Hierarchies without Symmetries from Extra Dimensions

Martin Schmaltz; Nima Arkani-Hamed

REVIEW

Hierarchies without Symmetries from Extra Dimensions

Nima Arkani-Hamed, Martin Schmaltz

High Energy Physics - Phenomenology · Submitted 20 Mar 1999 · 17 references

Pith's verdict: The overlap mechanism is right and the paper knows its own weak point; the mass-hierarchy claim is a framework, not a fit, and the APV remark is the one place it overreaches.

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arXiv IDhep-ph/9903417 (version 1)

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CitationMartin Schmaltz, Nima Arkani-Hamed. "Hierarchies without Symmetries from Extra Dimensions." arXiv:hep-ph/9903417 (1999). https://pith.science/paper/3KZUUIHU

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Editor's note

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This is the paper that made split fermions a working idea, and it holds up. The core observation — localize chiral zero modes at different points in a thick wall, and every coupling between them becomes a Gaussian overlap — is simple, correct, and generalizes far beyond what they do here. The derivations are things you can check on a napkin: the zero-mode profile (Eq. 11), the Yukawa overlap (Eq. 16), the proton-decay overlap (Eq. 19). Section 3.3's position-space rederivation, where the propagator into the bulk is literally the zero-mode wave function evaluated at the interaction point, is the best part of the paper and the reason the result survives loop corrections. That argument is worth the read on its own. The KK non-universality prediction in Section 4 is a genuine, model-independent consequence, not a fit, and it is the part that made people take TeV-scale extra dimensions seriously as a flavor probe. The reader's ACCEPT is right, and the stress-test's no-objection call is basically right too, with one correction: the Eq. (10) sign slip is real. With a† = -∂5 + Φ, the condition a†|L,0⟩ = 0 gives exp(+∫Φ), not exp(-∫Φ); the normalizable mode is annihilated by a. The operator algebra in Eq. (7) is fine, so it is a one-sentence typo, but it is there. Where I would push back on the paper rather than the review: the mass-hierarchy claim never touches the CKM matrix. Overlaps give you a Yukawa matrix as a product of Gaussians, and getting the observed mixing angles requires the up and down sectors to be misaligned in a specific way. The paper is silent on this, and it is not a small omission for a paper whose title is about hierarchies. Second, the atomic parity violation paragraph asserts the sign of the KK contribution and then picks the wall thickness to match the 2.5σ discrepancy. That is the one place the paper reaches past its evidence, and it is peripheral enough that it does not damage the rest. The 'no delocalized fermions lighter than M*' postulate in 3.3 is honestly stated and I would not hold it against them. Who should read it: anyone working on extra dimensions, flavor model building, or composite/Higgs-sector wave-function overlap — the logic transfers directly. Send it to referees; it earned that.

Referee report

Significance

If the mechanism holds, it is a genuinely useful addition to the model-building toolkit: it converts the fermion mass hierarchy and proton stability from problems requiring flavor or baryon-number symmetries into questions of higher-dimensional geography, and it does so with elementary, checkable Gaussian integrals rather than a fitted ansatz. The paper is commendably explicit about what it is and is not doing — it states that it drops power-law matching factors (§3), that the mass hierarchy is a 'framework' rather than a fit, and that the domain-wall profile is destabilized by fermion backreaction at a rate that can be suppressed (footnote on p. 4). The model-independent prediction of non-universal KK gauge couplings (§4, Eqs. (29)–(32)) is falsifiable at the LHC or NLC and is the kind of sharp, geometry-driven signature that makes the scenario worth taking seriously; the observation that the first KK mode can be leptophobic or baryophobic at nodes of its wave function is a concrete, testable statement. The position-space rederivation of §3.3 is a real consistency check, not a restatement, and the connection to Kaplan's domain-wall fermions is apt. The paper also correctly notes a

Major objections (3)

[Abstract (s3) and §1 vs. §3.3] The headline claim of proton stability 'without imposing symmetries' (abstract:s3, and the corresponding passage in §1) is stronger than what §3.3 actually establishes. There the authors state explicitly that the exponential overlap suppression can be bypassed by a delocalized light fermion with baryon- and lepton-number-violating couplings (Figure 6), whose amplitude is suppressed only by e^{-m_f L}, and they conclude: 'we must postulate that there are no delocalized fermions lighter than M*.' That postulate is an additional assumption about the ultraviolet spectrum, not a consequence of the geometry, and it belongs in the abstract and introduction alongside the proton-stability claim. As written, a reader of the abstract alone would not know that the proton result rests on a stated assumption about bulk fermion masses. I would ask the authors to qualify the abstract and the §1 summary accordingly, and, if possible, to indicate what class of ultraviolet completions (e.g., string constructions with bulk matter) would or would not satisfy the postulate.
[§4, Eqs. (27)–(32), and §3.1] The non-universal KK couplings that are the paper's signature are diagonal in the localization basis, g_n(i) ∝ cos(k_n x_i), whereas the four-dimensional Yukawa matrix is built from overlaps e^{-µ²(x_i-x_j)²/2} and is therefore off-diagonal in that same basis. Diagonalizing the mass matrix to reach the physical fermion states will rotate the KK coupling matrix and generically generate flavor-changing couplings of the KK gauge bosons, including KK gluons. The manuscript does not estimate these. Given that the wall thickness is taken near the TeV scale and that the quark separations are O(1) in units of the wave-function width, the KK-gluon contribution to ΔM_K and ε_K could be a real constraint on the same parameter region that produces the LHC signal. I would ask for at least an order-of-magnitude estimate, or an explicit statement of why the effect is under control (for example, an alignment or degeneracy argument). This is the one place where the phenomenological section and the flavor section are not joined up, and it bears on whether the framework survives its own TeV-scale regime.
[§2.2, Eq. (13)] The entire hierarchy is controlled by the five-dimensional masses m_i through r = m/(2µ²), and the exponent is µ²r²/2. A shift δm in a five-dimensional fermion mass changes the exponent by r δm/2, so a radiative correction δm of order µ moves a Yukawa coupling by roughly an order of magnitude, and a correction of order 10µ would destroy the hierarchy entirely. The paper asserts in §2.2 that 'the relative distances which control the size of coupling constants in the effective 4-d theory stay fixed' once interactions are turned on, but does not discuss what protects the m_i. Since a five-dimensional Dirac mass is not protected by a chiral symmetry, this is the naturalness question that the 'hierarchies without symmetries' framing has to answer. The authors hint in §3.3 that the m_ij could arise from a GUT-breaking VEV pointing in the B−L or hypercharge direction; that suggestion should be developed, or the radiative stability of the m_i should be addressed directly, before the mechanism can be said to explain the hierarchy rather than parametrize it.

Minor objections (9)

[§2.1, Eqs. (8) and (10)] There is a labeling inconsistency between the operators and the zero-mode solutions. With a = ∂5 + Φ and a† = −∂5 + Φ as defined in Eq. (8), the condition a†|L,0⟩ = 0 gives φ ∝ exp(+∫Φ), whereas Eq. (10) lists ⟨x5|L,0⟩ ∝ exp(−∫Φ). The normalizable mode in the profile of Figure 2 is annihilated by a, not by a†. The final results are unaffected, but the sentence introducing Eq. (10) should be corrected so that the operator assignments match the displayed solutions.
[§2.1, below Eq. (8)] The text states that for Φ = 2µ²x5 the operators a and a† become the usual SHO operators 'up to a normalization factor √2µ'. Direct computation gives a factor of 2µ, not √2µ. This is cosmetic but worth correcting for readers who check the algebra.
[§3.1, Eq. (16)] Carrying out the Gaussian integral with the normalized wave function of Eq. (11) gives an overall factor of µ^{-1/2} multiplying e^{-µ²r²/2}, which is dropped in Eq. (16). This is consistent with the stated policy of not tracking powers of scales, but a parenthetical note to that effect at Eq. (16) would prevent the reader from thinking the prefactor was lost by accident.
[§3.5, Eq. (25), and §3.2] Section 3.5 concludes that M* is bounded below by roughly 100 TeV, while §3.2 illustrates the proton-decay suppression with M* ~ 1 TeV. The two statements are not inconsistent, but the shift from the TeV-scale gravity motivation of refs. [1]–[6] to a 100 TeV cutoff deserves a more prominent remark, since it changes what the scenario is a solution to. A sentence in §1 or §5 acknowledging that the hierarchy problem itself is not addressed by this mechanism would help the reader place the result.
[§4, atomic parity violation paragraph] The claim that the KK contribution 'has the correct sign' and that 'the correct magnitude can be obtained if the wall thickness is ~1 TeV' is argued qualitatively from Figure 8 for the sign but is not backed by a numerical estimate for the magnitude. Either a short estimate should be supplied or the sentence should be softened to a statement of principle.
[§3.4, Eq. (23)] The neutrino-mass discussion correctly notes that the Majorana operator is unsuppressed and sketches three remedies, but the (B−L)-breaking-VEV option in footnote ‖ is stated only in one line. Since this is the one place where the 'no symmetries' logic does not automatically give a safe answer, a slightly fuller treatment of at least one option would strengthen the section.
[References] Reference [17] (L.E. Ibanez) is listed as Phys. Lett. B181 (1996) 269; volume B181 corresponds to 1987, so the year appears to be a typo. Reference [14] (Dvali and Shifman) is cited in the text as the origin of the gauge-field localization mechanism but is not among the numbered references in the list as printed; please check the numbering.
[Figures 4 and 5] The position-space proton-decay diagrams are rendered as dense character grids in the present version and are difficult to read. They should be redrawn as clean figures in the final version, since they carry the physical argument of §3.3.
[§1 and §2.2] There are several typographical errors in the introduction and §2.2, including 'extensions submof the SM', 'the SM fermion are are localized', and 'Our approach to to the fermion mass hierarchy similar in spirit'. A careful copy-edit pass is needed.

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The paper

The paper claims

Small couplings need not come from symmetries: if the fermions of the Standard Model sit at different points inside a thick wall in an extra dimension, their wave functions barely overlap, and that overlap alone can generate the fermionmass

The reading

The paper attacks a piece of standard lore: that any tiny coupling in a low-energy theory — a light fermion's Yukawa coupling, or the coupling that would let the proton decay — must be explained by a symmetry of the short-distance theory. The authors argue the lore fails once the Standard Model fields live on a thick wall in an extra dimension and the fermions are 'stuck' at different places inside that wall. Each fermion then has a narrow Gaussian profile in the fifth dimension, and any interaction that must connect two fermions at different locations is suppressed by the exponentially small overlap of those profiles, roughly $e^{-c(ar)^2}$ for separation $r$. If this is right, the fermion mass hierarchy and proton stability both stop being symmetry statements and become statements about higher-dimensional geography, with no symmetry imposed anywhere in the underlying theory. The authors also note a sharp, model-independent consequence: because the gauge fields spread across the whole wall, their Kaluza-Klein excitations couple differently to fermions at different locations, so a collider can in principle map where each fermion sits.

What carries the argument

The load-bearing object is the zero mode of a five-dimensional Dirac fermion in a domain-wall background, $S = ��d^4x��dx_5 ��[i��!!/��_4 + i��_5��_5 + ��(x_5)]��$. The operators $a = ��_5 + ��$ and $a^�� = -��_5 + ��$ turn the $x_5$-dependent part of the Dirac equation into a supersymmetric quantum-mechanics problem, so left- and right-handed eigenfunctions pair up except at zero eigenvalue, and exactly one chiral zero mode is normalizable, with profile $�� e^{-��^2x_5^2}$. Every suppression in the paper is then a Gaussian overlap integral: the Yukawa coupling is $��d x_5 ��_l(x_5)��_{e^c}(x_5) = e^{-��^2r^2/2}$, and the proton-decay coefficient is $��d x_5 (��_q)^3��_l$. The same wave functions, inserted into the Kaluza-Klein expansion of the gauge field, give position-dependent couplings $��_n �� (s_i)$ that differ from fermion to fermion.

Extended reading notes

Core claim

The central claim is that exponentially small four-dimensional couplings follow from exponentially small wave-function overlaps, with no symmetry in the fundamental theory. Coupling a five-dimensional fermion to a scalar whose expectation value has a domain-wall profile gives a single chiral zero mode localized at the zero of that scalar, with a Gaussian profile of width $1/��$; giving the fermion a bulk mass $m$ shifts its Gaussian to $x_5 = m/(2��^2)$. Two such fermions separated by $r$ then have a Yukawa coupling proportional to $e^{-��^2r^2/2}$, and a baryon- and lepton-number-violating operator built from four such fields is suppressed by $e^{-3��^2r^2/4}$. With $��r$ ranging from about 1 to 10, the same mechanism produces the top Yukawa, the electron Yukawa, and a proton lifetime far beyond existing bounds, even with the fundamental cutoff near a TeV. The paper stresses that chiral symmetry was maximally broken in the short-distance theory; an approximate chiral symmetry emerges at long distances purely because the fields are apart.

Load-bearing premise

The proton-stability claim rests on a postulate the authors state rather than derive: that there are no fermions propagating freely through the wall with mass below the ultraviolet cutoff, since such a fermion would mediate proton decay with only $e^{-m_fL}$ suppression instead of the much stronger Gaussian overlap factor.

Editorial extensions

If this is right

The charged-fermion mass hierarchy becomes a set of distances: order-one separations in units of the inverse wall width give the top Yukawa, larger separations give the electron Yukawa, and the observed ratios are reproduced for $��r$ between roughly 1 and 5.
Proton decay is exponentially suppressed even with a cutoff near a TeV and with baryon and lepton number maximally violated at short distances, because the quarks and leptons must be dragged to a common point in the fifth dimension to interact.
The Kaluza-Klein excitations of the gauge fields couple non-universally to the Standard Model fermions, with couplings proportional to the KK wave functions evaluated at each fermion's location, so some excitations can be leptophobic or baryophobic.
If the wall thickness is near $1\,\mathrm{TeV}^{-1}$, resonance cross sections at the LHC or NLC distinguish $1^+1^- \to 1^+1^-$ from $1^+1^- \to 2^+2^-$ by a factor $\cos^2(k_n(s_1-s_2))$, allowing the fermion separations to be measured.
The authors note that with their boundary conditions the product of quark and lepton couplings to the first KK excitation has the opposite sign to the Standard Model, giving an atomic-parity-violation contribution that moves in the direction of the reported discrepancy.

Reading between the lines

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

If the mechanism is right, the Yukawa matrix is literally a table of pairwise distances, so fitting the observed three-generation masses and mixing angles becomes a geometry-reconstruction problem with the CKM and PMNS matrices as by-products of where the fermions sit.
The same exponential factor should appear for any operator built from fields at separated points, so flavour-changing neutral currents and other higher-dimension operators get a correlated pattern of suppressions set by the same positions — a joint fit rather than independent tunings.
Because the suppression is a property of defects in general, the argument should transfer to fermions localized on orbifold fixed points or D-branes, where the same $e^{-r^2}$ factor between twisted sectors is expected; that makes the scenario testable in string constructions that do not use a field-theoretic domain wall.
The proton-stability claim is conditional on the bulk fermion spectrum, so a collider discovery of a light fermion propagating in the wall would count against the picture even if the Gaussian overlaps themselves were confirmed.

Original abstract

It is commonly thought that small couplings in a low-energy theory, such as those needed for the fermion mass hierarchy or proton stability, must originate from symmetries in a high-energy theory. We show that this expectation is violated in theories where the Standard Model fields are confined to a thick wall in extra dimensions, with the fermions "stuck" at different points in the wall. Couplings between them are then suppressed due to the exponentially small overlaps of their wave functions. This provides a framework for understanding both the fermion mass hierarchy and proton stability without imposing symmetries, but rather in terms of higher dimensional geography. A model independent prediction of this scenario is non-universal couplings of the Standard Model fermions to the ``Kaluza-Klein'' excitations of the gauge fields. This allows a measurement of the fermion locations in the extra dimensions at the LHC or NLC if the wall thickness is close to the TeV scale.

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, 4,961 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.67 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

It is commonly thought that small couplings in a low-energy theory, such as those needed for the fermion mass hierarchy or proton stability, must originate from symmetries in a high-energy theory. We show that this expectation is violated in theories where the Standard Model fields are confined to a thick wall in extra dimensions, with the fermions "stuck" at different points in the wall. Couplings between them are then suppressed due to the exponentially small overlaps of their wave functions. This provides a framework for understanding both the fermion mass hierarchy and proton stability without imposing symmetries, but rather in terms of higher dimensional geography. A model independent prediction of this scenario is non-universal couplings of the Standard Model fermions to the ``Kaluza-Klein'' excitations of the gauge fields. This allows a measurement of the fermion locations in the extra dimensions at the LHC or NLC if the wall thickness is close to the TeV scale.

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	It is commonly thought that small couplings in a low-energy theory, such as those needed for the fermion mass hierarchy or proton stability, must originate from symmetries in a high-energy theory.	background 1.00	0.03	0.04	asserted 0.61
s1	We show that this expectation is violated in theories where the Standard Model fields are confined to a thick wall in extra dimensions, with the fermions "stuck" at different points in the wall.	contribution 0.74	0.88	0.54	asserted 1.00
s2	Couplings between them are then suppressed due to the exponentially small overlaps of their wave functions.	result 0.53	0.62	0.11	asserted 1.00
s3	This provides a framework for understanding both the fermion mass hierarchy and proton stability without imposing symmetries, but rather in terms of higher dimensional geography.	interpretation 0.96	0.70	0.72	asserted 0.88
s4	A model independent prediction of this scenario is non-universal couplings of the Standard Model fermions to the ``Kaluza-Klein'' excitations of the gauge fields.	result 0.76	0.78	0.17	asserted 1.00
s5	This allows a measurement of the fermion locations in the extra dimensions at the LHC or NLC if the wall thickness is close to the TeV scale.	interpretation 0.77	0.44	0.08	hedged possibility 0.80

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 v1

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.** Profile of Standard Model fermion wave functions (vertical axis) in the extra dimensions (horizontal axis). The fermions freely propagate in 3+1 dimensions (not shown) and are “stuck” at different locations in the extra dimensions. The gauge and Higgs fields’ wave functions occupy the whole width of the thick wall. Direct couplings between the fermions are then suppressed by the exponentially small overlap of their wave functions. If – as shown here – quarks and leptons live on opposite ends of the wall profile protons become essentially stable. The hierarchy of Yukawa couplings…

**Figure 2.** Profile of the scalar domain wall field Φ in the x5 dimension. A chiral zero mode fermion is localized at the zero of Φ. to a four dimensional chiral fermion stuck at the zero of Φ [12]. A convenient representation for the 4 × 4 gamma matrices in five dimensions is γ i =

**Figure 3.** Yukawa coupling: the Gaussian wave functions of the fermions l and e c overlap only in an exponentially small region, suppressing the effective Yukawa coupling exponentially. suppressed because the two fields are separated in space. The coupling is then proportional to the exponentially small overlap of the wave functions. Note that we did not impose any chiral symmetries in the fundamental theory to obtain this result: the coupling κ can violate the electron chiral symmetry by O(1). Even with chiral symmetry maximally broken in the fundamental theory, we obtain an approximate…

**Figure 4.** Tree-level proton decay diagram, drawn in position space for the fifth dimension. The quarks stuck at one end of the wall and the lepton stuck at the other end propagate to some interior point s where they interact via the higher-dimensional QQQL operator. The “free” propagator to go to a point in the bulk is given by the value of the (Gaussian) zero-mode wave function at that point. quarks are getting more massive as they move into the bulk, the propagator from the plane where they live into the bulk is suppressed. Intuitively, for each slice between x5 and x5 + δx5, a Yukawa…

**Figure 5.** General proton decay diagram including higher order effects. The blobs on propagators denotes the all-order propagators, and the blob on the vertex denotes the corrected vertex. The corrected propagator is nothing other than the corrected zero-mode wave function. The corrected vertex is still local on scales larger than the width of the fermion wave function. This diagram is therefore well-approximated by the overlap between the corrected wave functions of the quark and lepton zero modes, which gives the enormous suppression of proton decay. implies that grand unification at a…

**Figure 6.** The exponential suppression of proton decay through small wave function overlaps can be avoided if there is a delocalized light fermion f with baryon and lepton number violating couplings as seen above. This amplitude is only suppressed by the Yukawa factor e −mf L. In order to avoid too large a rate for proton decay without imposing any symmetries, we must postulate that there are no delocalized fermions lighter than M∗. argument, we have to recall that it was Planck-scale sized wormholes giving the supposedly O(1) symmetry violating effects. Since these have a mass above the cutof

**Figure 7.** KK exchange diagrams. Suppose that we are sitting on the s-channel resonance for particleantiparticle annihilation mediated by the n’th KK modes of A and B. Then the relative cross section for 1+1 − → 1 +1 − (and 2+2 − → 2 +2 −) as calculated from the diagrams in

**Figure 8.** Since the wave functions of the usual SM gauge fields (zero modes) are flat in the extra dimensions, they have identical couplings to the quarks and leptons stuck at opposite ends of the wall, as required by gauge invariance. On the other hand, since the first KK excitation has a non-trivial wave function, its couplings can be different. In particular, the product of quark and lepton gauge couplings to the first KK excitation has the opposite sign as for the SM. opens a new arena for model-building, where a specific arrangement of the fermions in extra dimensions, and not familiar…

Figures reproduced from arXiv:hep-ph/9903417 by the authors.

References

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K. Dienes, E. Dudas and T. Gherghetta, Phys. Lett. B436, 55 (1998); hep-ph/9806292. ††The e−r2 suppression of Yukawa couplings between twisted sector ﬁel ds at diﬀerent orbifold ﬁxed points has been known for some time, see e.g. [1 7]. 23

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N. Arkani-Hamed and S. Dimopoulos, hep-ph/9811353

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D.B. Kaplan, Phys. Lett. B288 (1992) 342, hep-lat/9206013

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The idea of localizing fermions on a wall in a higher dime nsional space goes back to V. A. Rubakov and M.E. Shaposhnikov, Phys. Lett. B125 (1983) 136; which relied on the index theorem in soliton back - ground R. Jackiw and C. Rebbi, Phys. Rev. D13 (1976) 3398; E. Wein- berg, Phys. Rev. D24 (1981) 2669. Our discussion follows D.B. Kaplan and M. Schmaltz,...

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G. Dvali and M. Shifman, Phys. Lett. B399 (1997) 60

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N. Arkani-Hamed and M. Schmaltz, hep-th/9812010

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L.E. Ibanez, Phys. Lett. B181 (1996) 269. 24

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A Dark-Dimension Origin of Geometric Inelastic Dark Matter: The LUX-ZEPLIN High-Recoil Event and Multi-Target Tests
hep-ph 2026-09 conditional novelty 6.0 of 10

A pseudo-Dirac dark matter model with mass splitting generated by the Dark Dimension can explain the LZ high-recoil event and predicts distinctive multi-target signatures.
Conjugate Boundary Conditions, Kaluza-Klein Fermions, and an Extended Seesaw Model
hep-th 2026-07 conditional novelty 6.0 of 10

CBC zero modes are Majorana while free nonzero KK modes form Dirac fermions via accidental U(1); an extended seesaw then sources LNV from bulk CBC-chiral interactions rather than the Majorana mass.
Maximal Abelian Flavor Symmetries
hep-ph 2026-06 unverdicted novelty 6.0 of 10

MAFS describes 15 flavor observables in SU(5) and SO(10) GUTs using 5 or 3 fitted small parameters at factor-of-two accuracy, implying large neutrino mixings and approximate leptogenesis without extra parameters in SU(5).
The dark dimension, proton decay, and the length of the M-theory interval
hep-th 2025-10 conditional novelty 6.0 of 10

Proton decay limits force the M-theory interval in heterotic E8×E8 compactifications to be R ≲ 2.7×10^-28 m, ruling it out as a micron-sized dark dimension.
String Theory and Grand Unification Suggest a Sub-Microelectronvolt QCD Axion
hep-ph 2025-05 conditional novelty 6.0 of 10

String-theoretic axions consistent with grand unification and proton decay are predicted to have masses in the 3e-11 to 1e-8 eV window, with at most 47 axions in the Kreuzer-Skarke ensemble.
Electroweak constraints on flavorful effective theories
hep-ph 2015-03 accept novelty 6.0 of 10

Electroweak precision data constrain 20 flavor-diagonal and several flavor-changing new-physics couplings to the Z and W bosons, with limits ranging from about 10^-4 to order one depending on the fermion.
Flavourful Production at Hadron Colliders
hep-ph 2011-05 accept novelty 6.0 of 10

Diquark scalars with flavour-antisymmetric couplings evade tree-level flavour-changing neutral currents and electric dipole moments, so they can couple at order unity to light quarks and be searched for as dijet reson...
The Flavor of the Composite Pseudo-Goldstone Higgs
hep-ph 2008-04 accept novelty 6.0 of 10

Flavor constraints in warped composite-Higgs models push the Kaluza-Klein gluon mass above about 33 TeV, stronger than the 21 TeV Randall-Sundrum bound, implying anarchic warped flavor is implausible.
Warped/Composite Phenomenology Simplified
hep-ph 2006-12 accept novelty 6.0 of 10

A two-sector effective field theory reproduces the collider phenomenology of warped/composite models using only the Standard Model and its first heavy excitations, with UV-finite Higgs fine-tuning and explicit precisi...
Computing Yukawa Couplings from Magnetized Extra Dimensions
hep-th 2004-04 accept novelty 6.0 of 10

Yukawa couplings in magnetized toroidal compactifications are computed exactly as overlap integrals of theta-function wavefunctions, giving a closed-form answer controlled by complex structure and Wilson lines.
Phenomenological aspects of 10D SYM theory with magnetized extra dimensions
hep-ph 2012-11 conditional novelty 5.5 of 10

A magnetized-torus compactification of 10D SYM yields the MSSM with three generations, and at a hand-tuned moduli point it fits quark, lepton, and neutrino masses while predicting that only the first-torus shape modul...
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 ...
Interactions between different Kaluza-Klein modes in brane world
hep-th 2024-12 unverdicted novelty 5.0 of 10

The Orthonormal Completeness Hypothesis implies universal interactions between KK modes in brane-world effective actions for U(1) gauge and fermion fields.
Sterile neutrino portal to Dark Matter I: The $U(1)_{B-L}$ case
hep-ph 2016-06 conditional novelty 5.0 of 10

A global U(1)_{B-L} dark sector with a fermionic WIMP and a Majoron mediator can reproduce the observed dark matter abundance while evading Higgs and direct detection bounds, with annihilation into sterile neutrinos p...
A global fit of top quark effective theory to data
hep-ph 2015-06 conditional novelty 5.0 of 10

A global fit of nine dimension-six effective operators to top quark production data from the LHC and Tevatron finds every Wilson coefficient consistent with zero at 95% confidence.
String geometry phenomenology
hep-th 2025-11 reject novelty 4.0 of 10

Minimizing a potential from string geometry theory in a simple heterotic model relates the compactification scale to flux quanta and gives Mc ≤ 6.7×10^16 GeV for three generations.
Constraints on two-lepton, two quark operators
hep-ph 2010-08 accept novelty 4.0 of 10

Updated flavour-dependent bounds on two-lepton, two-quark contact operators are tabulated, and a Cheng-Sher-style Yukawa hierarchy estimate shows rare kaon decays are the observables closest to current sensitivity.
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.
Flavor Physics Constraints for Physics Beyond the Standard Model
hep-ph 2010-02 accept novelty 3.0 of 10

Existing flavor-changing and CP-violating measurements force TeV-scale new physics to have a highly non-generic flavor structure, and the review catalogs those bounds, the Minimal Flavor Violation escape route, and th...
Dark Matter and Collider Phenomenology of Universal Extra Dimensions
hep-ph 2007-01 accept novelty 3.0 of 10

A comprehensive review of universal extra dimensions argues that the lightest Kaluza-Klein particle is a viable thermal dark matter candidate and lays out the collider, direct-detection, and indirect-detection signatu...
Rich Phenomenology from Simple Ingredients: A Review of Confining Dark Sectors
hep-ph 2026-06 unverdicted novelty 2.0 of 10

Review of confining dark sectors summarizing dark matter candidates, abundance mechanisms, discovery channels, and applications to the abundance similarity puzzle.
Baryon Number Violation: From Nuclear Matrix Elements to BSM Physics
hep-ph 2025-04 unverdicted novelty 2.0 of 10

A workshop report that maps the current experimental and theoretical landscape for baryon number violation, from proton decay and neutron-antineutron oscillation searches to the EFT, lattice QCD, and astrophysical con...
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.
TASI Lectures on Extra Dimensions and Branes
hep-ph 2004-04 accept novelty 1.0 of 10

A pedagogical survey of brane and extra-dimension model building, covering large flat dimensions, split fermions, gaugino mediation, orbifold symmetry breaking, and the Randall-Sundrum warped solution with its gravito...

How the literature uses it

160 arXiv papers cite this in 189 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 · 115 sentences without a confident label

Uses its method or tool 2 papers

The model in Ref. [ref] made use of the mechanism of wave function overlap along the large extra dimension [ref] , which was originally employed to justify the smallness of Dirac neutrino mass [ref] .

Quark-lepton mass unification at TeV scales · Introduction · 0.83
Then, the quark and lepton masses can be obtained by an overlap integral of zero mode functions [ref] .

New Models of $SU(6)$ Grand Gauge-Higgs Unification · Higgs potential and Higgs mass · 0.81

Compares with it 4 papers

This idea is similar to Yukawa interactions from wave function overlap in theories with extra dimensions [ref] .

Flavor structure from misalignment of inner products in noncommutative geometry · Introduction · 0.85
To a certain extent, this approach to the flavor problem is similar to [ref] .

The cosmological constant problem in heterotic-M-theory and the orbifold of time · The scale invariant lagrangian from string theory · 1.00
The effective theory of the flavour obtained from the FCW resembles with the ones obtained from the theories with extra spatial dimensions upon compactification [ref] .

Clockwork Mechanism for Flavour Hierarchies · Flavoured Clockworks · 0.93

Cites it as background 63 papers

In theories with extra dimensions, wavefunction overlaps between $Φ$ and $H$ control the size of the 4D Yukawa couplings [ref] .

Naturally Flavorful Supersymmetry at the LHC · Framework I — Higgsphobic supersymmetry breaking · 0.88
If the SM fermions and gauge bosons are allowed to propagate in the bulk of the extra dimension [ref] , the RS model is in addition a promising theory of flavor [ref] .[A list of further relevant references can be found in [ref] .] Since the fermion zero modes are exponentially localized either in the UV (light SM fermions) or IR (heavy SM fermions), the effective Yukawa couplings resulting from their wave-function overlap with the Higgs boson naturally exhibit exponential hierarchies.

Top-Quark Forward-Backward Asymmetry in Randall-Sundrum Models Beyond the Leading Order · Cross Section and Asymmetry in RS Models · 0.90
It developed out of the suggestion that the basic RS1 warped hierarchy mechanism could operate with most of the SM fields propagating in the 5D bulk spacetime [ref] , that flavor hierarchies from extra-dimensional wavefunction overlaps [ref] could arise attractively in the warped setting [ref] [ref] [ref] , and out of studies of the implications of the host of precision experimental tests [ref] .

SUSY Splits, But Then Returns · Non-SUSY Warped Models from the CFT View · 0.83

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.

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