REVIEW
Neutrino Masses from Large Extra Dimensions
High Energy Physics - Phenomenology · Submitted 24 Nov 1998 · 21 references
Pith's verdict: Section 2 is the paper and it holds up; the real soft spots are the unknown UV cutoff coefficient c and the M_* bookkeeping in the Majorana section, not the masslessness of the bulk fermion.
T0 · AI review
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Referee report
The paper
The paper claims
The paper argues that if the fundamental Planck scale sits near the weak scale and gravity leaks into a few sub-millimeter extra dimensions, neutrino masses of order $10^{-1}$ to $10^{-4}$ eV follow naturally, with no superheavy see-saw and
The reading
What carries the argument
The load-bearing object is the overlap between a brane-localized operator and a bulk zero mode: a bulk field normalized over the extra volume meets wall fields carrying a factor $1/√V_{wall}$, so the effective four-dimensional coupling is suppressed by $√(V_{wall}/V_m)$, which for a symmetric internal manifold becomes $(M_*/M_{pl})^{m/n}$ when the fermion propagates in only $m$ of the $n$ dimensions. This single geometric factor explains both the weakness of gravity and the smallness of the Dirac neutrino mass. The supporting machinery is a Kaluza-Klein mass matrix whose off-diagonal entries are all equal to $m_ν$ and whose diagonal entries are $|n|/R$; its lightest eigenvalue stays at $m_ν$ to first order, with the leading correction coming from wavefunction renormalization by the tower, cut off at $M_*$. For the Majorana route the machinery is the Green's function $Δ_n(r) = (-∇^2_{(n)} + m_χ^2)^{-1}(r)$ of the bulk messenger, which falls as $1/r^{n-2}$ for a light field and exponentially for a heavy one, turning inter-brane distance into a mass suppression.
Extended reading notes
Core claim
The central claim is that neutrino mass is not evidence for a large energy desert. If standard-model fields live on a 3-brane inside $n$ large extra dimensions and $M_*$ is near a TeV, then a massless bulk fermion supplies a right-handed neutrino whose coupling to the brane is suppressed by the square root of the bulk volume, because its wavefunction is spread out while the Higgs and lepton doublet are confined to a thin wall. The resulting Dirac mass is $m_ν = κv/√(V_n M_*^n) = κvM_*/M_{pl}$, numerically about $10^{-4}$ eV times $κM_*/1$ TeV, which is the right order for the atmospheric and solar anomalies. The authors show this survives a careful treatment: integrating out the Kaluza-Klein tower renormalizes the left-handed neutrino wavefunction and imposes a ceiling $m_ν^{max} = c^{-(n-2)/2}M_*^2/M_{pl}$, so raising $κ$ cannot push the mass arbitrarily high. They note the $n=2$ case is marginal and restrict attention to $n>2$. A second, independent route generates Majorana masses by breaking lepton number on a distant brane and letting a bulk field with lepton number two shine the breaking across the gap, giving $m_ν^{Maj} ∼ v^2 Δ_n(r) M_*^{n-1}$ with $Δ_n$ the transverse Yukawa profile; for $n=4$ and the far brane at the compactification radius this reproduces the familiar see-saw-sized number.
Load-bearing premise
The Dirac mechanism requires the bulk fermion to be exactly massless, or at least much lighter than the Kaluza-Klein spacing $1/R$, so that a delocalized zero mode exists at all; the paper assumes this rather than deriving it, and a bulk mass of order $1/R$ would remove the zero mode and with it the suppression argument.
Editorial extensions
If this is right
- Neutrino mass becomes a probe of the same volume factor that fixes Newton's constant, so a measured neutrino mass and a measured $M_*$ are two handles on one quantity.
- The Dirac route predicts an absolute ceiling $m_ν^{max} = c^{-(n-2)/2}M_*^2/M_{pl}$ for each $n$ and $M_*$, so a heavy enough neutrino would rule the mechanism out rather than merely constrain it.
- For $n>2$ the Kaluza-Klein neutrino modes are never thermally populated after the universe becomes normal, so the cosmology of the scenario survives nucleosynthesis, whereas $n=2$ is disfavored.
- For $n=3$ the invisible Higgs width into $ν_L$ plus bulk neutrinos is large enough to be a collider signal, scaling as $m_H^n/M_*^{n+2}$.
- If the messenger field carrying lepton number is light, its exchange produces isotope-dependent sub-millimeter forces roughly $10^6$ times stronger than gravity, within reach of upcoming short-range gravity experiments.
Reading between the lines
- The same volume-suppression argument applies to any standard-model singlet that propagates in the bulk, so the mechanism is really a statement about where fields live rather than about neutrinos specifically; one could ask whether it also sets the size of other apparently unexplained small couplings.
- Because the suppression depends on how many dimensions the fermion inhabits ($m$) rather than on how many gravity inhabits ($n$), the framework contains a dial that is not fixed by any observation in the paper; a bulk fermion localized on a sub-brane gives an intermediate mass without changing $M_*$.
- The ceiling on the Dirac mass means that if a future $M_*$ is pushed upward by collider limits, the predicted neutrino mass rises quadratically, so the scenario becomes testable by the combination of collider and neutrino-mass data rather than by either alone.
- The note on magnetic moments suggests an observable that decouples from mass: a flavor symmetry that forbids the Majorana mass term need not forbid $νσ_{μν}F^{μν}ν$, so a large moment without a mass would be a signature of the low cutoff rather than of heavy new particles.
Original abstract
Recently it was proposed that the standard model (SM) degrees of freedom reside on a $(3+1)$-dimensional wall or ``3-brane'' embedded in a higher-dimensional spacetime. Furthermore, in this picture it is possible for the fundamental Planck mass $\mst$ to be as small as the weak scale $\mst\simeq O(\tev)$ and the observed weakness of gravity at long distances is due the existence of new sub-millimeter spatial dimensions. We show that in this picture it is natural to expect neutrino masses to occur in the $10^{-1} - 10^{-4}\ev$ range, despite the lack of any fundamental scale higher than $\mst$. Such suppressed neutrino masses are not the result of a see-saw, but have intrinsically higher-dimensional explanations. We explore two possibilities. The first mechanism identifies any massless bulk fermions as right-handed neutrinos. These give naturally small Dirac masses for the same reason that gravity is weak at long distances in this framework. The second mechanism takes advantage of the large {\it infrared} desert: the space in the extra dimensions. Here, small Majorana neutrino masses are generated by breaking lepton number on distant branes.
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
Recently it was proposed that the standard model (SM) degrees of freedom reside on a $(3+1)$-dimensional wall or ``3-brane'' embedded in a higher-dimensional spacetime. Furthermore, in this picture it is possible for the fundamental Planck mass $\mst$ to be as small as the weak scale $\mst\simeq O(\tev)$ and the observed weakness of gravity at long distances is due the existence of new sub-millimeter spatial dimensions. We show that in this picture it is natural to expect neutrino masses to occur in the $10^{-1} - 10^{-4}\ev$ range, despite the lack of any fundamental scale higher than $\mst$. Such suppressed neutrino masses are not the result of a see-saw, but have intrinsically higher-dimensional explanations. We explore two possibilities. The first mechanism identifies any massless bulk fermions as right-handed neutrinos. These give naturally small Dirac masses for the same reason that gravity is weak at long distances in this framework. The second mechanism takes advantage of the large {\it infrared} desert: the space in the extra dimensions. Here, small Majorana neutrino masses are generated by breaking lepton number on distant branes.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recently it was proposed that the standard model (SM) degrees of freedom reside on a $(3+1)$-dimensional wall or ``3-brane'' embedded in a higher-dimensional spacetime. | background 1.00 | 0.04 | 0.03 | asserted 0.89 |
| s1 | Furthermore, in this picture it is possible for the fundamental Planck mass $\mst$ to be as small as the weak scale $\mst\simeq O(\tev)$ and the observed weakness of gravity at long distances is due the existence of new sub-millimeter spatial dimensions. | background 1.00 | 0.06 | 0.05 | hedged possibility 0.86 |
| s2 | We show that in this picture it is natural to expect neutrino masses to occur in the $10^{-1} - 10^{-4}\ev$ range, despite the lack of any fundamental scale higher than $\mst$. | result 0.97 | 0.87 | 0.83 | asserted 0.86 |
| s3 | Such suppressed neutrino masses are not the result of a see-saw, but have intrinsically higher-dimensional explanations. | interpretation 0.86 | 0.59 | 0.20 | asserted 1.00 |
| s4 | We explore two possibilities. | contribution 0.59 | 0.60 | 0.02 | unclear 0.64 |
| s5 | The first mechanism identifies any massless bulk fermions as right-handed neutrinos. | method 0.79 | 0.50 | 0.05 | asserted 0.99 |
| s6 | These give naturally small Dirac masses for the same reason that gravity is weak at long distances in this framework. | interpretation 0.55 | 0.53 | 0.09 | asserted 0.97 |
| s7 | The second mechanism takes advantage of the large {\it infrared} desert: the space in the extra dimensions. | method 0.74 | 0.43 | 0.04 | asserted 0.89 |
| s8 | Here, small Majorana neutrino masses are generated by breaking lepton number on distant branes. | method 0.80 | 0.69 | 0.11 | asserted 0.99 |
What was examined, and what was not
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References
How the literature uses it
107 arXiv papers cite this in 157 sentences
Papers citing it · 95 sentences without a confident label
Builds on it 3 papers
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Our further step was to apply this generally derived formulas to the explicit theories of neutrino masses such as the proposal of ADDM [ref] within ADD and the one of DR [ref] within Many Species frameworks respectively.
Neutrino Physics in TeV Scale Gravity Theories · Conclusions · 0.86
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In the Appendix we generalized studies of large-extra-dimension models originally set up to interpret the smallness of neutrino masses by postulating that right-handed neutrinos, unlike SM fields, do propagate in the bulk [ref] .[Neutrino masses in relation to the swampland program were discussed in [ref] .] We showed that when interpreted in the context of the dark dimension, neutrino oscillation data constrain $m_KK > 2.5 eV$ at the 99% CL.
Aspects of the Dark Dimension in Cosmology · Conclusions · 0.95
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In Section [ref], we revisit the models of Refs. [ref] , which generate small Dirac neutrino masses with right-handed neutrinos identified with the zero modes of gauge singlet fermions propagating in a large compactified volume, by adapting this idea to our spacetime geometries.
Large Star/Rose Extra Dimension with Small Leaves/Petals · Introduction · 1.00
Compares with it 3 papers
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The structures unitarity-violation in the two different theories (ADDM [ref] of ADD versus Dvali-Redi [ref] of Many Species) differ from each other.
Neutrino Physics in TeV Scale Gravity Theories · Conclusions · 0.95
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This fact should be compared with the analog mechanism in large extra dimensions [ref] .
Phenomenology of 10^32 Dark Sectors · Small Neutrino Masses from Large Number of Species · 1.00
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The normalised eigenvectors $u_λ$ relative to the eigenvalue $m_λ$ are found to be [equation] The above results are in agreement with previous works [ref] .
Do neutrinos dream in 5D? Towards a comprehensive extra-dimensional neutrino phenomenology · Dirac Brane Term · 0.98
Cites it as support 1 paper
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This setup generates a naturally small Dirac mass for neutrinos [ref] .
Neutrino Physics in TeV Scale Gravity Theories · The ADDM model · 0.98
Cites it as background 50 papers
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In LED models, SM singlets such as sterile neutrinos can propagate in a higher-dimensional bulk [ref] , giving rise to a tower of Kaluza–Klein (KK) excitations in the effective four-dimensional theory.
Neutrino Portal to Extra Dimensions: Unified Origin of Dark Radiation, Dark Matter, and Neutrino Decay · Introduction · 0.82
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One interesting proposal envisions the right-handed neutrinos as five-dimensional (5D) bulk states, with Yukawa couplings to the left-handed lepton and Higgs doublets that are localized states on the Standard Model (SM) brane [ref] .
Cosmological Constraints on Dark Neutrino Towers · Introduction · 0.98
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This mechanism first appeared in the model of large extra dimensions [ref] in which the Kaluza-Klein (KK) modes of a right-handed bulk neutrino played the role of the mixing partners for the neutrino [ref] .
Searching for the $N$-naturalness tower of neutrinos · Introduction · 0.86
Discussion
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