Light Neutrinos without Heavy Mass Scales: A Higher-Dimensional Seesaw Mechanism

Emilian Dudas; Keith R. Dienes; Tony Gherghetta

REVIEW

Light Neutrinos without Heavy Mass Scales: A Higher-Dimensional Seesaw Mechanism

Keith R. Dienes, Emilian Dudas, Tony Gherghetta

High Energy Physics - Phenomenology · Submitted 21 Nov 1998 · 29 references

Pith's verdict: The linear algebra is correct and the mechanisms are new, but the reader's 'weakest assumption' is inverted and the numerology is never closed.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 9 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/9811428 (version 3)

Pith IDNBMFQSBG, Pith's permanent record of this paper and its review

CitationEmilian Dudas, Keith R. Dienes, Tony Gherghetta. "Light Neutrinos without Heavy Mass Scales: A Higher-Dimensional Seesaw Mechanism." arXiv:hep-ph/9811428 (1998). https://pith.science/paper/NBMFQSBG

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Quick read on the Dienes-Dudas-Gherghetta paper. The core is right: they write down the mass matrix for a brane-localized left-handed neutrino mixing with an infinite KK tower of a bulk right-handed neutrino, diagonalize it analytically, and get a light eigenvalue suppressed by the radius rather than by a heavy scale. The linear algebra in Sects. 2.3, 2.4, 2.6 and 4 checks out — the characteristic equations (2.17), (2.33), (4.2) are solved explicitly, and the exact masslessness at epsilon = 1/(2R) is verified from the determinant, not just asserted. The Scherk-Schwarz twist that produces that value without fine-tuning is a nice observation and is the kind of thing that makes the paper worth keeping on the shelf. The paper is also candid about its limitations — the classifier's 'none found' is wrong; Section 5 lists brane dynamics, higher-order KK-mixing operators, the pi-to-mu-nu spectrum, and the unphysical n-to-infinity limit. That candor counts for something. One correction to the reader's report: the 'weakest assumption' is inverted. Equal couplings m_N = m_M = m do not produce a light mass — Sect. 2.4 shows they give exactly degenerate eigenvalues and no seesaw. The light mass requires the splitting [m_N]^2 - [m_M]^2, which the paper itself flags in (2.13). So the load-bearing premise is whether brane-shifting or M0 actually generates that splitting at the right size, not the equal-coupling structure. The real soft spot is quantitative, and the stress-test is right about it in spirit: no parameter point is exhibited that simultaneously gives mR << 1, R^-1 ~ 10^-2 eV, and m_nu ~ 10^-2 eV. Section 3.3 does a rough estimate (R ~ 10^-5 m, M_s <~ 1 TeV for delta=2), but the authors themselves call the analysis 'at best only qualitative.' I haven't reproduced the stress-test's specific numbers and they look off to me, but the gap is real. Who should read it: anyone working on large extra dimensions and neutrino mass, and string model-builders looking for lepton-number violation. It is a foundational reference in that literature. Recommendation: send it out. The mechanisms are new, the math is checkable, and the open questions are the right ones. Expect a referee to push hard on the numerology.

Referee report

Significance

If the mechanisms hold, the paper reframes the standard seesaw argument that light neutrinos require a heavy scale, and it does so in the same large-extra-dimension setting that lowers the GUT, Planck, and string scales. The technical execution is a genuine strength: the characteristic equations (2.17), (2.33), and (4.2) are solved exactly, the U-matrix (3.7)–(3.8) is given in closed form for all mR, and the observation that a bare Majorana mass M0 is replaced by ε ≡ M0 mod R⁻¹ (Sect. 2.6) is a clean and surprising result that follows from the regular spacing of the tower rather than from any tuning. The paper also makes a falsifiable structural prediction: the multi-state oscillation profile of Figs. 4 and 6 is jagged, deficits and regenerations are never total in the orbifold case, and in the Scherk-Schwarz case the deficits are total while the regenerations are not. No parameter is fitted to data, and the one data comparison (Sect. 3.3) is presented as an estimate. These are real virtues and should be weighed in the assessment.

Major objections (3)

[Abstract and Sect. 2.4, Eqs. (2.13), (2.32), (2.34)] The abstract and introduction present the higher-dimensional seesaw as a generic consequence of giving N a KK tower, but Sect. 2.4 shows that for the most natural orbifold coupling, m_N^(n) = m_M^(n) = m, the characteristic equation (2.33) is invariant under λ → −λ, all eigenvalues are exactly degenerate, and there is no seesaw at all. The mechanism therefore rests entirely on the splitting [m_N^(n)]² − [m_M^(n)]² of Eq. (2.13), whose origin is model-dependent: brane-shifting (2.39), a Scherk-Schwarz twist, or a bare M0. This is stated clearly in Sects. 2.4 and 2.5, but the abstract's phrasing ('a higher-dimensional analogue of the seesaw mechanism may also be capable of generating naturally light neutrino masses') does not convey that the effect vanishes identically in the default configuration. The abstract and the bullet list in the introduction should be qualified to say that the light mass requires a non-zero splitting, and that generating that splitting is a model-building input rather than an automatic feature of the tower.
[Sect. 2.3, Eq. (2.31) and the sentence following it; Sect. 3.3] The sentence following Eq. (2.31) states that the substitution m → m²R ln(RM_s) 'may therefore enable a useful enhancement of the naïve value of m', but in the regime mR ≪ 1 assumed throughout Sects. 2.2–2.3 this substitution is a suppression, not an enhancement; it is an enhancement only when mR > 1, which is the δ = 1 case discussed separately in Sect. 2.2. The text should state which regime is meant. More importantly, the paper never exhibits an explicit parameter point that simultaneously satisfies mR ≪ 1, R⁻¹ ≈ 10⁻² eV (the estimate of Sect. 3.3), and m_ν ≈ 10⁻² eV. Using the paper's own Eq. (2.9), m_ν ≈ (mR)²/R × ln(RM_s), so for δ = 2 and m̂ ≈ M_s one finds mR ≈ 1/(2π) and m_ν parametrically of order R⁻¹ × O(10⁻²) × ln(RM_s); this may well land near the observed scale, but the manuscript does not show it, and the reader cannot check consistency from the text as written. Since the phenomenological claim of Sect. 3.3 is the paper's only contact with data, at least one worked parameter point (with δ, m̂/M_s, M_sR, and the resulting m_ν stated) should be given, or the text should state explicitly that no such point is claimed and that the estimate is purely parametric.
[Abstract, Sect. 4, Eq. (4.10)] The abstract states that the higher-dimensional seesaw 'may even be able to explain neutrino oscillations without neutrino masses', and Sect. 4 shows that exact masslessness requires ε = 1/(2R) and, as the authors themselves note below Eq. (4.5), 'relies rather crucially on taking the full n → ∞ limit'. When the tower is truncated at n_max ≈ M_sR, Eq. (4.10) gives m_ν ≈ m²/M_s ≈ 10⁻¹⁵ eV for the quoted values, which is not zero. The abstract and the Sect. 4 heading should be qualified accordingly: the claim that survives truncation is that oscillations occur with a neutrino mass far below the scale set by the oscillation wavelength, not that the neutrino is massless. The distinction matters because the Scherk-Schwarz realization is one of the paper's most attractive features, and overstating it invites the objection that the exact zero is an artifact of an unphysical limit.

Minor objections (9)

[Sect. 2.2] The phrase 'over a very short energy internal' appears twice in Sect. 2.2 and should read 'over a very short energy interval'.
[Sect. 2.5, Eq. (2.13) and surrounding text] The text writes the splitting as [m_N^(n)]² − [m_M^(m)]², with a stray index m in the second factor; it should be [m_M^(n)]² to match Eq. (2.13).
[Sect. 3.3] The sentence 'one would one would also need to take into account the energy-dependence' contains a duplicated phrase, and 'Howeever' appears in Sect. 4.
[Sect. 3.3] The conclusion that the SuperKamiokande mixing bound 'rules out larger values of δ, so that only two extra dimensions felt by the higher-dimensional neutrino field are consistent' is drawn from a rough estimate in which n is identified with M_sR. Given the stated qualitative character of this section, the claim should be softened to a parametric expectation, or the assumptions entering it should be stated explicitly.
[Sect. 2.2, Eq. (2.9) and following paragraph] The estimate 'mR ranging from O(10⁵) for n = 2 to O(1) for n = 6' in the δ = 1 case depends on the assumed relation between M_s and R in the full n-dimensional compactification. The relation used should be stated so the reader can reproduce the numbers.
[Figs. 4 and 6] The captions describe the oscillation probabilities as functions of time but do not state the units of the horizontal axis or the value of the momentum p used in Eq. (3.10). Since the physical period is set by λ²_{±1} − λ²_± ≈ R⁻², giving the axis in units of R would make the figures considerably easier to interpret.
[Sect. 2.6, footnote on Eq. (2.44)] The pairing prescription for the KK summations (pairing N^(k) with M^(k), equivalently positive with negative KK modes) is a genuine subtlety that determines the finite part of (2.44) and (2.45). Consider promoting at least the statement of the prescription from the footnote into the main text, since a reader who reorganizes the sum differently will not reproduce the quoted result.
[Reference [26]] The volume-suppression observation in Sect. 2.2 is credited to Dimopoulos and March-Russell via private communication and a conference talk. Since this is an unpublished attribution, it would be helpful to state in the text which of the two observations in Sect. 2.2 is the authors' own and which is credited.
[Note Added] The Note Added clarifies lepton-number conservation in Eq. (2.14) and the features of the Sect. 4 scenario. Since these points are central rather than peripheral, consider integrating the relevant sentences into Sects. 2.3 and 4 rather than appending them, so that a reader of the main text does not need the addendum to follow the argument.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

The paper argues that a light neutrino mass does not need a heavy right-handed partner: if the right-handed neutrino propagates in an extra dimension, its infinite tower of Kaluza-Klein states mixes with the left-handed neutrino and drives,

The reading

The standard explanation of small neutrino masses requires a very heavy right-handed neutrino, whose large mass suppresses the light eigenvalue through the seesaw mechanism. This paper asks whether that heavy scale can be avoided if the right-handed neutrino, alone among the Standard Model fermions, is allowed to propagate in an extra compactified dimension while the left-handed neutrino stays on a brane. Because the left-handed neutrino then couples to every member of an infinite Kaluza-Klein tower, the usual two-by-two seesaw is replaced by an infinite-dimensional mass matrix whose lightest eigenvalue is pushed toward zero as more and more tower states are included. The authors work out this matrix in several limits and find that the role of the heavy scale is taken over by the compactification radius $R^{-1}$, so the neutrino mass is set by $m^2 R$ times a slowly growing logarithm rather than by $m^2/M$. They also show that a bare Majorana mass $M_0$ for the bulk field drops out of the physics except through $M_0$ modulo $R^{-1}$, and that for one special residue the neutrino becomes exactly massless while still oscillating.

What carries the argument

The load-bearing object is the infinite-dimensional neutrino mass matrix of Eq. (2.11), in which the first row and column hold the common coupling $m$ of the brane neutrino to each Kaluza-Klein mode and the diagonal holds the tower masses $n/R$ together with the bare Majorana mass $M_0$. Its characteristic equation reduces to a transcendental condition such as $lambda R = pi (mR)^2 cot(pi lambda R)$ in the orbifold case, whose graphical solutions show how the tower shifts the light eigenvalues. The same physics can be read off a tree-level diagram in which the tower states are integrated out one by one, producing an effective $nu_L nu_L$ mass term $mu$ and reducing the problem to a two-by-two seesaw between $nu_L$ and the surviving zero mode. Brane-shifting in Type I string theory, which makes $m_N^{(n)}$ and $m_M^{(n)}$ unequal through factors of $cos(ny_*/R) pm sin(ny_*/R)$, is the proposed source of the lepton-number violation the mechanism needs.

Extended reading notes

Core claim

The central claim is that mixing between a brane-localized left-handed neutrino and the infinite Kaluza-Klein tower of a bulk right-handed neutrino generates a naturally light neutrino mass without any heavy mass scale. In the cleanest limit, where the left-handed neutrino couples with equal strength $m$ to every tower mode and the odd-mode couplings vanish, the mass matrix has one eigenvalue that falls to zero and one that grows without bound as the tower is taken to infinity; the two light eigenvalues are $lambda_pm = tfrac{1}{2}[mu pm sqrt{mu^2+4m^2}]$ with $mu = -m^2 R sum_{k=1}^{n} 1/k approx -m^2 R ln n$, so that the light mass behaves as $m^2 R ln n$ and the effective seesaw scale is $M_{rm eff} = 1/(R ln n)$ rather than a GUT-scale mass. The authors note that this inverts the usual four-dimensional seesaw: it is the would-be zero mode that becomes light while the neutrino direction becomes heavy. They then show that when the bulk field carries a bare Majorana mass $M_0$, only $epsilon equiv M_0$ modulo $R^{-1}$ survives in the eigenvalue equations, so a heavy $M_0$ is replaced by the radius scale; at $epsilon = 1/(2R)$ the lightest eigenvalue is exactly zero for all values of $mR$, giving oscillations mediated entirely by the tower masses. A Scherk-Schwarz twist with $omega = 1/2$ supplies precisely this residue topologically, without fine-tuning.

Load-bearing premise

The whole suppression rests on the left-handed neutrino coupling with the same strength to every Kaluza-Klein mode while all bulk-to-bulk off-diagonal entries vanish, an equal-coupling structure that the authors themselves note could be spoiled by brane dynamics and by higher-order momentum-violating operators.

Editorial extensions

If this is right

A neutrino mass in the range suggested by atmospheric oscillation data can arise from a compactification radius near $10^{-5}$ m, with no heavy right-handed mass anywhere in the spectrum.
A bare Majorana mass for the bulk neutrino, however large, is physically irrelevant except through its residue modulo $R^{-1}$, which removes one common route to generating small neutrino masses.
For a Scherk-Schwarz twist, the lightest neutrino eigenstate is exactly massless while the mixing matrix remains non-diagonal, so oscillation deficits and regenerations occur with no neutrino mass at all.
Because the tower is truncated at $n_{max} sim M_s R$, the residual mass is of order $m^2/M_s$, which for $m lesssim R^{-1} approx 10^{-2}$ eV and $M_s approx 10$ TeV gives $m_nu approx 10^{-15}$ eV.
Lepton-number violation can be generated geometrically by displacing D-branes from orbifold fixed points, so the size of the shift controls whether the light eigenvalues are split (Majorana) or degenerate (Dirac).

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the mechanism is right, the cleanest experimental handle is not the neutrino mass itself but the admixture of tower states in the weak eigenstate: the pion decay muon spectrum should be quasi-continuous rather than a sharp line, suppressed only by powers of $mR$.
The same infinite-matrix structure should apply to any Standard Model singlet that can live in the bulk, so the argument generalizes to sterile neutrinos and to other hidden-sector fermions that mix with brane fields.
The exact masslessness at $epsilon = 1/(2R)$ is a resonance condition on the tower spacing; a small departure from it should give a small but calculable mass, which makes the scenario testable by how sharply the residue must be tuned.
Because the light eigenvalue depends on $ln n_{max}$, the prediction is only logarithmically sensitive to the string scale, so a future determination of $R$ from short-range gravity would sharply fix the neutrino mass scale in this framework.

Original abstract

Recent theoretical developments have shown that extra spacetime dimensions can lower the fundamental GUT, Planck, and string scales. However, recent evidence for neutrino oscillations suggests the existence of light non-zero neutrino masses, which in turn suggests the need for a heavy mass scale via the seesaw mechanism. In this paper, we make several observations in this regard. First, we point out that allowing the right-handed neutrino to experience extra spacetime dimensions naturally permits the left-handed neutrino mass to be power-law suppressed relative to the masses of the other fermions. This occurs due to the power-law running of the neutrino Yukawa couplings, and therefore does not require a heavy scale for the right-handed neutrino. Second, we show that a higher-dimensional analogue of the seesaw mechanism may also be capable of generating naturally light neutrino masses without the introduction of a heavy mass scale. Third, we show that such a higher-dimensional seesaw mechanism may even be able to explain neutrino oscillations without neutrino masses, with oscillations induced indirectly via the masses of the Kaluza-Klein states. Fourth, we point out that even when higher-dimensional right-handed neutrinos are given a bare Majorana mass, the higher-dimensional seesaw mechanism surprisingly replaces this mass scale with the radius scale of the extra dimensions. Finally, we also discuss a possible new mechanism for inducing lepton-number violation by shifting the positions of D-branes in Type I string theory.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,026 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.50 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Recent theoretical developments have shown that extra spacetime dimensions can lower the fundamental GUT, Planck, and string scales. However, recent evidence for neutrino oscillations suggests the existence of light non-zero neutrino masses, which in turn suggests the need for a heavy mass scale via the seesaw mechanism. In this paper, we make several observations in this regard. First, we point out that allowing the right-handed neutrino to experience extra spacetime dimensions naturally permits the left-handed neutrino mass to be power-law suppressed relative to the masses of the other fermions. This occurs due to the power-law running of the neutrino Yukawa couplings, and therefore does not require a heavy scale for the right-handed neutrino. Second, we show that a higher-dimensional analogue of the seesaw mechanism may also be capable of generating naturally light neutrino masses without the introduction of a heavy mass scale. Third, we show that such a higher-dimensional seesaw mechanism may even be able to explain neutrino oscillations without neutrino masses, with oscillations induced indirectly via the masses of the Kaluza-Klein states. Fourth, we point out that even when higher-dimensional right-handed neutrinos are given a bare Majorana mass, the higher-dimensional seesaw mechanism surprisingly replaces this mass scale with the radius scale of the extra dimensions. Finally, we also discuss a possible new mechanism for inducing lepton-number violation by shifting the positions of D-branes in Type I string theory.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Recent theoretical developments have shown that extra spacetime dimensions can lower the fundamental GUT, Planck, and string scales.	background 1.00	0.04	0.02	asserted 0.99
s1	However, recent evidence for neutrino oscillations suggests the existence of light non-zero neutrino masses, which in turn suggests the need for a heavy mass scale via the seesaw mechanism.	background 0.92	0.03	0.03	hedged possibility 0.95
s2	In this paper, we make several observations in this regard.	contribution 0.94	0.31	0.02	unclear 0.91
s3	First, we point out that allowing the right-handed neutrino to experience extra spacetime dimensions naturally permits the left-handed neutrino mass to be power-law suppressed relative to the masses of the other fermions.	result 0.69	0.89	0.30	asserted 0.54
s4	This occurs due to the power-law running of the neutrino Yukawa couplings, and therefore does not require a heavy scale for the right-handed neutrino.	interpretation 0.70	0.70	0.22	asserted 1.00
s5	Second, we show that a higher-dimensional analogue of the seesaw mechanism may also be capable of generating naturally light neutrino masses without the introduction of a heavy mass scale.	result 0.58	0.91	0.33	hedged possibility 0.92
s6	Third, we show that such a higher-dimensional seesaw mechanism may even be able to explain neutrino oscillations without neutrino masses, with oscillations induced indirectly via the masses of the Kaluza-Klein states.	result 0.74	0.89	0.17	hedged possibility 0.96
s7	Fourth, we point out that even when higher-dimensional right-handed neutrinos are given a bare Majorana mass, the higher-dimensional seesaw mechanism surprisingly replaces this mass scale with the radius scale of the extra dimensions.	result 0.94	0.89	0.12	asserted 0.88
s8	Finally, we also discuss a possible new mechanism for inducing lepton-number violation by shifting the positions of D-branes in Type I string theory.	contribution 0.98	0.73	0.04	hedged possibility 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.66.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Typical one-loop diagram that can induce power-law

**Figure 2.** Tree-level diagram showing the generation of an effe

**Figure 3.** (a) Eigenvalue solutions to (2.34), represented a

**Figure 4.** Higher-dimensional neutrino oscillations in the

**Figure 5.** Eigenvalue solutions to (4.3), represented as tho

**Figure 6.** Higher-dimensional neutrino oscillations, even

Figures reproduced from arXiv:hep-ph/9811428 by the authors.

References

Works cited (29)

[1]

K.R. Dienes, E. Dudas, and T. Gherghetta, Phys. Lett. B436 (1998) 55 [ hep-ph/9803466]; Nucl. Phys. B537 (1999) 47 [ hep-ph/9806292]; hep-ph/9807522

View on Pith Pith review arXiv 1998
[2]

N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, hep-ph/9803315; hep-ph/9807344; I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, hep-ph/9804398

View on Pith Pith review arXiv
[3]

E. Witten, Nucl. Phys. B471 (1996) 135

View on Pith 1996
[4]

J.D. Lykken, Phys. Rev. D54 (1996) 3693

View on Pith 1996
[5]

G. Shiu and S.-H.H. Tye, hep-th/9805157

View on Pith Pith review arXiv
[6]

C. Bachas, hep-ph/9807415

View on Pith Pith review arXiv
[7]

P.C. Argyres, S. Dimopoulos, and J. March-Russell, hep-th/9808138

View on Pith Pith review arXiv
[8]

K.R. Dienes, E. Dudas, T. Gherghetta, and A. Riotto, hep-ph/9809406 (to appear in Nucl. Phys. B)

View on Pith Pith review arXiv
[9]

N. Arkani-Hamed, S. Dimopoulos, and J. March-Russell, hep-th/9809124

View on Pith Pith review arXiv
[10]

K. Benakli and S. Davidson, hep-ph/9810280

View on Pith Pith review arXiv
[11]

D.H. Lyth, hep-ph/9810320; N. Kaloper and A. Linde, hep-th/9811141

View on Pith Pith review arXiv
[12]

M. Lanzagorta and G.G. Ross, Phys. Lett. B349 (1995) 319; D. Ghilencea and G.G. Ross, hep-ph/9809217; S.A. Abel and S.F. King, hep-ph/9809467

View on Pith Pith review arXiv 1995
[13]

I. Antoniadis, S. Dimopoulos, A. Pomarol, and M. Quir´ os, hep-ph/9810410. 35

View on Pith Pith review arXiv
[14]

R. Sundrum, hep-ph/9805471; hep-ph/9807348; L. Randall and R. Sundrum, hep-th/9810155

View on Pith Pith review arXiv
[15]

I. Antoniadis, Phys. Lett. B246 (1990) 377; I. Antoniadis, C. Mu˜ noz, and M. Quir´ os,Nucl. Phys. B397 (1993) 515; I. Antoniadis and K. Benakli, Phys. Lett. B326 (1994) 69; I. Antoniadis, K. Benakli, and M. Quir´ os, Phys. Lett. B331 (1994) 313; A. Pomarol and M. Quir´ os, hep-ph/9806263

View on Pith Pith review arXiv 1990
[16]

G.F. Giudice, R. Rattazzi, and J.D. Wells, hep-ph/9811291; E.A. Mirabelli, M. Perelstein, and M.E. Peskin, hep-ph/9811337; T. Han, J.D. Lykken, and R.-J. Zhang, hep-ph/9811350; J.L. Hewett, hep-ph/9811356

View on Pith Pith review arXiv
[17]

Z. Kakushadze and S.-H.H. Tye, hep-th/9809147; K. Benakli, hep-ph/9809582; C.P. Burgess, L.E. Ib´ a˜ nez, and F. Quevedo,hep-ph/9810535; S. Nussinov and R. Shrock, hep-ph/9811323; N. Arkani-Hamed and S. Dimopoulos, hep-ph/9811353; Z. Berezhiani and G. Dvali, hep-ph/9811378

View on Pith Pith review arXiv
[18]

J.C. Pati, hep-ph/9807315; hep-ph/9811442

View on Pith Pith review arXiv
[19]

P. Ramond, hep-ph/9809401

View on Pith Pith review arXiv
[20]

F. Wilczek, hep-ph/9809509

View on Pith Pith review arXiv
[21]

Y. Fukuda et al. , hep-ex/9807003

View on Pith Pith review arXiv
[22]

M. Gell-Mann, P. Ramond, and R. Slansky, in Supergravity (edited by P. van Nieuwenhuizen and D.Z. Freedman), North-Holland, Amsterdam (19 79); T. Yanagida, in Proceedings of the Workshop on Uniﬁed Theories and Baryon Number in the Universe (edited by A. Sawada and A. Sugamoto), K.E.K. preprint 79-18 (1979); R.N. Mohapatra and G. Senjanovic, Phys. Rev. Let...

View on Pith 1979
[23]

K.R. Dienes and J. March-Russell, Nucl. Phys. B479 (1996) 113 [hep-th/9604112]; K.R. Dienes, Nucl. Phys. B488 (1997) 141 [ hep-ph/9606467]

View on Pith Pith review arXiv 1996
[24]

For a review, see K.R. Dienes, Phys. Reports 287 (1997) 447 [ hep-th/9602045]

View on Pith Pith review arXiv 1997
[25]

K.S. Babu and R.N. Mohapatra, Phys. Rev. Lett. 74 (1995) 2418

View on Pith 1995
[26]

S. Dimopoulos and J. March-Russell, private communication; S. Dimopoulos, talk at SUSY ’98 conference (July 1998). 36

View on Pith 1998
[27]

See, e.g., E.G. Gimon and J. Polchinski, Phys. Rev. D54 (1996) 1667; E.G. Gimon and C.V. Johnson, Nucl. Phys. B477 (1996) 715; M. Berkooz et al. , Nucl. Phys. B475 (1996) 115

View on Pith 1996
[28]

K.S. Babu, J.C. Pati, and F. Wilczek, Phys. Lett. B359 (1995) 351

View on Pith 1995
[29]

R. Hagedorn, Nuovo Cimento Suppl. 3 (1965) 147; ibid 6 (1965) 311; Nuovo Cimento 52A (1967) 1336; ibid 56A (1968) 1027. 37

View on Pith 1965

Forward citations

Cited by 28 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Localized Neutrinos in Two Dark Dimensions
hep-ph 2026-10 accept novelty 7.0 of 10

Localizing sterile neutrinos near the SM brane in two dark dimensions gives realistic Dirac masses with O(1) Yukawa couplings and a shell spectrum of sterile states with masses proportional to sqrt(s) and mixings fall...
The Dark Dimension and the Swampland
hep-th 2022-05 conditional novelty 7.0 of 10

Combining the Swampland distance conjecture with the observed cosmological constant implies one extra dimension of order a micron, a sterile neutrino tower near 2 meV, and a new quantum gravity scale near 10^10 GeV.
Dark Energy from Mass Varying Neutrinos
astro-ph 2003-09 conditional novelty 7.0 of 10

Coupling neutrinos to a light scalar makes the cosmic neutrino background a negative-pressure fluid whose density tracks dark energy, tying the dark energy scale to the neutrino mass.
Relating Dark Dimension Size with Dark Energy via 5D Quintessence Potential and Casimir Energy
hep-th 2026-10 conditional novelty 6.0 of 10

A 5D model with induced gravity can relate the dark dimension size to dark energy, but requires a large number of species and a tuned hierarchy, while other models face insurmountable obstacles.
The Dark Dimension and Majorana Neutrinos
hep-ph 2026-09 conditional novelty 6.0 of 10

Terrestrial neutrino experiments constrain the Dark Dimension scenario, with KATRIN beta decay forcing Yukawa couplings to O(10^{-3}) in the favored parameter window.

Show 23 more citing papers

The FL bound and its phenomenological implications
hep-th 2021-06 conditional novelty 6.0 of 10

Fixing the Festina Lente bound's order-one coefficient to the square root of six and extending it to higher dimensions and rolling scalars yields a lower bound on charged particle masses that forbids an unbroken elect...
A Model for Neutrino and Charged Lepton Masses in Extra Dimensions
hep-ph 2006-03 conditional novelty 6.0 of 10

A 5D model with differently sized fat branes for the three SM families and a bulk Dirac neutrino reproduces charged lepton hierarchy, small non-hierarchical Dirac neutrino masses, and large neutrino mixing.
Family Symmetry and Single Right-Handed Neutrino Dominance in Five Dimensions
hep-ph 2006-03 conditional novelty 6.0 of 10

Five-dimensional versions of the see-saw mechanism can restore single right-handed neutrino dominance in U(1) family symmetry models, with explicit parameter sets matching observed neutrino data.
Schur elimination of brane-localised Higgs mass spectra, and the criteria for the $\epsilon\to0$/$N\to\infty$ non-commutativity
hep-ph 2026-09 conditional novelty 5.0 of 10

A brane-localised Higgs reaches the KK tower through a rank-two coupling, so the tower can be eliminated by a Schur complement, and the order-of-limits ambiguity reduces to one sum taking value 1/2 or 0.
A geometric origin for the radiative neutrino portal to secluded dark matter
hep-ph 2026-07 conditional novelty 5.0 of 10

A brane-separated fifth dimension gives a geometric origin for the vanishing tree-level Higgs-hidden-scalar portal, leaving seesaw neutrinos to generate a small radiative portal that makes secluded dark matter viable ...
Searching for a Dark Dimension Right-handed Neutrino in KATRIN
hep-ph 2025-09 unverdicted novelty 5.0 of 10

The paper derives KATRIN signatures for a 5D right-handed neutrino and shows that a large part of the compactification scale, bulk mass, and Yukawa coupling parameter space lies within experimental sensitivity, with m...
Primordial Black Holes are 5D
hep-ph 2025-06 conditional novelty 5.0 of 10

In the Dark Dimension scenario, quantum gravity bounds force all viable primordial black hole formation channels to yield five-dimensional, slowly evaporating black holes, with lifetimes up to about 10^13 years.
Two Micron-Size Dark Dimensions
hep-th 2025-01 conditional novelty 5.0 of 10

Two micron-size dark dimensions are consistent with observations only if the compact space has no isometries and the normalcy temperature is fine-tuned to about 2 MeV.
Can heavy neutrinos dominate neutrinoless double beta decay?
hep-ph 2012-09 conditional novelty 5.0 of 10

Once one-loop light neutrino masses are included, heavy sterile neutrinos can dominate neutrinoless double beta decay only for a hierarchical spectrum straddling 100 MeV, or in a small quasi-degenerate window near 5 GeV.
Fermionic Kaluza-Klein mode mixing in braneworlds
hep-th 2026-06 unverdicted novelty 4.0 of 10

Perturbations induce KK mode mixing resolved by SVD of the Dirac mass matrix, with parity-odd operators preserving Z2 symmetry and parity-even operators breaking it to polarize wavefunctions toward the brane.
Dark Dimension Right-handed Neutrinos Confronted with Long-Baseline Oscillation Experiments
hep-ph 2026-01 unverdicted novelty 4.0 of 10

T2K and NOvA data exclude dark-dimension neutrino models with bulk mass |c| < ~0.1 eV for a 10 µm extra dimension.
Neutrino Portal to Extra Dimensions: Unified Origin of Dark Radiation, Dark Matter, and Neutrino Decay
hep-ph 2025-06 reject novelty 4.0 of 10

A model with a bulk sterile neutrino and a Majoron claims to unify dark matter, dark radiation, and invisible neutrino decay, but its quoted parameter space is internally inconsistent.
Physics at a future Neutrino Factory and super-beam facility
hep-ph 2007-10 conditional novelty 4.0 of 10

A common-tool simulation ranks the Neutrino Factory, beta-beam and super-beam against each other, and finds the winner depends on how large the unmeasured mixing angle theta-13 turns out to be.
Breaking Free from the Swampland of Impossible Universes through the DESI Portal
astro-ph.CO 2026-05 unverdicted novelty 3.0 of 10

DESI data indicating evolving dark energy may allow string theory to describe observed universes without violating swampland constraints on constant dark energy.
Do neutrinos dream in 5D? Towards a comprehensive extra-dimensional neutrino phenomenology
hep-ph 2025-12 unverdicted novelty 3.0 of 10

Surveys neutrino masses and mixing in 5D large extra dimension scenarios across four mass-generation cases and derives constraints from oscillation data.
Snowmass White Paper: Beyond the Standard Model effects on Neutrino Flavor
hep-ph 2022-03 accept novelty 3.0 of 10

A community roadmap arguing that neutrino oscillation, scattering, and telescope experiments spanning meV to EeV energies can test sterile states, non-standard interactions, decay, and CPT or Lorentz violation over th...
Sterile Neutrino Dark Matter
hep-ph 2018-07 accept novelty 3.0 of 10

Sterile neutrinos in the keV range remain a viable dark matter candidate, but the minimal version produced only by neutrino mixing is squeezed into a narrow, soon-testable window by X-ray and structure-formation data.
The Phenomenology of Right Handed Neutrinos
hep-ph 2013-03 accept novelty 3.0 of 10

Right-handed neutrinos with masses from eV to the GUT scale can plausibly address neutrino oscillations, baryogenesis, dark matter, and dark radiation, but the evidence remains indirect and scenario-dependent.
Dark Energy and the Symbiosis Between Micro-physics and Cosmology (Naturally)
hep-th 2025-08 unverdicted novelty 2.0 of 10

A review arguing that technical naturalness, powered by low-energy scale invariance and supersymmetric extra dimensions, is the most promising route to solving the cosmological constant problem.
Neutrino Mass and Mixing with Modular Symmetry
hep-ph 2023-11 accept novelty 2.0 of 10

Modular symmetry can organize neutrino masses and lepton mixing through a single modulus and modular forms, but the reviewed models still fit several parameters to data.
Neutrinoless Double Beta Decay
hep-ph 2015-07 accept novelty 2.0 of 10

Neutrinoless double beta decay, if seen, would establish lepton number violation, and this review maps how its short-range variants link to LHC signals and to the baryon asymmetry.
CP Violation and Neutrino Oscillations
hep-ph 2007-10 accept novelty 2.0 of 10

The paper reviews leptonic CP violation in neutrino oscillations and projects that T2K and NOvA can probe the Dirac phase for sufficiently large θ13, with matter effects and parameter degeneracies as the main complications.
Neutrino masses and mixings and...
hep-ph 2006-06 accept novelty 2.0 of 10

The review consolidates the evidence that solar and atmospheric neutrino deficits are explained by three-neutrino oscillations with large mixing angles, and surveys remaining anomalies and theoretical models.

How the literature uses it

69 arXiv papers cite this in 117 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 80 sentences without a confident label

Builds on it 3 papers

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
The Yukawa couplings will induce a Dirac mass connecting the left- and the right-handed neutrinos and we will find the eigenvalues (Dirac or Majorana) of the effective mass matrix in an extra dimensional generalization of the 4D see-saw mechanism [See Ref. [ref] for a previous non-supersymmetric analysis.].

Dirac Vs. Majorana Neutrino Masses From a TeV Interval · Fermionic solutions · 0.87
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

Uses its method or tool 2 papers

Formally, the mass eigenvalues and the eigenvectors of $M_i$ in Eq. ([ref]) are obtained from the diagonalization of the matrix $R_ED^2 M_i^†M_i$ by assuming a maximum integer value for the KK-modes $k_max$ and then taking the limit $k_max→∞$ [ref] .

A Short Travel for Neutrinos in Large Extra Dimensions · Formalism · 0.96
Now we can find the eigenvalues of the infinite mass matrix ([ref]) by computing its characteristic polynomial [ref]

Dirac Vs. Majorana Neutrino Masses From a TeV Interval · Effective action for neutrinos · 0.89

Compares with it 3 papers

The result is in agreement with what had been found in previous works, e.g. in Ref. [ref] .

Do neutrinos dream in 5D? Towards a comprehensive extra-dimensional neutrino phenomenology · Dirac Brane Term · 0.98
Let us remark that this mechanism to obtain very light Dirac neutrinos is slightly different to that considered in [ref] .

Towers and Hierarchies in the Standard Model from Emergence in Quantum Gravity · Dirac Neutrino masses and an extra dimension · 1.00
It is essentially different to higher-dimensional theories where right-handed neutrinos propagate in a five-dimensional space and conformal invariance is broken by an IR brane [ref] .

Conformal Neutrinos: an Alternative to the See-saw Mechanism · Introduction · 0.90

Cites it as background 26 papers

A Dirac fermion $Ψ^α$ in five dimensions can be decomposed into two component spinors (Weyl fermions), $ψ_L$ and $ψ_R$ and after the extra dimension is compactified a natural coupling with $ν_L$ emerges [ref] and, as a result, Dirac neutrino masses are obtained [ref] .

A Short Travel for Neutrinos in Large Extra Dimensions · Formalism · 0.84
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
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

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

K.R. Dienes, E. Dudas, and T. Gherghetta, Phys. Lett. B436 (1998) 55 [ hep-ph/9803466]; Nucl. Phys. B537 (1999) 47 [ hep-ph/9806292]; hep-ph/9807522

View on Pith Pith review arXiv 1998

[2] [2]

N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, hep-ph/9803315; hep-ph/9807344; I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, hep-ph/9804398

View on Pith Pith review arXiv

[3] [3]

E. Witten, Nucl. Phys. B471 (1996) 135

View on Pith 1996

[4] [4]

J.D. Lykken, Phys. Rev. D54 (1996) 3693

View on Pith 1996

[5] [5]

G. Shiu and S.-H.H. Tye, hep-th/9805157

View on Pith Pith review arXiv

[6] [6]

C. Bachas, hep-ph/9807415

View on Pith Pith review arXiv

[7] [7]

P.C. Argyres, S. Dimopoulos, and J. March-Russell, hep-th/9808138

View on Pith Pith review arXiv

[8] [8]

K.R. Dienes, E. Dudas, T. Gherghetta, and A. Riotto, hep-ph/9809406 (to appear in Nucl. Phys. B)

View on Pith Pith review arXiv

[9] [9]

N. Arkani-Hamed, S. Dimopoulos, and J. March-Russell, hep-th/9809124

View on Pith Pith review arXiv

[10] [10]

K. Benakli and S. Davidson, hep-ph/9810280

View on Pith Pith review arXiv

[11] [11]

D.H. Lyth, hep-ph/9810320; N. Kaloper and A. Linde, hep-th/9811141

View on Pith Pith review arXiv

[12] [12]

M. Lanzagorta and G.G. Ross, Phys. Lett. B349 (1995) 319; D. Ghilencea and G.G. Ross, hep-ph/9809217; S.A. Abel and S.F. King, hep-ph/9809467

View on Pith Pith review arXiv 1995

[13] [13]

I. Antoniadis, S. Dimopoulos, A. Pomarol, and M. Quir´ os, hep-ph/9810410. 35

View on Pith Pith review arXiv

[14] [14]

R. Sundrum, hep-ph/9805471; hep-ph/9807348; L. Randall and R. Sundrum, hep-th/9810155

View on Pith Pith review arXiv

[15] [15]

I. Antoniadis, Phys. Lett. B246 (1990) 377; I. Antoniadis, C. Mu˜ noz, and M. Quir´ os,Nucl. Phys. B397 (1993) 515; I. Antoniadis and K. Benakli, Phys. Lett. B326 (1994) 69; I. Antoniadis, K. Benakli, and M. Quir´ os, Phys. Lett. B331 (1994) 313; A. Pomarol and M. Quir´ os, hep-ph/9806263

View on Pith Pith review arXiv 1990

[16] [16]

G.F. Giudice, R. Rattazzi, and J.D. Wells, hep-ph/9811291; E.A. Mirabelli, M. Perelstein, and M.E. Peskin, hep-ph/9811337; T. Han, J.D. Lykken, and R.-J. Zhang, hep-ph/9811350; J.L. Hewett, hep-ph/9811356

View on Pith Pith review arXiv

[17] [17]

Z. Kakushadze and S.-H.H. Tye, hep-th/9809147; K. Benakli, hep-ph/9809582; C.P. Burgess, L.E. Ib´ a˜ nez, and F. Quevedo,hep-ph/9810535; S. Nussinov and R. Shrock, hep-ph/9811323; N. Arkani-Hamed and S. Dimopoulos, hep-ph/9811353; Z. Berezhiani and G. Dvali, hep-ph/9811378

View on Pith Pith review arXiv

[18] [18]

J.C. Pati, hep-ph/9807315; hep-ph/9811442

View on Pith Pith review arXiv

[19] [19]

P. Ramond, hep-ph/9809401

View on Pith Pith review arXiv

[20] [20]

F. Wilczek, hep-ph/9809509

View on Pith Pith review arXiv

[21] [21]

Y. Fukuda et al. , hep-ex/9807003

View on Pith Pith review arXiv

[22] [22]

M. Gell-Mann, P. Ramond, and R. Slansky, in Supergravity (edited by P. van Nieuwenhuizen and D.Z. Freedman), North-Holland, Amsterdam (19 79); T. Yanagida, in Proceedings of the Workshop on Uniﬁed Theories and Baryon Number in the Universe (edited by A. Sawada and A. Sugamoto), K.E.K. preprint 79-18 (1979); R.N. Mohapatra and G. Senjanovic, Phys. Rev. Let...

View on Pith 1979

[23] [23]

K.R. Dienes and J. March-Russell, Nucl. Phys. B479 (1996) 113 [hep-th/9604112]; K.R. Dienes, Nucl. Phys. B488 (1997) 141 [ hep-ph/9606467]

View on Pith Pith review arXiv 1996

[24] [24]

For a review, see K.R. Dienes, Phys. Reports 287 (1997) 447 [ hep-th/9602045]

View on Pith Pith review arXiv 1997

[25] [25]

K.S. Babu and R.N. Mohapatra, Phys. Rev. Lett. 74 (1995) 2418

View on Pith 1995

[26] [26]

S. Dimopoulos and J. March-Russell, private communication; S. Dimopoulos, talk at SUSY ’98 conference (July 1998). 36

View on Pith 1998

[27] [27]

See, e.g., E.G. Gimon and J. Polchinski, Phys. Rev. D54 (1996) 1667; E.G. Gimon and C.V. Johnson, Nucl. Phys. B477 (1996) 715; M. Berkooz et al. , Nucl. Phys. B475 (1996) 115

View on Pith 1996

[28] [28]

K.S. Babu, J.C. Pati, and F. Wilczek, Phys. Lett. B359 (1995) 351

View on Pith 1995

[29] [29]

R. Hagedorn, Nuovo Cimento Suppl. 3 (1965) 147; ibid 6 (1965) 311; Nuovo Cimento 52A (1967) 1336; ibid 56A (1968) 1027. 37

View on Pith 1965