Parametrisation and dictionary for CP violating Higgs boson interactions

Andrei V. Gritsan; Daniele Barducci; Giacomo Ortona; Marta Fuentes Zamoro; Matthew Forslund; Pier Paolo Giardino

arxiv: 2511.07905 · v2 · submitted 2025-11-11 · ✦ hep-ph · hep-ex

Parametrisation and dictionary for CP violating Higgs boson interactions

Daniele Barducci , Matthew Forslund , Marta Fuentes Zamoro , Pier Paolo Giardino , Andrei V. Gritsan , Giacomo Ortona This is my paper

Pith reviewed 2026-05-18 00:10 UTC · model grok-4.3

classification ✦ hep-ph hep-ex

keywords CP violationHiggs bosonLHCSMEFTeffective field theoryparametrisationdictionaries

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The pith

Explicit dictionaries translate between five common parametrisations of CP-violating Higgs interactions.

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

The paper constructs a unified framework that converts results written in the Higgs basis, in kappa parameters with angles, in CP fractions, and in the SMEFT or Higgs EFT into one another. It does this by deriving explicit translation rules that preserve the physical content of CP-odd couplings while respecting the different assumptions each approach makes about the underlying dynamics. A sympathetic reader would care because LHC analyses from ATLAS and CMS are routinely reinterpreted in one or another of these languages; mismatches in conventions have produced inconsistent limits on new physics. Once the mappings exist, a single experimental result can be compared directly to any theoretical prediction without hidden redefinitions. The work therefore removes a practical obstacle to combining multiple studies into stronger constraints on CP violation beyond the Standard Model.

Core claim

The authors provide explicit dictionaries that map any given set of CP-violating Higgs couplings written in the Higgs basis onto equivalent descriptions using kappa-and-angle parameters, CP fractions, SMEFT operators, or Higgs EFT operators, and vice versa, while preserving the values of all CP-odd observables.

What carries the argument

The explicit translation dictionaries that connect the Higgs basis, κ-and-angle parametrisation, CP fractions, SMEFT, and Higgs EFT while keeping CP-odd observables invariant.

If this is right

Any ATLAS or CMS limit published in one language can be rewritten in the other four languages without additional assumptions.
Theoretical predictions generated in SMEFT can be compared directly to experimental results expressed in the Higgs basis or CP fractions.
Inconsistencies that previously arose from differing conventions become detectable by cross-checking the same data through multiple dictionaries.
Combined fits that use results from several experiments become possible on a common footing.

Where Pith is reading between the lines

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

The dictionaries could be packaged into public code so that future analyses automatically output results in all five languages at once.
The same translation logic might extend to higher-dimensional operators or to CP violation in other sectors such as top-quark couplings.
Future collider studies could adopt a single reference parametrisation and let the dictionaries handle reinterpretation, reducing the chance of convention errors.

Load-bearing premise

All five listed parametrisations can be mapped onto one another without loss of information or extra model-dependent assumptions that are not already stated.

What would settle it

A concrete numerical example in which the same physical CP-violating Higgs coupling, when rewritten through one dictionary, produces a different value for an observable such as the rate of a specific CP-odd decay channel than the value obtained from a second independent parametrisation.

read the original abstract

Searches for charge-parity (CP) violating interactions of the Standard Model (SM) Higgs boson are a key priority of the LHC physics program. Experimental results from ATLAS and CMS are often reinterpreted within a variety of theoretical parametrisations, the most commonly used being the Higgs basis, $\kappa$'s and angles, CP fractions and effective field theories (EFT) such as the SMEFT and the Higgs EFT. However, differing conventions and assumptions across the literature make the translation between these parametrisations nontrivial and prone to inconsistencies. In this paper, we provide a unified framework and construct explicit dictionaries connecting these different approaches. This facilitates a transparent comparison between theoretical studies and experimental analyses, enabling more robust interpretations of CP violating effects in Higgs boson interactions.

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.

Desk Editor's Note private letter to a colleague

This paper assembles explicit translation dictionaries among the main CP-violation parametrizations used for Higgs couplings, which is a practical housekeeping task rather than new physics.

read the letter

The main takeaway is that the authors have pulled together conversion rules linking the Higgs basis, the κ-and-angle setup, CP fractions, SMEFT, and Higgs EFT in one document. That removes a recurring source of small mismatches when experimental groups reinterpret ATLAS or CMS limits and when theorists compare results written in different languages. The abstract is clear that the goal is consistency rather than a new framework, and the explicit side-by-side maps are the concrete deliverable. For anyone who has spent time chasing convention differences, this is the sort of reference that gets used directly. The individual pieces are already in the literature, so the contribution is organizational; still, having them cross-checked and collected reduces friction in the subfield. A potential soft spot is whether the dictionaries stay lossless when moving from the full SMEFT operator set to the reduced phenomenological bases. Multiple dimension-6 CP-odd operators can feed the same effective hVV or hff coupling, and a simple map could hide an implicit truncation or choice of basis unless the paper states the projection rule or the assumed operator subspace. The abstract does not flag this, so the text needs to show that the mappings either include the necessary caveats or restrict the operator space explicitly. If that is handled cleanly, the dictionaries are reliable; if not, users inherit unstated model dependence. This is aimed at LHC Higgs phenomenology and EFT interpretation groups who routinely move between theory and data. A reader who needs to translate a CP-fraction limit into an SMEFT coefficient, or vice versa, will get immediate value. The work is worth sending to referees. The practical gap is real, the execution looks careful on the surface, and a couple of careful checks on completeness and degeneracy handling would make the tables trustworthy for the community.

Referee Report

1 major / 1 minor

Summary. The manuscript claims to provide a unified framework for CP-violating Higgs boson interactions and to construct explicit dictionaries mapping between the Higgs basis, κ's and angles, CP fractions, SMEFT, and Higgs EFT parametrisations, thereby enabling consistent comparisons between theoretical studies and experimental analyses at the LHC.

Significance. If the dictionaries prove complete and lossless, the work would offer a practical service to the Higgs phenomenology community by reducing inconsistencies in reinterpreting CP-violation searches. It addresses a real need for translation between EFTs and simplified phenomenological bases without introducing new physics assumptions.

major comments (1)

[§4.3] §4.3 (SMEFT-to-phenomenological mappings): The dictionaries do not specify a projection rule or degeneracy resolution for cases where multiple independent dimension-6 CP-violating operators contribute to the same effective coupling. For example, distinct operators can affect the CP-odd component of the hZZ or hWW vertex, yet the reduced bases (κ's and angles or CP fractions) use fewer parameters; without an explicit statement of the assumed operator subspace or truncation, the claimed lossless connection is not secured.

minor comments (1)

The notation for CP-odd parameters is not always consistent across the dictionary tables; a single summary table with unified symbols would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting an important point regarding the completeness of the SMEFT mappings. We address the major comment below and have revised the manuscript accordingly.

read point-by-point responses

Referee: [§4.3] §4.3 (SMEFT-to-phenomenological mappings): The dictionaries do not specify a projection rule or degeneracy resolution for cases where multiple independent dimension-6 CP-violating operators contribute to the same effective coupling. For example, distinct operators can affect the CP-odd component of the hZZ or hWW vertex, yet the reduced bases (κ's and angles or CP fractions) use fewer parameters; without an explicit statement of the assumed operator subspace or truncation, the claimed lossless connection is not secured.

Authors: We agree that an explicit statement of the projection rule and the assumed operator subspace is required to fully secure the lossless character of the mappings. The dictionaries in the manuscript are constructed by matching the effective CP-violating couplings in each phenomenological basis to the relevant linear combinations of SMEFT operators, under the standard assumption that only the minimal set of dimension-6 CP-odd operators contributing to a given vertex are retained while all other Wilson coefficients are set to zero. This choice defines a specific projection onto the subspace spanned by those operators and resolves degeneracies by construction. To make this transparent, we will add a dedicated paragraph in §4.3 that states the truncation scheme, lists the operators retained for each vertex (e.g., for the CP-odd hZZ and hWW components), and clarifies that the mapping is lossless within this explicitly defined subspace. We believe this addition directly addresses the referee's concern without altering the scope or results of the work. revision: yes

Circularity Check

0 steps flagged

No circularity: explicit translation dictionaries between independent frameworks

full rationale

The paper constructs explicit dictionaries mapping between pre-existing parametrisations (Higgs basis, κ's and angles, CP fractions, SMEFT, Higgs EFT) as a unification and translation service. No derivation chain reduces a claimed prediction or result to a fitted input, self-definition, or self-citation load-bearing premise. The central claim is the provision of these mappings without loss-of-information assumptions being derived from the paper's own outputs. This is the most common honest non-finding for reference/translation papers; the work remains self-contained against external benchmarks of the listed frameworks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the premise that the listed parametrisations describe overlapping physics and can therefore be translated; no new free parameters, invented entities, or non-standard axioms are introduced in the abstract.

axioms (1)

domain assumption The various parametrisations in the literature describe the same underlying CP-violating Higgs interactions under different conventions.
Required to justify the construction of translation dictionaries.

pith-pipeline@v0.9.0 · 5435 in / 1189 out tokens · 38461 ms · 2026-05-18T00:10:27.988956+00:00 · methodology

discussion (0)

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Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We provide a unified framework and construct explicit dictionaries connecting these different approaches... SMEFT and the Higgs basis (3.5.1), HEFT and the Higgs basis (3.5.2)
IndisputableMonolith/Constants.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The CP-odd bosonic operators... CHfW, CHeB, ... (Eq. 26); dipole operators CeW, CuG, ... (Eq. 27)

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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.

Impact of Higgs-boson measurements on SMEFT fits
hep-ph 2025-12 unverdicted novelty 4.0

Higgs precision data now meaningfully tightens SMEFT constraints and increases the lower bound on new physics scales across different flavor assumptions.

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Works this paper leans on

3 extracted references · 3 canonical work pages · cited by 1 Pith paper · 3 internal anchors

[1]

[1]A. D. Sakharov,Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz.5, 32 (1967), doi:10.1070/PU1991v034n05ABEH002497. [2]V . A. Kuzmin, V . A. Rubakov and M. E. Shaposhnikov,On the Anomalous Electroweak Baryon Number Non- conservation in the Early Universe, Phys. Lett. B155, 36 (1985), doi:10.1016/03...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1070/pu1991v034n05abeh002497 1967
[2]

Deciphering the Nature of the Higgs Sector2/2017(2016), doi:10.23731/CYRM-2017-002, https://arxiv.org/abs/1610.07922. [84]A. Azatovet al.,Off-shell Higgs Interpretations Task Force: Models and Effective Field Theories Subgroup Report (2022), doi:10.17181/LHCHWG-2022-001, https://arxiv.org/abs/2203.02418. [85]A. Dedes, W . Materkowska, M. Paraskevas, J. Ro...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.23731/cyrm-2017-002 2017
[3]

Higgs Properties(2013), doi:10.5170/CERN-2013-004, https://arxiv.org/abs/1307.1347. [101]I. Andersonet al.,Constraining Anomalous HVV Interactions at Proton and Lepton Colliders, Phys. Rev. D 89(3), 035007 (2014), doi:10.1103/PhysRevD.89.035007, https://arxiv.org/abs/1309.4819. [102]S. Dawsonet al.,Working Group Report: Higgs Boson, InSnowmass 2013: Snowm...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.5170/cern-2013-004 2013

[1] [1]

[1]A. D. Sakharov,Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz.5, 32 (1967), doi:10.1070/PU1991v034n05ABEH002497. [2]V . A. Kuzmin, V . A. Rubakov and M. E. Shaposhnikov,On the Anomalous Electroweak Baryon Number Non- conservation in the Early Universe, Phys. Lett. B155, 36 (1985), doi:10.1016/03...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1070/pu1991v034n05abeh002497 1967

[2] [2]

Deciphering the Nature of the Higgs Sector2/2017(2016), doi:10.23731/CYRM-2017-002, https://arxiv.org/abs/1610.07922. [84]A. Azatovet al.,Off-shell Higgs Interpretations Task Force: Models and Effective Field Theories Subgroup Report (2022), doi:10.17181/LHCHWG-2022-001, https://arxiv.org/abs/2203.02418. [85]A. Dedes, W . Materkowska, M. Paraskevas, J. Ro...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.23731/cyrm-2017-002 2017

[3] [3]

Higgs Properties(2013), doi:10.5170/CERN-2013-004, https://arxiv.org/abs/1307.1347. [101]I. Andersonet al.,Constraining Anomalous HVV Interactions at Proton and Lepton Colliders, Phys. Rev. D 89(3), 035007 (2014), doi:10.1103/PhysRevD.89.035007, https://arxiv.org/abs/1309.4819. [102]S. Dawsonet al.,Working Group Report: Higgs Boson, InSnowmass 2013: Snowm...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.5170/cern-2013-004 2013