Naive Dimensional Analysis and Supersymmetry

Markus A. Luty

REVIEW

Naive Dimensional Analysis and Supersymmetry

Markus A. Luty

High Energy Physics - Phenomenology · Submitted 3 Jun 1997 · 19 references

Pith's verdict: The paper that gives strongly coupled SUSY its 4π bookkeeping; the F ~ Λ²/(4π) rule and the §4 spurion weights are the parts people actually use, and they hold up.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 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 →

· 2 major objections · 6 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/9706235 (version 1)

Pith IDYFKX53RU, Pith's permanent record of this paper and its review

CitationMarkus A. Luty. "Naive Dimensional Analysis and Supersymmetry." arXiv:hep-ph/9706235 (1997). https://pith.science/paper/YFKX53RU

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

Short version: this is where the 4π counting for strongly coupled supersymmetry gets written down, and the two things people actually use — F ~ Λ²/(4π) and the spurion weight rules in §4 — are both here and both fine. The method is heuristic and Luty says so; that is the honest limitation, not a hidden one. It deserves a referee, mostly to check the §5.3 algebra and to push the caveat earlier than §6. On the stress-test's §5.1 worry: it does not land. Eq. 5.2 already carries the 1/16π² — F²/Λ³ with F ~ Λ²/(4π) gives Λ/(16π²), which is the standard gauge-mediation answer with M_mess ~ Λ. And Eq. 5.4's identification is λ ~ 4π, m_q ~ Λ, not M_mess ~ Λ/(4π). The gaugino mass estimate is consistent. Who should read it: anyone estimating operator coefficients or soft masses in a strongly coupled hidden sector. Would cite: yes. Peer review: yes, though a referee would mostly be checking the §5.3 algebra and asking for the heuristic caveat to be moved up front.

Referee report

Significance

The paper is a careful and useful methods paper. Its strengths are concrete: the linear sigma model argument of §2.1 is exact at tree level and makes the origin of the 4π's transparent; the O'Raifeartaigh rescaling of §3.1-3.2 is explicit algebra that can be checked line by line; the result is cross-checked against the QCD relation Λ ~ 4πf and against global symmetry breaking (Eq. 3.21); and the applications in §5 yield parametric predictions that are in principle falsifiable (a rich resonance spectrum near Λ ~ 10 TeV in the direct-coupling scenario, and the (λ/4π)⁴ suppression of Eq. 5.16). The paper is also candid about the status of its central premise, stating in §6 that the arguments are 'at best heuristic.' The spurion generalization of §4 is the part most likely to be reused by others, and the phenomenological estimates of §5.1 and §5.3 are the parts most likely to be quoted.

Major objections (2)

[§3.2, Eq. (3.19); §6, Eq. (6.1); footnote 6] The central result F ~ Λ²/(4π) follows from setting the loop-counting parameter ℓ ~ 1/(16π²F²) of Eq. (3.19) to one at the matching scale. The paper is explicit that this is heuristic (§6) and notes in §2.2 that in a large-N theory the analogous relation becomes Λ ~ 4πf/√N, but footnote 6 defers the large-N generalization of the supersymmetric case to 'elsewhere,' and Eqs. (3.10) and (6.1) are stated without qualification. Since the abstract's headline claim (abstract:s4) is likewise unqualified, a sentence in §3.2 or §6 identifying the class of theories for which ℓ ~ 1 — namely those with no additional small parameter such as 1/N or a weak coupling — would make the stated domain of validity match the derivation. This is a request for a scope statement, not a claim that the derivation is wrong.
[§4, Eq. (4.6)] The general 'weight' rule stated after Eq. (4.6) — that a spurion J coupled to an operator of weight w enters the effective lagrangian with coefficient F^{w−2}, with strong chiral fields and W^α of weight 1 and covariant derivatives of weight 0 — is justified only by the sentence 'It is straightforward to analyze general operators in the same way.' Because the systematic inclusion of small parameters and couplings to weakly-interacting fields is one of the paper's advertised contributions (abstract:s1), one explicit worked example containing a gauge field strength or a superspace covariant derivative would substantiate the rule and demonstrate that the weight-0 assignment for derivatives is consistent with the superspace measure. As written, the rule is a conjecture supported by the d = 2 case that agrees with Ref. [12].

Minor objections (6)

[References] Reference [7] (Affleck, Dine, and Seiberg, Nucl. Phys. B256, 557 (1985)) does not appear to be cited anywhere in the text; it should either be cited at the appropriate point or removed from the list.
[§5.1, Eqs. (5.2) and (5.4)] The apparent factor-of-4π difference between Eq. (5.2) and the standard gauge-mediation estimate m_λ ~ (g²/16π²)(⟨F_S⟩/⟨S⟩) is resolved by the identification λ ~ 4π in Eq. (5.4), which gives ⟨S⟩ ~ Λ/(4π) and ⟨F_S⟩ ~ Λ²/(4π). It would help to say this explicitly, since λ ~ 4π means the messenger sector invoked in the comparison is not weakly coupled and the agreement is parametric rather than a controlled matching.
[§2.1, Eq. (2.3)] The coefficient 1/(2m²_σ) of the four-derivative term is presented as the tree-level result; a sentence stating whether this coefficient is exact at tree level or only schematic would help the reader follow the subsequent claim that the scaling holds to all orders.
[§3.1, Eq. (3.5)] The '−1' inside |½λ̂φ̂²_Φ − 1|² and the ellipsis in the kinetic terms are not explained; a short note identifying which terms were dropped and where the constant term originates would make the rescaling check easier to follow.
[§5.3, Eq. (5.16)] The (λ/4π)⁴ scaling of the S₀ scalar mass should be accompanied by an indication of which terms in K̂_dyn generate it, since the quadratic term in K̂_dyn only shifts the wavefunction normalization and does not by itself produce an S-dependent mass at that order.
[§5.2, Eq. (5.7)] The statement that the confined description is strongly coupled at Λ but renormalizes logarithmically to weak coupling in the infrared is central to the top-quark discussion that follows; a reference or a one-line argument would strengthen it.

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

The paper

The paper claims

Luty argues that when supersymmetry breaks in a strongly coupled sector with no small parameters, the Goldstino decay constant is not of order $F$ of order $F$ of order $F$ of order $F$ of order $F$ of order $F$ of order $F$ of order $F$ of

The reading

The paper asks a bookkeeping question with physical teeth: when a strongly coupled theory has no small parameters, how do the factors of $4π$ sit in the low-energy effective lagrangian? Luty's answer, extended from ordinary 'naive dimensional analysis' to supersymmetric theories, is that the effective lagrangian must be written as $L_{eff} = (1/16π^2) L̂_{eff}$, with every coupling in $L̂_{eff}$ of order one in units of the strong scale $Λ$. The concrete payoff is a statement about dynamical supersymmetry breaking: if supersymmetry is broken by strong dynamics with no small parameters, the Goldstino decay constant is $F ∼ Λ^2/(4π)$, not $Λ^2$. That single factor of $4π$ propagates into every mass formula for superpartners, so estimates of the scale of new physics shift by roughly an order of magnitude. The paper then shows how to insert small couplings and weakly interacting fields into this counting, and works three phenomenological examples where the factors of $4π$ change the answer.

What carries the argument

The engine is a rescaling argument plus a criterion. Rescale superfields by the supersymmetry-breaking order parameter and superpotential couplings by matching powers of $F$, so that the whole classical lagrangian is $F^2$ times a lagrangian whose couplings are all order one in units of the heavy mass scale; then $1/F^2$ plays the role of $1/ħ$, and loops are suppressed by $ℓ ∼ 1/(16π^2 F^2)$. 'Strong coupling' is then defined as loop democracy — all loop orders equally important, i.e. $ℓ ∼ 1$ — which converts the rescaling into the numerical statement $Λ^2 ∼ 4π F$. A spurion analysis extends this to small couplings and weakly coupled fields: a source $J$ coupled to a strong operator of weight $w$ enters the effective lagrangian with coefficient $F^{w-2}$, where strong chiral superfields and strong field-strength superfields count as weight one and covariant derivatives as weight zero. This is what lets the author read off gaugino masses, scalar masses, and Yukawa couplings in strongly coupled models without doing the strong dynamics.

Extended reading notes

Core claim

The central claim is that a strongly coupled supersymmetric theory with a single scale $Λ$ and no small parameters produces a low-energy effective theory of the form $L_{eff} = (1/16π^2) L̂_{eff}$, where all couplings in $L̂_{eff}$ are order one in units of $Λ$ (Eq. 6.1). For supersymmetry breaking this gives the Goldstino decay constant $F ∼ Λ^2/(4π)$ (Eq. 3.10), derived by rescaling the chiral superfields $Φ = F Φ̂$ and the superpotential couplings $λ^{(n)} = F^{2-n} λ̂^{(n)}$ so that all nonzero $λ̂^{(n)}$ are order one, which makes the loop-counting parameter $ℓ ∼ 1/(16π^2 F^2)$ (Eq. 3.19); requiring $ℓ ∼ 1$ at the matching scale then fixes $Λ^2 ∼ 4π F$. The same logic applied to a confining theory says that dynamically generated cubic superpotential couplings are of order $4π$, not one, when written in canonically normalized fields, so the confined description is not weakly coupled at $Λ$ but flows to weak coupling in the infrared. Applied to the deformed-moduli-space model, it gives $⟨F_{S_0}⟩ ∼ λΛ^2/(16π^2)$ and scalar masses suppressed by $(λ/4π)^4$.

Load-bearing premise

The load-bearing premise is that 'strongly coupled' can be equated with 'all loop orders equally important,' so the loop-counting parameter $ℓ ∼ 1/(16π^2 F^2)$ is set to one at the matching scale; the author states in the conclusions that the arguments for this counting are at best heuristic.

Editorial extensions

If this is right

In models where standard-model gauge bosons couple directly to strong supersymmetry breaking near the weak scale, the gaugino mass is $m_λ ∼ g^2 I_2(r) F^2/Λ^3 ∼ (g^2 I_2(r)/16π^2) Λ$, so 100 GeV gauginos require $Λ ∼ 10$ TeV, with a spectrum of strong resonances at that scale.
Sfermion masses in the same class of models come out as $m_φ^2 ∼ I_2(r) C_2(r) (g^2/16π^2)^2 Λ^2$, the same parametric size as a minimal messenger sector with $λ ∼ 4π$.
In confining theories, dynamically generated cubic superpotential terms are of order $4π$ in canonically normalized fields, so identifying such a term with the top Yukawa forces the compositeness scale high enough that the coupling can renormalize down to a perturbative value at the weak scale.
In the deformed-moduli-space model, the supersymmetry-breaking order parameter is $⟨F_{S_0}⟩ ∼ λΛ^2/(16π^2)$ and the surviving scalar masses are of order $(λ/4π)^4 Λ$, a suppression of order $10^{-4}$ for moderate $λ$.
More generally, any estimate of a strong-sector coupling made by dimensional analysis in units of $Λ$ should be multiplied by the appropriate power of $1/(4π)$ before being compared with data.

Reading between the lines

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

The counting gives a clean diagnostic for whether a proposed model is genuinely strongly coupled at its matching scale: compute $ℓ$ from the rescaled lagrangian and check whether it is order one. If it is not, the model secretly has a small parameter and the $4π$ factors should be rederived rather than assumed.
Because the argument is about matching at a single scale, it should be checkable in any strongly coupled supersymmetric theory with a dual weakly coupled description, such as Seiberg duality with a large number of colors, where the $1/N$ suppression of the loop-counting parameter is already known and provides a controlled test of the $4π$ bookkeeping.
The suppression $(λ/4π)^4$ found in the deformed-moduli-space example suggests that strong dynamics can generate hierarchically light scalars without fine tuning, which is a mechanism worth checking against the radiatively generated masses that usually spoil such hierarchies.
The same rescaling logic applies to any Goldstone-like mode whose decay constant is set by strong dynamics, so the $Λ^2/(4π)$ result is a template for translating between a strong scale and a decay constant in other non-supersymmetric contexts.

Original abstract

In strongly-coupled theories with no small parameters, there are factors of 4\pi that appear when the couplings of the low-energy effective lagrangian are written in units of the effective cutoff \Lambda. These numerical factors can be explained using "naive dimensional analysis." We extend these ideas to supersymmetric theories, and show how to systematically include small parameters and couplings to weakly-interacting fields. The basic principle is that if the fundamental theory is strongly coupled, then the effective theory must also be strongly coupled at the scale \Lambda. We use our results to analyze several examples where strong supersymmetric dynamics may be relevant for phenomenology. For models that break supersymmetry through strong dynamics with no small parameters, we show that the Goldstino decay constant F is of order \La^{2} / (4\pi). We also consider theories with standard-model gauge bosons coupled directly to strong supersymmetry-breaking dynamics near the weak scale; smoothly-confining theories; and a model that breaks supersymmetry through the mechanism of a deformed moduli space.

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, 5,085 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.93 · compares with prior results 0.22 · 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.

In strongly-coupled theories with no small parameters, there are factors of 4\pi that appear when the couplings of the low-energy effective lagrangian are written in units of the effective cutoff \Lambda. These numerical factors can be explained using "naive dimensional analysis." We extend these ideas to supersymmetric theories, and show how to systematically include small parameters and couplings to weakly-interacting fields. The basic principle is that if the fundamental theory is strongly coupled, then the effective theory must also be strongly coupled at the scale \Lambda. We use our results to analyze several examples where strong supersymmetric dynamics may be relevant for phenomenology. For models that break supersymmetry through strong dynamics with no small parameters, we show that the Goldstino decay constant F is of order \La^{2} / (4\pi). We also consider theories with standard-model gauge bosons coupled directly to strong supersymmetry-breaking dynamics near the weak scale; smoothly-confining theories; and a model that breaks supersymmetry through the mechanism of a deformed moduli space.

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	In strongly-coupled theories with no small parameters, there are factors of 4\pi that appear when the couplings of the low-energy effective lagrangian are written in units of the effective cutoff \Lambda.	background 1.00	0.14	0.08	asserted 1.00
s1	These numerical factors can be explained using "naive dimensional analysis." We extend these ideas to supersymmetric theories, and show how to systematically include small parameters and couplings to weakly-interacting fields.	contribution 0.95	0.88	0.17	asserted 1.00
s2	The basic principle is that if the fundamental theory is strongly coupled, then the effective theory must also be strongly coupled at the scale \Lambda.	method 0.70	0.29	0.24	asserted 0.99
s3	We use our results to analyze several examples where strong supersymmetric dynamics may be relevant for phenomenology.	contribution 0.99	0.87	0.05	hedged possibility 0.78
s4	For models that break supersymmetry through strong dynamics with no small parameters, we show that the Goldstino decay constant F is of order \La^{2} / (4\pi).	result 1.00	0.94	0.38	asserted 1.00
s5	We also consider theories with standard-model gauge bosons coupled directly to strong supersymmetry-breaking dynamics near the weak scale; smoothly-confining theories; and a model that breaks supersymmetry through the mechanism of a deformed moduli space.	contribution 1.00	0.78	0.05	asserted 0.66

What kind of paper the classifier reports this is: theoretical result 0.63 · evidence from proof or derivation 0.64.

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.** Typical diagrams contributing to (a) gaugino masses and (b) scalar masses in theories where fields are coupled weakly to the strongly interacting fields. The shaded blob denotes strong interactions. The term in the fundamental lagrangian that couples the standard-model gauginos 4There are models in the literature in which the electroweak gauge bosons are coupled directly to a supersymmetry breaking sector with a large scale hierarchy [15]. In these models, the scale of strong dynamics Λ is far above the weak scale. 10

Figures reproduced from arXiv:hep-ph/9706235 by the authors.

References

Works cited (19)

[12]

A.G. Cohen, D.B. Kaplan, A.E. Nelson, hep-ph/9607394, Phys. Lett. 388B, 588 (1996)

View on Pith Pith review arXiv 1996
[1]

A. Manohar, H. Georgi, Nucl. Phys. B234, 189 (1984); H. Georgi, Weak Inter- actions and Modern Particle Theory, Benjamin/Cummings, (Menlo Park, 1984); H. Georgi, L. Randall, Nucl. Phys. B276, 241 (1986)

View on Pith 1984
[2]

S. Weinberg, Physica 96A, 327 (1979)

View on Pith 1979
[3]

I. Aﬄeck, M. Dine, N. Seiberg, Phys. Lett. 137B, 187 (1984)

View on Pith 1984
[4]

I. Aﬄeck, M. Dine, N. Seiberg, Phys. Lett. 140B, 59 (1984)

View on Pith 1984
[5]

N. Seiberg, hep-th/9402044, Phys. Rev. D49, 6857 (1994); C. Csaki, M. Schmaltz, W. Skiba, hep-ph/9612207

View on Pith Pith review arXiv 1994
[6]

K.-I. Izawa, T. Yanagida, hep-th/9602180, Prog. Theor. Phys. 95, 829 (1996); K. Intriligator, S. Thomas, hep-th/9603158, Nucl. Phys. B473, 121 (1996)

View on Pith Pith review arXiv 1996
[7]

I. Aﬄeck, M. Dine, and N. Seiberg, Nucl. Phys. B256, 557 (1985)

View on Pith 1985
[8]

See e.g. E. Witten, Ann. Phys. 128, 363 (1980)

View on Pith 1980
[9]

D.V. Volkov, V.P. Akulov, JETP Lett. 16, 438 (1972)

View on Pith 1972
[10]

E. Witten, Nucl. Phys. B202, 253 (1982)

View on Pith 1982
[11]

E. Witten, Phys. Lett. 105B, 267 (1981)

View on Pith 1981
[13]

M. Dine and A.E. Nelson, hep-ph/9303230, Phys. Rev. D48, 1277 (1993); M. Dine, A.E. Nelson, Y. Shirman, hep-ph/9408384, Phys. Rev. D51, 1362 (1995); M. Dine, A.E. Nelson, Y. Nir, Y. Shirman, hep-ph/9507378, Phys. Rev. D53, 2658 (1996)

View on Pith Pith review arXiv 1993
[14]

I. Dasgupta, B.A. Dobrescu, L. Randall, hep-ph/960748 7, Nucl. Phys. B483, 95 (1997)

View on Pith 1997
[15]

E. Poppitz, S.P. Trivedi, hep-ph/9609529, to be publis hed in Phys. Rev. D; N. Arkani-Hamed, J. March-Russell, H. Murayama, hep-ph/9701 286

View on Pith Pith review arXiv
[16]

M.J. Strassler, hep-ph/9510342, Phys. Lett. 376B, 119 (1996); A.E. Nel- son, M.J. Strassler, hep-ph/9607362; M.A. Luty and R.N. Moh apatra, hep- ph/9611343, to be published in Phys. Lett. B. 16

View on Pith Pith review arXiv 1996
[17]

D.B. Kaplan, F. Lepeintre, M. Schmaltz, hep-ph/970541 1

View on Pith
[18]

C.T. Hill, Phys. Rev. D24, 691 (1981); W.A. Bardeen, C.T. Hill, M. Lindner, Phys. Rev. D41, 1647 (1990)

View on Pith 1981
[19]

I. Aﬄeck, M. Dine, N. Seiberg, Nucl. Phys. B241, 493 (1984). 17

View on Pith 1984

Forward citations

Cited by 32 Pith papers

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

From Linear SUSY to Constrained Superfields
hep-th 2009-07 accept novelty 8.0 of 10

The Goldstino of broken supersymmetry lives in a chiral superfield X with X^2 = 0, and light matter and gauge fields obey analogous constraints that remove their heavy superpartners.
General Gauge Mediation
hep-ph 2008-01 accept novelty 8.0 of 10

A single definition and formalism unifies all gauge mediation models and yields model-independent sfermion mass sum rules.
The Minimal Moose for a Little Higgs
hep-ph 2002-06 conditional novelty 8.0 of 10

A two-site, four-link moose model realizes the Higgs as a pseudo-Goldstone boson whose one-loop quadratic divergences are cancelled by same-statistics TeV partners, with the full Higgs potential generated by the top Y...
The Littlest Higgs
hep-ph 2002-06 accept novelty 8.0 of 10

An SU(5)/SO(5) nonlinear sigma model makes the Higgs a pseudo-Goldstone boson whose one-loop quadratic mass divergence is cancelled by a heavy triplet scalar, extra gauge bosons, and a heavy top partner, leaving only ...
Novel Phases of a Baryon-Dense QCD-like Theory
hep-ph 2025-06 conditional novelty 7.0 of 10

Adding a baryon chemical potential to AMSB-deformed s-confining SQCD produces novel finite-density vacua with baryon-number and parity breaking, with both first- and second-order transitions.

Show 27 more citing papers

ALPs Effective Field Theory and Collider Signatures
hep-ph 2017-01 accept novelty 7.0 of 10

A complete next-to-leading chiral effective basis for a singlet axion-like particle is derived, and LHC mono-boson and mono-Higgs searches are shown to probe its couplings to electroweak gauge bosons and the Higgs.
The Minimal Supersymmetric Fat Higgs Model
hep-ph 2003-11 accept novelty 7.0 of 10

The Higgs can be a composite meson of a confining SU(2) gauge theory, raising its mass to 200-450 GeV and relieving the supersymmetric little hierarchy problem without fine-tuning.
Environment-Dependent Annihilation of Axion-Coupled Higgsino Dark Matter
hep-ph 2026-10 conditional novelty 6.0 of 10

A subthreshold axion mediator plus a change in the annihilating Higgsino population makes annihilation environment-dependent, decoupling the solar-neutrino bound from Galactic and terrestrial signals for a few-percent...
Precise predictions for double Higgs production in association with a vector boson in Effective Field Theory
hep-ph 2026-07 conditional novelty 6.0 of 10

First NNLO QCD cross sections for pp→Vhh in SMEFT and HEFT, provided as interpolated coefficients; W±hh K-factors are almost EFT-independent while Zhh is sensitive to gluon-initiated contributions.
ALP-SMEFT Interference
hep-ph 2021-05 conditional novelty 6.0 of 10

A light axion-like particle coupled through dimension-5 operators sources almost the entire set of dimension-6 SMEFT Wilson coefficients at one loop, and the authors tabulate every source term.
The Low-Energy Effective Theory of Axions and ALPs
hep-ph 2020-12 accept novelty 6.0 of 10

A complete renormalization-group and matching calculation, at two loops in gauge couplings and one loop in Yukawa couplings, carries axion-like-particle couplings from the new-physics scale down to a chiral Lagrangian...
Which EFT
hep-ph 2019-02 accept novelty 6.0 of 10

A Higgs-sector effective theory whose Lagrangian is non-analytic in the Higgs doublet reaches strong coupling near 4πv ≈ 3 TeV regardless of how small its cubic-Higgs deformation is, while an analytic one can be pushe...
The Higgs Trilinear Coupling and the Scale of New Physics
hep-ph 2019-02 accept novelty 6.0 of 10

A fractional deviation in the Higgs trilinear coupling implies new physics below about 13 TeV divided by the square root of that deviation, from tree-level unitarity of multi-boson scattering.
Axion Misalignment Driven to the Hilltop
hep-ph 2018-12 conditional novelty 6.0 of 10

A dynamical mechanism drives the QCD axion to the hilltop of its potential during inflation, predicting a decay constant of 3×10^9 to 10^10 GeV.
Collider Probes of Axion-Like Particles
hep-ph 2017-08 accept novelty 6.0 of 10

Exotic on-shell Higgs and Z decays at the LHC can probe axion-like particle couplings to photons and leptons orders of magnitude beyond existing bounds, including the parameter space that could explain the muon g-2 anomaly.
Scheming in the SMEFT... and a reparameterization invariance!
hep-ph 2017-01 conditional novelty 6.0 of 10

A reparameterization invariance in the SMEFT explains the flat directions in global fits to fermion scattering data, and those flat directions are shown to be independent of the input parameter scheme.
Minimal Mirror Twin Higgs
hep-ph 2016-09 conditional novelty 6.0 of 10

Breaking the mirror Z2 symmetry only in the Yukawa couplings is enough to make the Mirror Twin Higgs viable, and it predicts an invisible Higgs branching ratio of a few percent, extra dark radiation near 0.3, and mirr...
Footprints of New Strong Dynamics via Anomaly and the 750 GeV Diphoton
hep-ph 2015-12 conditional novelty 6.0 of 10

A QCD-like confining theory whose singlet pseudo-Goldstone boson decays to two photons through the chiral anomaly can reproduce the 750 GeV diphoton excess, with the rate fixed by anomaly matching.
Peccei-Quinn Symmetry from Dynamical Supersymmetry Breaking
hep-ph 2015-05 conditional novelty 6.0 of 10

Embedding the Peccei-Quinn mechanism in the IYIT model of dynamical supersymmetry breaking, protected by an anomaly-free Z4R symmetry, yields an axion decay constant of order 10^10 GeV and requires five extra 5/5* mat...
Cosmic Signals from the Hidden Sector
hep-ph 2009-05 conditional novelty 6.0 of 10

Composite hidden-sector dark matter at about 10 TeV, decaying via a light axion-like state with a lifetime near 10^26 seconds, reproduces the PAMELA, FERMI, and H.E.S.S. electron and positron data.
Sweet Spot Supersymmetry
hep-ph 2007-05 conditional novelty 6.0 of 10

Supersymmetric models with a gravitino mass near 1 GeV and a mediation scale near the GUT scale simultaneously avoid the flavor, CP, mu, moduli, and proton-decay problems, and predict a long-lived stau NLSP.
Supersymmetry, Naturalness, and Signatures at the LHC
hep-ph 2006-02 accept novelty 6.0 of 10

A large top-squark A term removes the fine-tuning of minimal supersymmetry, and the resulting light Higgsinos leave a short, P-wave dilepton edge at the LHC that the authors show can be measured in simulated 30 invers...
The Art of Counting: a reappraisal of the HEFT expansion
hep-ph 2025-11 unverdicted novelty 5.0 of 10

HEFT admits two consistent power counting schemes, one with a single low-energy scale v and one with two scales v < f, each allowing systematic truncation of operators and amplitudes for any normalization choice.
Primordial black holes as dark matter and gravitational waves from single-field polynomial inflation
astro-ph.CO 2020-01 conditional novelty 5.0 of 10

Single-field polynomial inflation with a tuned near-inflection point can generate primordial black holes comprising all dark matter, plus an induced gravitational-wave signal within reach of LISA and DECIGO.
Axion Misalignment Driven to the Bottom
hep-ph 2018-12 conditional novelty 5.0 of 10

An assumed approximate CP symmetry plus a Higgs-driven enhancement of the QCD scale during inflation can relax the axion to a minimum close to today's, making the misalignment angle small without fine-tuning.
On the Validity of the Effective Field Theory Approach to SM Precision Tests
hep-ph 2016-04 accept novelty 5.0 of 10

Limits on dimension-6 EFT operators should be reported as functions of the kinematic energy cut, because only then can the truncation error of the EFT expansion be assessed and the result reinterpreted across UV models.
Heavy Dark Matter Through the Higgs Portal
hep-ph 2008-01 conditional novelty 5.0 of 10

Including non-perturbative Sommerfeld enhancement of the annihilation rate lets a Higgs-portal singlet fermion saturate the measured dark matter density at masses up to about 25 TeV, well above the usual thermal-relic...
Phenomenology of the Little Higgs Model
hep-ph 2003-01 conditional novelty 5.0 of 10

The littlest Higgs model predicts heavy SU(2) gauge bosons visible at the LHC up to several TeV, a possibly lighter U(1) boson whose signal depends on unfixed fermion charges, a heavy top partner, and a doubly charged Higgs.
Gaugino Mediated Supersymmetry Breaking
hep-ph 1999-11 conditional novelty 5.0 of 10

Supersymmetry breaking communicated through bulk gauge and Higgs fields, with matter sequestered on a brane, yields a natural, flavor-safe superpartner spectrum distinct from no-scale supergravity.
Counting 4 pi 's in Strongly Coupled Supersymmetry
hep-ph 1997-06 accept novelty 5.0 of 10

The authors give explicit rules for counting factors of 4 pi in strongly coupled supersymmetric effective theories and apply them to composite models and supersymmetry breaking.
The Standard Model Effective Field Theory and Next to Leading Order
hep-ph 2016-10 conditional novelty 3.0 of 10

The paper argues that leading-order SMEFT fits to LHC data are insufficient at current and projected precision, and specifies a Warsaw-basis leading-order construction designed to be extended to next-to-leading order.
TASI Lectures on Effective Field Theories
hep-ph 2003-08 accept novelty 2.0 of 10

A pedagogical survey of effective field theory techniques, covering perturbative matching, renormalization group running, non-relativistic effective theories, and applications to compactified and warped extra dimensions.

How later papers used it

60 later papers cite it

Evidence: substantial. 59 of the citing papers share no author with it, and 23 of those carry a confident label from Pith's citation classifier.

Pith read 12 of the 75 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

7 later papers by other authors are listed below: 7 used its method or tool.

Uses its method or tool 7 of 22 papers with this label

Used the rules of naive dimensional analysis from this paper, with factors of N included, to estimate the sizes of its parameters.

A Conformal Gauge Mediation and Dark Matter with Only One Parameter (2010) · 0.82 · paraphrased: the licence does not allow quoting
Used naive dimensional analysis from this paper to estimate the sizes of the coefficients in the superpotential and the field VEVs.

Dark matter from dynamical SUSY breaking (2010) · 1.00 · paraphrased: the licence does not allow quoting
Used the naive dimensional analysis method of this paper, which assumes the confined theory is strongly coupled, to estimate the Kähler potential normalization.

Decaying Dark Matter Baryons in a Composite Messenger Model (2008) · 1.00 · paraphrased: the licence does not allow quoting
Adopted the naive dimensional analysis of this paper to estimate the masses of SUSY particles.

Strongly Interacting Gauge Mediation at the LHC (2008) · 0.98 · paraphrased: the licence does not allow quoting
Used the naive dimensional analysis of this paper.

Low-Scale Gauge Mediation and Composite Messenger Dark Matter (2009) · 0.97 · paraphrased: the licence does not allow quoting
Took advantage of naive dimensional analysis from this paper because the Kähler potential cannot be determined from holomorphy alone.

A light Higgs scenario based on the TeV-scale supersymmetric strong dynamics (2012) · 0.99 · paraphrased: the licence does not allow quoting
Estimated the coupling of the cubic term as κ ∼ 4π by using naive dimensional analysis from this paper.

SUSY Higgs Mass and Collider Signals with a Hidden Valley (2015) · 0.93 · paraphrased: the licence does not allow quoting

How the literature uses it

57 arXiv papers cite this in 73 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 · 40 sentences without a confident label

Uses its method or tool 23 papers

[Whatever the value of $ℓ$ is, one may write down a planar diagram so as to avoid $1/N$ suppressions.] The model is very strongly coupled [ref] , then using the rules of naive dimensional analysis [ref] with factors of $N$'s included (and assuming $N_C, N_Q$ and $N_P$ are all of the same order, say $N$), we may have $|m_P| ∼Ł$, $N_C g_h^2/16π^2 ∼1$, and $łS^j̃_ i ∼(Ł+Ł^2 ^2) ^̣j̃_ i$.

A Conformal Gauge Mediation and Dark Matter with Only One Parameter · Conformal gauge mediation · 0.82
By solving $∂_|α| V=0$ and $∂_|M|V=0$ order by order in powers of the SUSY-breaking scale $m$, we find the potential is minimized at θ_α=π, θ_M=0, |α|= m/|λ_1|^2/N_f≃m/4π, |M̂|= Λ/|λ_1|^1/N_f≃Λ/√(4π) , and at this minimum the potential value is V_min= -N_f m^2 Λ^2 |λ_1|^-2/N_f≃- N_f m^2 Λ^2/4π , where NDA implies $λ_1≃(4π)^N_c/2$ [ref] .

On the Derivation of Chiral Symmetry Breaking in QCD-like Theories and S-confining Theories · $rank(M)=N_f$ · 0.86
To address this question, notice that there are non-calculable contributions to the effective Kähler potential of the singlet $S$ from the strong interactions below the scale $Λ$, [equation] Here, we have used the “naive dimensional analysis” [ref] , and we expect that the non-calculable contribution $δK(x)$ has no small parameter.

Minimal Direct Gauge Mediation · Dynamical supersymmetry breaking/messenger sector · 0.86

Compares with it 1 paper

Our results are compatible with the ones obtained earlier in e.g. [ref] , our new output is the derivation of a general set of simple rules which are also able to account for irrelevant interactions.

Naive Dimensional Analysis and Irrelevant Operators · Introduction · 0.86

Cites it as background 4 papers

All explicit references to the underlying theory are introduced via the matching procedure in the standard approach to EFTs and power counting, see Refs. [ref] for reviews.

The Standard Model Effective Field Theory and Next to Leading Order · Introduction to the SMEFT · 0.87
All explicit references to the underlying theory are introduced via the matching procedure in the standard approach to EFTs and power counting, see Refs. [ref] for reviews.

Higgs boson couplings: measurements and theoretical interpretation · The bottom-up approach · 0.82
There is a canonical interpretation of this concept that runs through Refs. [ref] and many other works.

The Standard Model as an Effective Field Theory · Power counting · 0.95

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] [12]

A.G. Cohen, D.B. Kaplan, A.E. Nelson, hep-ph/9607394, Phys. Lett. 388B, 588 (1996)

View on Pith Pith review arXiv 1996

[2] [1]

A. Manohar, H. Georgi, Nucl. Phys. B234, 189 (1984); H. Georgi, Weak Inter- actions and Modern Particle Theory, Benjamin/Cummings, (Menlo Park, 1984); H. Georgi, L. Randall, Nucl. Phys. B276, 241 (1986)

View on Pith 1984

[3] [2]

S. Weinberg, Physica 96A, 327 (1979)

View on Pith 1979

[4] [3]

I. Aﬄeck, M. Dine, N. Seiberg, Phys. Lett. 137B, 187 (1984)

View on Pith 1984

[5] [4]

I. Aﬄeck, M. Dine, N. Seiberg, Phys. Lett. 140B, 59 (1984)

View on Pith 1984

[6] [5]

N. Seiberg, hep-th/9402044, Phys. Rev. D49, 6857 (1994); C. Csaki, M. Schmaltz, W. Skiba, hep-ph/9612207

View on Pith Pith review arXiv 1994

[7] [6]

K.-I. Izawa, T. Yanagida, hep-th/9602180, Prog. Theor. Phys. 95, 829 (1996); K. Intriligator, S. Thomas, hep-th/9603158, Nucl. Phys. B473, 121 (1996)

View on Pith Pith review arXiv 1996

[8] [7]

I. Aﬄeck, M. Dine, and N. Seiberg, Nucl. Phys. B256, 557 (1985)

View on Pith 1985

[9] [8]

See e.g. E. Witten, Ann. Phys. 128, 363 (1980)

View on Pith 1980

[10] [9]

D.V. Volkov, V.P. Akulov, JETP Lett. 16, 438 (1972)

View on Pith 1972

[11] [10]

E. Witten, Nucl. Phys. B202, 253 (1982)

View on Pith 1982

[12] [11]

E. Witten, Phys. Lett. 105B, 267 (1981)

View on Pith 1981

[13] [13]

M. Dine and A.E. Nelson, hep-ph/9303230, Phys. Rev. D48, 1277 (1993); M. Dine, A.E. Nelson, Y. Shirman, hep-ph/9408384, Phys. Rev. D51, 1362 (1995); M. Dine, A.E. Nelson, Y. Nir, Y. Shirman, hep-ph/9507378, Phys. Rev. D53, 2658 (1996)

View on Pith Pith review arXiv 1993

[14] [14]

I. Dasgupta, B.A. Dobrescu, L. Randall, hep-ph/960748 7, Nucl. Phys. B483, 95 (1997)

View on Pith 1997

[15] [15]

E. Poppitz, S.P. Trivedi, hep-ph/9609529, to be publis hed in Phys. Rev. D; N. Arkani-Hamed, J. March-Russell, H. Murayama, hep-ph/9701 286

View on Pith Pith review arXiv

[16] [16]

M.J. Strassler, hep-ph/9510342, Phys. Lett. 376B, 119 (1996); A.E. Nel- son, M.J. Strassler, hep-ph/9607362; M.A. Luty and R.N. Moh apatra, hep- ph/9611343, to be published in Phys. Lett. B. 16

View on Pith Pith review arXiv 1996

[17] [17]

D.B. Kaplan, F. Lepeintre, M. Schmaltz, hep-ph/970541 1

View on Pith

[18] [18]

C.T. Hill, Phys. Rev. D24, 691 (1981); W.A. Bardeen, C.T. Hill, M. Lindner, Phys. Rev. D41, 1647 (1990)

View on Pith 1981

[19] [19]

I. Aﬄeck, M. Dine, N. Seiberg, Nucl. Phys. B241, 493 (1984). 17

View on Pith 1984