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arxiv: 2511.23410 · v2 · submitted 2025-11-28 · ✦ hep-ph

The Art of Counting: a reappraisal of the HEFT expansion

Ilaria Brivio , Ramona Gr\"ober , Konstantin Schmid This is my paper

Pith reviewed 2026-05-17 04:15 UTC · model grok-4.3

classification ✦ hep-ph
keywords Higgs Effective Field Theorypower countingHEFTeffective field theoryoperator normalizationHiggs phenomenologytruncation prescriptions
0
0 comments X

The pith

HEFT admits two consistent power counting rules derived by requiring observable predictions to expand in small dimensionless quantities.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reappraises the power counting of the Higgs Effective Field Theory from first principles. It starts from the demand that physical predictions must form a series expansion in small dimensionless quantities. This requirement yields two viable power counting schemes, one when a single low-energy scale v is used and another when two scales v less than f are distinguished. The schemes work for arbitrary choices of how operators are normalized. A sympathetic reader cares because these rules supply concrete prescriptions for truncating the infinite tower of HEFT operators and amplitudes so that theoretical uncertainties remain under control in Higgs analyses.

Core claim

Depending on whether HEFT is formulated in terms of a unique low-energy scale v or in terms of two scales v<f, the requirement that predictions for physical observables follow a series expansion in small, dimensionless quantities identifies two viable power counting rules that can accommodate any operator normalization choice. The authors supply quantitative prescriptions for consistent truncation of operators, amplitudes, and observable contributions and illustrate them with explicit examples.

What carries the argument

The demand that observable predictions expand in small dimensionless quantities, which selects the two viable power counting rules for any operator normalization in HEFT.

If this is right

  • Any operator normalization choice can be accommodated by selecting the appropriate one-scale or two-scale counting rule.
  • Truncation of the HEFT operator set at a given order produces controlled errors in amplitudes.
  • Observable predictions can be organized so that higher-order contributions are systematically smaller.
  • The same counting applies uniformly across different processes once the rule is chosen.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same first-principles logic could be used to re-derive power counting in other effective theories that face normalization ambiguities.
  • Phenomenological fits to collider data could adopt one of the two rules as a default to standardize uncertainty estimates across analyses.
  • Direct comparison of the two rules on the same process would quantify how much the extracted bounds on new physics change with the choice of scale counting.

Load-bearing premise

Requiring that predictions for physical observables follow a series expansion in small dimensionless quantities is sufficient to determine viable power counting rules uniquely for any operator normalization.

What would settle it

An explicit one-loop or tree-level calculation of a specific HEFT-mediated process in a concrete UV completion where the leading correction appears at an order different from the one predicted by either of the two truncation rules.

read the original abstract

We revisit the power counting of the Higgs Effective Field Theory (HEFT) from first principles, by requiring that predictions for physical observables follow a series expansion in small, dimensionless quantities. Depending on whether HEFT is formulated in terms of a unique low-energy scale $v$ or in terms of two scales $v<f$, this approach identifies two viable power counting rules that can accommodate any operator normalization choice. We provide quantitative prescriptions for the consistent truncation of HEFT operators, amplitudes and observable contributions and we illustrate our arguments with a number of examples.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript reappraises the power counting of the Higgs Effective Field Theory (HEFT) from first principles by requiring that predictions for physical observables follow a series expansion in small, dimensionless quantities. Depending on whether HEFT is formulated in terms of a unique low-energy scale v or in terms of two scales v<f, this approach identifies two viable power counting rules that can accommodate any operator normalization choice. Quantitative prescriptions for the consistent truncation of HEFT operators, amplitudes and observable contributions are provided and illustrated with examples.

Significance. If the derivation avoids circularity in identifying the small parameters, the result would provide a flexible, normalization-independent framework for organizing HEFT expansions. This is relevant for precision Higgs phenomenology and BSM searches, as it offers explicit truncation rules rather than ad-hoc choices. The inclusion of quantitative prescriptions and concrete examples is a practical strength that would aid consistent application if the foundational step is secured.

major comments (2)
  1. The central construction begins from the demand that observables admit a series expansion in small dimensionless quantities and uses this to derive the two viable counting rules. However, this step implicitly assumes that the small parameters (such as v/f or loop factors) and their ratios can be identified a priori independently of the counting scheme and operator normalizations. The manuscript should provide an explicit demonstration that this identification does not rely on the very normalizations being accommodated, to substantiate the uniqueness and viability claims.
  2. The distinction between the one-scale (v) and two-scale (v<f) formulations is presented as yielding two viable rules, but the manuscript does not include a direct side-by-side comparison of how these rules produce different truncation orders for the same physical observable (e.g., a Higgs decay width or scattering amplitude). Such a comparison would be needed to show that the rules are not merely reparametrizations of existing schemes.
minor comments (1)
  1. The abstract and introduction use the phrase 'any operator normalization choice' without a precise definition of what constitutes a normalization choice; a short clarifying paragraph or table early in the text would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. The report correctly identifies the core of our reappraisal and its potential utility for precision Higgs phenomenology. Below we respond point by point to the major comments. We will incorporate revisions that directly address the concerns while preserving the first-principles logic of the work.

read point-by-point responses

  1. Referee: The central construction begins from the demand that observables admit a series expansion in small dimensionless quantities and uses this to derive the two viable counting rules. However, this step implicitly assumes that the small parameters (such as v/f or loop factors) and their ratios can be identified a priori independently of the counting scheme and operator normalizations. The manuscript should provide an explicit demonstration that this identification does not rely on the very normalizations being accommodated, to substantiate the uniqueness and viability claims.

    Authors: We agree that an explicit demonstration is needed to remove any appearance of circularity. In the manuscript the small dimensionless quantities are fixed by the physical scales of the problem (e.g., v/E for a process at energy E, or v/f when a new-physics scale f is present) before any operator normalization is chosen. These ratios are determined by kinematics and the underlying theory setup. The counting rules are then obtained by demanding that every contribution to a given observable organizes into a consistent series in those fixed parameters. To make this separation fully transparent we will insert a short subsection (new Section 2.3) that walks through the identification procedure for a concrete example, showing that the small parameters are set by physics independently of how the operators are normalized. This addition will strengthen the uniqueness and viability claims without altering the central construction. revision: yes

  2. Referee: The distinction between the one-scale (v) and two-scale (v<f) formulations is presented as yielding two viable rules, but the manuscript does not include a direct side-by-side comparison of how these rules produce different truncation orders for the same physical observable (e.g., a Higgs decay width or scattering amplitude). Such a comparison would be needed to show that the rules are not merely reparametrizations of existing schemes.

    Authors: We concur that a direct comparison would make the practical distinction between the two schemes clearer. Although the manuscript already supplies quantitative truncation prescriptions and separate examples for each scheme, it lacks a single observable treated under both rules. We will add a new subsection (in the examples section) that applies both counting schemes to the same process, for instance the partial width for h → γγ or the amplitude for WW scattering. The addition will include a table listing the operators retained at a given order, the resulting truncation of the amplitude, and the order at which the observable is predicted in each scheme. This explicit side-by-side analysis will demonstrate that the two rules yield distinct but internally consistent truncations and are therefore not equivalent reparametrizations. revision: yes

Circularity Check

0 steps flagged

Derivation from external series-expansion requirement is self-contained with no circular reductions

full rationale

The paper derives its two viable HEFT power-counting rules directly from the external first-principles requirement that predictions for physical observables must admit a series expansion in small dimensionless quantities. This starting point is independent of the resulting counting schemes and does not reduce to any internal fit, self-definition, or self-citation chain. The abstract explicitly frames the work as revisiting the counting 'from first principles' by imposing the expansion condition, then distinguishing one-scale (v) versus two-scale (v<f) formulations to accommodate arbitrary normalizations. No equations or steps in the provided description equate a derived rule back to its own inputs by construction, and the approach remains falsifiable against external observables without presupposing the normalizations it accommodates.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that observable predictions must admit a series expansion in small dimensionless quantities; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Predictions for physical observables in HEFT must follow a series expansion in small, dimensionless quantities.
    This is the first-principles requirement used to identify the two viable power counting rules.

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Forward citations

Cited by 1 Pith paper

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

  1. Recent Developments in SMEFT: Theory, Tools, and Phenomenology

    hep-ph 2026-04 unverdicted novelty 1.0

    A review summarizing recent theory, tools, and phenomenology in the Standard Model Effective Field Theory.

Reference graph

Works this paper leans on

140 extracted references · 140 canonical work pages · cited by 1 Pith paper · 58 internal anchors

  1. [1]

    Buchmuller and D

    W. Buchmuller and D. Wyler,Effective Lagrangian Analysis of New Interactions and Flavor Conservation,Nucl. Phys. B268(1986) 621–653

    work page 1986

  2. [2]

    Dimension-Six Terms in the Standard Model Lagrangian

    B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek,Dimension-Six Terms in the Standard Model Lagrangian,JHEP10(2010) 085, [1008.4884]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  3. [3]

    The Effective Chiral Lagrangian for a Light Dynamical "Higgs Particle"

    R. Alonso, M. B. Gavela, L. Merlo, S. Rigolin and J. Yepes,The Effective Chiral Lagrangian for a Light Dynamical ”Higgs Particle”,Phys. Lett. B722(2013) 330–335, [1212.3305]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  4. [4]

    Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO

    G. Buchalla, O. Cat` a and C. Krause,Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO,Nucl. Phys. B880(2014) 552–573, [1307.5017]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  5. [5]

    Disentangling a dynamical Higgs

    I. Brivio, T. Corbett, O. J. P. ´Eboli, M. B. Gavela, J. Gonzalez-Fraile, M. C. Gonzalez-Garcia et al.,Disentangling a dynamical Higgs,JHEP03(2014) 024, [1311.1823]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  6. [6]

    M. B. Gavela, J. Gonzalez-Fraile, M. C. Gonzalez-Garcia, L. Merlo, S. Rigolin and J. Yepes, CP violation with a dynamical Higgs,JHEP10(2014) 044, [1406.6367]. – 78 –

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  7. [7]

    The complete HEFT Lagrangian after the LHC Run I

    I. Brivio, J. Gonzalez-Fraile, M. C. Gonzalez-Garcia and L. Merlo,The complete HEFT Lagrangian after the LHC Run I,Eur. Phys. J. C76(2016) 416, [1604.06801]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  8. [8]

    Sun, M.-L

    H. Sun, M.-L. Xiao and J.-H. Yu,Complete NLO operators in the Higgs effective field theory,JHEP05(2023) 043, [2206.07722]

    work page arXiv 2023

  9. [9]

    Sun, M.-L

    H. Sun, M.-L. Xiao and J.-H. Yu,Complete NNLO operator bases in Higgs effective field theory,JHEP04(2023) 086, [2210.14939]

    work page arXiv 2023

  10. [10]

    The Standard Model as an Effective Field Theory

    I. Brivio and M. Trott,The Standard Model as an Effective Field Theory,Phys. Rept.793 (2019) 1–98, [1706.08945]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  11. [11]

    Isidori, F

    G. Isidori, F. Wilsch and D. Wyler,The standard model effective field theory at work,Rev. Mod. Phys.96(2024) 015006, [2303.16922]

    work page arXiv 2024

  12. [12]

    Susskind,Dynamics of Spontaneous Symmetry Breaking in the Weinberg-Salam Theory, Phys

    L. Susskind,Dynamics of Spontaneous Symmetry Breaking in the Weinberg-Salam Theory, Phys. Rev. D20(1979) 2619–2625

    work page 1979

  13. [13]

    Dimopoulos and L

    S. Dimopoulos and L. Susskind,Mass Without Scalars,Nucl. Phys. B155(1979) 237–252

    work page 1979

  14. [14]

    Dimopoulos and J

    S. Dimopoulos and J. Preskill,Massless Composites With Massive Constituents,Nucl. Phys. B199(1982) 206–222

    work page 1982

  15. [15]

    D. B. Kaplan, H. Georgi and S. Dimopoulos,Composite Higgs Scalars,Phys. Lett. B136 (1984) 187–190

    work page 1984

  16. [16]

    D. B. Kaplan and H. Georgi,SU(2) x U(1) Breaking by Vacuum Misalignment,Phys. Lett. B136(1984) 183–186

    work page 1984

  17. [17]

    Georgi and D

    H. Georgi and D. B. Kaplan,Composite Higgs and Custodial SU(2),Phys. Lett. B145 (1984) 216–220

    work page 1984

  18. [18]

    The Minimal Composite Higgs Model

    K. Agashe, R. Contino and A. Pomarol,The Minimal composite Higgs model,Nucl. Phys. B 719(2005) 165–187, [hep-ph/0412089]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  19. [19]

    Light custodians in natural composite Higgs models

    R. Contino, L. Da Rold and A. Pomarol,Light custodians in natural composite Higgs models,Phys. Rev. D75(2007) 055014, [hep-ph/0612048]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  20. [20]

    Appelquist and C

    T. Appelquist and C. W. Bernard,Strongly Interacting Higgs Bosons,Phys. Rev. D22 (1980) 200

    work page 1980

  21. [21]

    A. C. Longhitano,Heavy Higgs Bosons in the Weinberg-Salam Model,Phys. Rev. D22 (1980) 1166

    work page 1980

  22. [22]

    A. C. Longhitano,Low-Energy Impact of a Heavy Higgs Boson Sector,Nucl. Phys. B188 (1981) 118–154

    work page 1981

  23. [23]

    The Chiral Approach to the Electroweak Interactions

    F. Feruglio,The Chiral approach to the electroweak interactions,Int. J. Mod. Phys. A8 (1993) 4937–4972, [hep-ph/9301281]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  24. [24]

    The Electroweak Chiral Lagrangian and New Precision Measurements

    T. Appelquist and G.-H. Wu,The Electroweak chiral Lagrangian and new precision measurements,Phys. Rev. D48(1993) 3235–3241, [hep-ph/9304240]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  25. [25]

    Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO

    G. Buchalla and O. Cata,Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO,JHEP07(2012) 101, [1203.6510]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  26. [26]

    Falkowski and R

    A. Falkowski and R. Rattazzi,Which EFT,JHEP10(2019) 255, [1902.05936]

    work page arXiv 2019

  27. [27]

    Banta, T

    I. Banta, T. Cohen, N. Craig, X. Lu and D. Sutherland,Non-decoupling new particles, JHEP02(2022) 029, [2110.02967]. – 79 –

    work page arXiv 2022

  28. [28]

    Crawford and D

    G. Crawford and D. Sutherland,Scalars with non-decoupling phenomenology at future colliders,JHEP04(2025) 197, [2409.18177]

    work page arXiv 2025

  29. [29]

    Cohen, N

    T. Cohen, N. Craig, X. Lu and D. Sutherland,Is SMEFT Enough?,JHEP03(2021) 237, [2008.08597]

    work page arXiv 2021

  30. [30]

    A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space

    R. Alonso, E. E. Jenkins and A. V. Manohar,A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space,Phys. Lett. B754(2016) 335–342, [1511.00724]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  31. [31]

    Geometry of the Scalar Sector

    R. Alonso, E. E. Jenkins and A. V. Manohar,Geometry of the Scalar Sector,JHEP08 (2016) 101, [1605.03602]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  32. [32]

    Alonso,A primer on Higgs Effective Field Theory with Geometry,2307.14301

    R. Alonso,A primer on Higgs Effective Field Theory with Geometry,2307.14301

    work page arXiv

  33. [33]

    Z.-Y. Dong, T. Ma, J. Shu and Z.-Z. Zhou,The new formulation of higgs effective field Theory,JHEP09(2023) 101, [2211.16515]

    work page arXiv 2023

  34. [34]

    H. Liu, T. Ma, Y. Shadmi and M. Waterbury,An EFT hunter’s guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes,JHEP05(2023) 241, [2301.11349]

    work page arXiv 2023

  35. [35]

    J. M. Goldberg, H. Liu and Y. Shadmi,Dimension-8 SMEFT contact-terms for vector-pair production via on-shell Higgsing,JHEP12(2024) 057, [2407.07945]

    work page arXiv 2024

  36. [36]

    Gr¨ ober, A

    R. Gr¨ ober, A. N. Rossia and M. Ryczkowski,Multi-Higgs Amplitudes Bootstrapped: Dissecting SMEFT and HEFT,2509.02680

    work page arXiv

  37. [37]

    G´ omez-Ambrosio, F

    R. G´ omez-Ambrosio, F. J. Llanes-Estrada, A. Salas-Bern´ ardez and J. J. Sanz-Cillero, Distinguishing electroweak EFTs with WLWL→n×h,Phys. Rev. D106(2022) 053004, [2204.01763]

    work page arXiv 2022

  38. [38]

    R. L. Delgado, R. G´ omez-Ambrosio, J. Mart´ ınez-Mart´ ın, A. Salas-Bern´ ardez and J. J. Sanz-Cillero,Production of two, three, and four Higgs bosons: where SMEFT and HEFT depart,JHEP03(2024) 037, [2311.04280]

    work page arXiv 2024

  39. [39]

    J. M. D´ avila, D. Domenech, M. J. Herrero and R. A. Morales,Exploring correlations between HEFT Higgs couplingsκ V andκ 2V via HH production ate +e− colliders,Eur. Phys. J. C84(2024) 503, [2312.03877]

    work page arXiv 2024

  40. [40]

    Domenech, C

    Anisha, D. Domenech, C. Englert, M. J. Herrero and R. A. Morales,Bosonic multi-Higgs correlations beyond leading order,Phys. Rev. D110(2024) 095016, [2405.05385]

    work page arXiv 2024

  41. [41]

    Domenech, C

    Anisha, D. Domenech, C. Englert, M. J. Herrero and R. A. Morales,HEFT’s appraisal of triple (versus double) Higgs weak boson fusion,2407.20706

    work page arXiv

  42. [42]

    Englert, R

    Anisha, C. Englert, R. Kogler and M. Spannowsky,Higgs boson off-shell measurements probe non-linearities,2402.06746

    work page arXiv

  43. [43]

    Bhardwaj, C

    A. Bhardwaj, C. Englert, D. Gon¸ calves and A. Navarro,Nonlinear gauge-Higgs CP violation,Phys. Rev. D110(2024) 115011, [2407.14608]

    work page arXiv 2024

  44. [44]

    Englert, T

    C. Englert, T. Ingebretsen Carlson, J. Sj¨ olin and M. Spannowsky,Harnessing Higgs Kinematics for HEFT Constraints,2506.19401

    work page arXiv

  45. [45]

    Domenech, M

    D. Domenech, M. Herrero, R. A. Morales and A. Salas-Bern´ ardez,Matching HEFT and SMEFT in double and triple Higgs production from weak boson fusion,2506.21716

    work page arXiv

  46. [46]

    Higgs form factors in Associated Production

    G. Isidori and M. Trott,Higgs form factors in Associated Production,JHEP02(2014) 082, [1307.4051]. – 80 –

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  47. [47]

    Probing the nature of the Higgs-like Boson via h -> VF decays

    G. Isidori, A. V. Manohar and M. Trott,Probing the nature of the Higgs-like Boson via h→VFdecays,Phys. Lett. B728(2014) 131–135, [1305.0663]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  48. [48]

    Nonstandard Higgs Couplings from Angular Distributions in $h\to Z \ell^+\ell^-$

    G. Buchalla, O. Cata and G. D’Ambrosio,Nonstandard Higgs couplings from angular distributions inh→Zℓ +ℓ−,Eur. Phys. J. C74(2014) 2798, [1310.2574]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  49. [49]

    O. J. P. Eboli, M. C. Gonzalez-Garcia and M. Martines,Electroweak Higgs effective field theory after LHC run 2,Phys. Rev. D105(2022) 053003, [2112.11468]

    work page arXiv 2022

  50. [50]

    R. L. Delgado, A. Dobado, M. J. Herrero and J. J. Sanz-Cillero,One-loopγγ→W + L W− L andγγ→Z L ZL from the Electroweak Chiral Lagrangian with a light Higgs-like scalar, JHEP07(2014) 149, [1404.2866]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  51. [51]

    O. J. P. Eboli, M. C. Gonzalez-Garcia and M. Martines,Bounds on quartic gauge couplings in HEFT from electroweak gauge boson pair production at the LHC,Phys. Rev. D109 (2024) 033007, [2311.09300]

    work page arXiv 2024

  52. [52]

    Mahmud and K

    S. Mahmud and K. Tobioka,High energy vector boson scattering in four-body final states to probe Higgs cubic, quartic, and HEFT interactions,JHEP06(2025) 153, [2501.16439]

    work page arXiv 2025

  53. [53]

    Minimal Flavour Violation with Strong Higgs Dynamics

    R. Alonso, M. B. Gavela, L. Merlo, S. Rigolin and J. Yepes,Minimal Flavour Violation with Strong Higgs Dynamics,JHEP06(2012) 076, [1201.1511]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  54. [54]

    Flavour with a Light Dynamical "Higgs Particle"

    R. Alonso, M. B. Gavela, L. Merlo, S. Rigolin and J. Yepes,Flavor with a light dynamical ”Higgs particle”,Phys. Rev. D87(2013) 055019, [1212.3307]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  55. [55]

    Fortuna, J

    F. Fortuna, J. M. M´ arquez and P. Roig,HEFT approach to investigate the muon g-2 anomaly at a muon collider,Phys. Rev. D111(2025) 075012, [2408.16954]

    work page arXiv 2025

  56. [56]

    Computing tools for effective field – 55 – theories: SMEFT-Tools 2022 Workshop Report, 14–16th September 2022, Zürich,

    L. Allwicher et al.,Computing tools for effective field theories: SMEFT-Tools 2022 Workshop Report, 14–16th September 2022, Z¨ urich,Eur. Phys. J. C84(2024) 170, [2307.08745]

    work page arXiv 2022

  57. [57]

    The Non-Linear Higgs Legacy of the LHC Run I

    T. Corbett, O. J. P. Eboli, D. Goncalves, J. Gonzalez-Fraile, T. Plehn and M. Rauch,The Non-Linear Higgs Legacy of the LHC Run I,1511.08188

    work page internal anchor Pith review Pith/arXiv arXiv

  58. [58]

    Weinberg,Phenomenological Lagrangians,Physica A96(1979) 327–340

    S. Weinberg,Phenomenological Lagrangians,Physica A96(1979) 327–340

    work page 1979

  59. [59]

    Gasser and H

    J. Gasser and H. Leutwyler,Chiral Perturbation Theory to One Loop,Annals Phys.158 (1984) 142

    work page 1984

  60. [60]

    On the Power Counting in Effective Field Theories

    G. Buchalla, O. Cat´ a and C. Krause,On the Power Counting in Effective Field Theories, Phys. Lett. B731(2014) 80–86, [1312.5624]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  61. [61]

    B. M. Gavela, E. E. Jenkins, A. V. Manohar and L. Merlo,Analysis of General Power Counting Rules in Effective Field Theory,Eur. Phys. J. C76(2016) 485, [1601.07551]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  62. [62]

    Comment on "Analysis of General Power Counting Rules in Effective Field Theory"

    G. Buchalla, O. Cata, A. Celis and C. Krause,Comment on ”Analysis of General Power Counting Rules in Effective Field Theory”,1603.03062

    work page internal anchor Pith review Pith/arXiv arXiv

  63. [63]

    Manohar and H

    A. Manohar and H. Georgi,Chiral Quarks and the Nonrelativistic Quark Model,Nucl. Phys. B234(1984) 189–212

    work page 1984

  64. [64]

    Dawson, D

    S. Dawson, D. Fontes, C. Quezada-Calonge and J. J. Sanz-Cillero,Is the HEFT matching unique?,Phys. Rev. D109(2024) 055037, [2311.16897]

    work page arXiv 2024

  65. [65]

    Dawson, D

    S. Dawson, D. Fontes, C. Quezada-Calonge and J. J. Sanz-Cillero,Matching the 2HDM to the HEFT and the SMEFT: Decoupling and perturbativity,Phys. Rev. D108(2023) 055034, [2305.07689]. – 81 –

    work page arXiv 2023

  66. [66]

    Buchalla, F

    G. Buchalla, F. K¨ onig, C. M¨ uller-Salditt and F. Pandler,Two-Higgs-doublet model matched to nonlinear effective theory,Phys. Rev. D110(2024) 016015, [2312.13885]

    work page arXiv 2024

  67. [67]

    Song and X

    H. Song and X. Wan,A non-linear representation of general scalar extensions of the Standard Model for HEFT matching,JHEP06(2025) 021, [2412.00355]

    work page arXiv 2025

  68. [68]

    A. G. Cohen, D. B. Kaplan and A. E. Nelson,Counting 4 pis in strongly coupled supersymmetry,Phys. Lett. B412(1997) 301–308, [hep-ph/9706275]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  69. [69]

    M. A. Luty,Naive dimensional analysis and supersymmetry,Phys. Rev. D57(1998) 1531–1538, [hep-ph/9706235]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  70. [70]

    Gr´ af, B

    L. Gr´ af, B. Henning, X. Lu, T. Melia and H. Murayama,Hilbert series, the Higgs mechanism, and HEFT,JHEP02(2023) 064, [2211.06275]

    work page arXiv 2023

  71. [71]

    Weinberg,Baryon and Lepton Nonconserving Processes,Phys

    S. Weinberg,Baryon and Lepton Nonconserving Processes,Phys. Rev. Lett.43(1979) 1566–1570

    work page 1979

  72. [72]

    Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators

    L. Lehman,Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators,Phys. Rev. D90(2014) 125023, [1410.4193]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  73. [73]

    Henning, X

    B. Henning, X. Lu, T. Melia and H. Murayama,2, 84, 30, 993, 560, 15456, 11962, 261485, ...: Higher dimension operators in the SM EFT,JHEP08(2017) 016, [1512.03433]

    work page arXiv 2017

  74. [74]

    H.-L. Li, Z. Ren, J. Shu, M.-L. Xiao, J.-H. Yu and Y.-H. Zheng,Complete set of dimension-eight operators in the standard model effective field theory,Phys. Rev. D104 (2021) 015026, [2005.00008]

    work page arXiv 2021

  75. [75]

    C. W. Murphy,Dimension-8 operators in the Standard Model Effective Field Theory,JHEP 10(2020) 174, [2005.00059]

    work page arXiv 2020

  76. [76]

    H.-L. Li, Z. Ren, M.-L. Xiao, J.-H. Yu and Y.-H. Zheng,Complete set of dimension-nine operators in the standard model effective field theory,Phys. Rev. D104(2021) 015025, [2007.07899]

    work page arXiv 2021

  77. [77]

    Liao and X.-D

    Y. Liao and X.-D. Ma,An explicit construction of the dimension-9 operator basis in the standard model effective field theory,JHEP11(2020) 152, [2007.08125]

    work page arXiv 2020

  78. [78]

    R. V. Harlander, T. Kempkens and M. C. Schaaf,Standard model effective field theory up to mass dimension 12,Phys. Rev. D108(2023) 055020, [2305.06832]

    work page arXiv 2023

  79. [79]

    Baryon Number, Lepton Number, and Operator Dimension in the Standard Model

    A. Kobach,Baryon Number, Lepton Number, and Operator Dimension in the Standard Model,Phys. Lett. B758(2016) 455–457, [1604.05726]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  80. [80]

    A Higgs-Higgs bound state due to New Physics at a TeV

    B. Grinstein and M. Trott,A Higgs-Higgs bound state due to new physics at a TeV,Phys. Rev. D76(2007) 073002, [0704.1505]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

Showing first 80 references.