2$ are safe due mainly to the infrared softness of higher dimensional gravity. For $n=2$, the six dimensional Planck scale must be pushed above $\sim 30$ TeV to avoid cooling SN1987A and distortions of the diffuse photon background. Nevertheless, the particular implementation of our framework within type I string theory can evade all constraints, for any $n \geq 2$, with string scale $m_s \sim 1$ TeV. We also explore novel phenomena resulting from the existence of new states propagating in the higher dimensional space. The Peccei-Quinn solution to the strong CP problem is revived with a weak scale axion in the bulk. Gauge fields in the bulk can mediate repulsive forces $\sim 10^6 - 10^8$ times stronger than gravity at sub-mm distances, and may help stabilize the proton. Higher-dimensional gravitons produced on our brane and captured on a different "fat" brane can provide a natural dark matter candidate.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We recently proposed a solution to the hierarchy problem not relying on low-energy supersymmetry or technicolor. | background 0.64 | 0.73 | 0.06 | asserted 1.00 |
| s1 | Instead, the problem is nullified by bringing quantum gravity down to the TeV scale. | contribution 0.65 | 0.34 | 0.13 | asserted 1.00 |
| s2 | This is accomplished by the presence of $n \geq 2$ new dimensions of sub-millimeter size, with the SM fields localised on a 3-brane in the higher dimensional space. | method 0.50 | 0.25 | 0.06 | asserted 1.00 |
| s3 | In this paper we systematically study the experimental viability of this scenario. | contribution 1.00 | 0.71 | 0.04 | asserted 0.93 |
| s4 | Constraints arise both from strong quantum gravitational effects at the TeV scale, and more importantly from the production of massless higher dimensional gravitons with TeV suppressed couplings. | result 0.60 | 0.48 | 0.09 | asserted 1.00 |
| s5 | Theories with $n>2$ are safe due mainly to the infrared softness of higher dimensional gravity. | result 0.96 | 0.67 | 0.14 | asserted 1.00 |
| s6 | For $n=2$, the six dimensional Planck scale must be pushed above $\sim 30$ TeV to avoid cooling SN1987A and distortions of the diffuse photon background. | result 0.97 | 0.70 | 0.10 | asserted 0.99 |
| s7 | Nevertheless, the particular implementation of our framework within type I string theory can evade all constraints, for any $n \geq 2$, with string scale $m_s \sim 1$ TeV. | result 0.96 | 0.78 | 0.32 | asserted 0.90 |
| s8 | We also explore novel phenomena resulting from the existence of new states propagating in the higher dimensional space. | contribution 0.99 | 0.80 | 0.03 | asserted 0.79 |
| s9 | The Peccei-Quinn solution to the strong CP problem is revived with a weak scale axion in the bulk. | result 0.78 | 0.65 | 0.04 | asserted 1.00 |
| s10 | Gauge fields in the bulk can mediate repulsive forces $\sim 10^6 - 10^8$ times stronger than gravity at sub-mm distances, and may help stabilize the proton. | result 0.83 | 0.64 | 0.04 | hedged possibility 0.94 |
| s11 | Higher-dimensional gravitons produced on our brane and captured on a different "fat" brane can provide a natural dark matter candidate. | result 0.59 | 0.64 | 0.06 | hedged possibility 0.80 |
What was examined, and what was not
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References
How later papers used it
296 later papers cite it
2 later papers by other authors are listed below: 1 used its method or tool and 1 compared its own results with it.
Uses its method or tool 1 of 2 papers with this label
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Simulated a model for quantum black holes decaying to two jets with n = 6 extra spatial dimensions in the context of this paper's ADD model.
Search for new phenomena in the dijet mass distribution using $p-p$ collision data at $\sqrt{s}=8$ TeV with the ATLAS detector (2014) · 1.00 · paraphrased: the licence does not allow quoting
Compares with it 1 of 11 papers with this label
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Contrasted its own case, where chameleon constraints only allow n=2, with this paper's ADD scenario, where n > 2 is generically allowed.
Chameleonic inflation (2013) · 0.95 · paraphrased: the licence does not allow quoting
How the literature uses it
269 arXiv papers cite this in 399 sentences
Papers citing it · 167 sentences without a confident label
Contests it 1 paper
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However, these authors put aside the loopholes pointed out in the previous analyses of [ref] which significantly weaken the bounds.
Kaluza-Klein Spectroscopy from Neutron Oscillations into Hidden Dimensions · General Framework · contest 0.73
Uses its method or tool 2 papers
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As in [ref] , we pass for simplicity of the calculations from the compact $d-$torus to its covering space $ℝ^d$.
Non-relativistic limit of multidimensional gravity: exact solutions and applications · The gravitational force law under dimensional reduction · 0.92
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A model for quantum black holes (QBH) that decay to two jets is simulated using both the [ref] and the [ref] generators, to produce a simple two-body final-state scenario of quantum gravitational effects at the fundamental Planck scale $M_D$, with $n$ = 6 extra spatial dimensions in the context of the ADD model [ref] .
Search for new phenomena in the dijet mass distribution using $p-p$ collision data at $\sqrt{s}=8$ TeV with the ATLAS detector · Simulation of hypothetical new phenomena · 1.00
Compares with it 11 papers
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Correspondingly, the phenomenology of the gravitational sector of the cyclically symmetric extension of the SM shares some qualitative features with the one of the large extra dimensions [ref] , but there are crucial differences, for example the evaporation rate of the microscopic BHs.
Phenomenology of 10^32 Dark Sectors · Introduction · 0.96
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These values of large extra dimensions $a$ are much bigger than in the standard approach $a ∼10^(32/6)-17$cm $≈10^-11.7$cm [ref] .
Non-relativistic limit of multidimensional gravity: exact solutions and applications · Model: $𝒟=10$ with $d=6, p=3$ · 0.98
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These values of large extra dimensions $a$ are much bigger than in the standard approach $a ∼10^(32/6)-17$cm $≈10^-11.7$cm [ref] .
Multidimensional gravity in non-relativistic limit · Introduction · 0.98
Cites it as background 176 papers
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Using the idea of large extra dimensions, Arkani-Hamed, Dimopoulos, and Dvali (ADD) suggested a phenomenological brane-world scenario for unifying the elementary particle forces with gravity near the electroweak energy scale [ref] .
Minimum length, extra dimensions, modified gravity and black hole remnants · Introduction · 0.96
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ADD models [ref] consist of a four-dimensional spacetime with a set of $n$ compact extra dimensions, with typical length $R$.
Updated limits on extra dimensions through torsion and LHC data · ADD models · 0.98
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Models of large extra dimensions allow the fundamental scale of gravity to be as low as the electroweak scale [ref] .
Missing energy in black hole production and decay at the Large Hadron Collider · Introduction · 0.94
Discussion
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