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arxiv: 2412.07651 · v2 · pith:S6B4PTHDnew · submitted 2024-12-10 · ✦ hep-ph

An EWPD SMEFT likelihood for the LHC -- and how to improve it with measurements of W and Z boson properties

Hannes Mildner This is my paper

Pith reviewed 2026-05-23 07:04 UTC · model grok-4.3

classification ✦ hep-ph
keywords SMEFTEWPDLHCWilson coefficientsDrell-Yanlepton flavour universalityweak mixing angleW boson properties
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0 comments X

The pith

A new likelihood for electroweak precision data in the SMEFT framework improves constraints on Wilson coefficients when added to LHC measurements.

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

The paper supplies a computer code that returns the likelihood of SMEFT Wilson coefficients given precision measurements of W and Z pole observables. The code supplies interpolation formulas for Standard Model predictions, modular SMEFT parametrizations that include next-to-leading-order effects, and support for five different electroweak input schemes. It corrects earlier treatments of parametric uncertainties so the likelihood can be dropped directly into fits of LHC data. When the code is combined with an ATLAS Drell-Yan triple-differential cross-section measurement, the resulting fit tightens bounds on muon couplings beyond the world average and extracts a linear combination of the light-quark asymmetry parameters A_u and A_d at a precision comparable to the heavy-flavor parameters A_c and A_b.

Core claim

The paper constructs and releases an EWPD likelihood in the SMEFT that incorporates NLO perturbative and operator corrections, works across five electroweak input schemes, and resolves prior shortcomings in the propagation of parametric uncertainties, allowing the likelihood to be used directly in global SMEFT fits of LHC data; the same framework is then applied to recent ATLAS and CMS measurements of the W mass, width, branching ratios, and effective weak mixing angle, and to a reinterpretation of the ATLAS Drell-Yan measurement that improves muon-coupling bounds and yields a competitive determination of a combination of A_u and A_d.

What carries the argument

The EWPD SMEFT likelihood code that supplies interpolated Standard Model predictions and modular SMEFT parametrizations for W and Z pole observables across five input schemes.

If this is right

  • The likelihood can be included without further modification in SMEFT fits that also use LHC data.
  • Recent ATLAS and CMS measurements of W mass, width, lepton-flavour-universality ratios, and the effective leptonic weak mixing angle produce measurable shifts in the allowed ranges of Wilson coefficients.
  • A lepton-flavour-universality test based on the weak mixing angle measurement reaches higher precision than existing tests.
  • Reinterpretation of the ATLAS Drell-Yan data together with the EWPD likelihood tightens muon-coupling limits and extracts a light-quark asymmetry combination at the same precision as A_c and A_b.

Where Pith is reading between the lines

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

  • The modular structure of the likelihood would allow future addition of other LHC observables without rebuilding the electroweak sector from scratch.
  • The documented scheme-dependence study supplies a practical criterion for choosing an input scheme in combined fits that include both precision and high-energy data.
  • The proposed lepton-flavour-universality test could be carried out with existing or near-future LHC datasets once the likelihood is made public.

Load-bearing premise

The interpolation formulas for Standard Model predictions and the modular SMEFT parametrizations remain accurate when next-to-leading-order perturbative corrections and SMEFT operator corrections are included simultaneously across the five electroweak input schemes.

What would settle it

A global fit performed with the released likelihood that returns central values for the muon-coupling Wilson coefficients or the A_u–A_d combination lying more than two standard deviations outside the intervals obtained from the same data without the new likelihood would falsify the claim of improved constraints.

read the original abstract

This paper presents a computer code for analyzing electroweak precision data (EWPD) in the framework of the Standard Model Effective Field Theory (SMEFT), highlights the importance of recent ATLAS and CMS precision measurements, and introduces a novel analysis of the forward-backward asymmetry at the LHC. The computer code provides the likelihood of SMEFT Wilson coefficients based on precision measurements of $W$ and $Z$ pole observables, interpolation formulas for Standard Model predictions, and modular SMEFT parametrizations. SMEFT predictions including next-to-leading-order (NLO) effects in perturbative and SMEFT expansion are available and five alternative electroweak input parameter schemes are supported. The likelihood addresses shortcomings of previous formulations in the treatment of parametric uncertainties and can be straightforwardly included in SMEFT fits of LHC data. The input parameter scheme dependence and role of NLO corrections is studied for the EWPD fit in the SMEFT. Furthermore, the impact of recent ATLAS and CMS measurements - of the $W$ boson mass and width, of the lepton flavour universality (LFU) of $W$ branching fractions, and the effective leptonic weak mixing angle - is analyzed. A test of LFU that surpasses the precision of existing measurements is proposed based on the weak mixing angle measurement. Finally, an ATLAS Drell-Yan triple-differential cross-section measurement is reinterpreted in the SMEFT and combined with the EWPD likelihood. This analysis demonstrates the feasibility of the LFU precision test, improves constraints on muon couplings with respect to the world average, and determines a combination of the quark-coupling asymmetry parameters $A_u$ and $A_d$ with a precision comparable to that of the heavy flavour parameters $A_c$ and $A_b$.

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 / 2 minor

Summary. The manuscript presents a computer code implementing an EWPD likelihood in the SMEFT, featuring interpolation formulas for SM predictions, modular SMEFT parametrizations, NLO effects in both perturbative QCD/EW and SMEFT expansions, and support for five electroweak input schemes. It studies input-scheme dependence and NLO corrections in the EWPD fit, quantifies the impact of recent ATLAS/CMS measurements of the W mass/width, LFU in W decays, and the effective leptonic weak mixing angle, proposes an LFU test based on the weak mixing angle, and combines the likelihood with an ATLAS Drell-Yan triple-differential cross section to tighten constraints on muon couplings and extract a linear combination of A_u and A_d at a precision comparable to A_c and A_b.

Significance. If the interpolation formulas remain accurate under simultaneous NLO perturbative and SMEFT corrections, the work supplies a reusable, modular tool that corrects shortcomings in prior parametric-uncertainty treatments and can be directly embedded in global SMEFT fits of LHC data. The explicit study of five input schemes, the proposed LFU test, and the competitive A_u/A_d extraction from Drell-Yan plus EWPD constitute concrete advances in precision. Release of the code itself is a positive contribution to reproducibility.

major comments (2)
  1. [Section on input parameter scheme dependence and NLO effects] Section discussing the interpolation formulas for Standard Model predictions and the modular SMEFT parametrizations: no quantitative error budget, residual plots, or direct comparison against independent NLO calculations is provided for the case in which perturbative NLO and SMEFT corrections are applied simultaneously across the five electroweak input schemes. Because the central claim of improved parametric-uncertainty treatment and tighter constraints on muon couplings and A_u/A_d rests on these formulas remaining accurate at the per-mille level demanded by the data, the absence of such validation is load-bearing.
  2. [Section on the ATLAS Drell-Yan reinterpretation and combination] Analysis combining the EWPD likelihood with the ATLAS Drell-Yan measurement: the text does not specify how correlations between the EWPD observables and the Drell-Yan triple-differential cross sections are propagated when both are expressed in the same SMEFT basis and input scheme; without this information it is impossible to confirm that the reported improvement on muon couplings and the A_u/A_d combination is not inflated by double-counting or inconsistent scheme choices.
minor comments (2)
  1. [Abstract and Introduction] The abstract and introduction refer to “five alternative electroweak input parameter schemes” without an explicit table listing the five schemes and the corresponding input observables; adding such a table would improve clarity.
  2. [Section on the ATLAS Drell-Yan reinterpretation] Notation for the quark-coupling asymmetry parameters A_u and A_d is introduced without a dedicated equation defining the linear combination extracted from the Drell-Yan fit; a short equation would remove ambiguity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment of the work's significance, and constructive major comments. We address each point below and will revise the manuscript accordingly to strengthen the presentation of the interpolation validation and the combination procedure.

read point-by-point responses

  1. Referee: [Section on input parameter scheme dependence and NLO effects] Section discussing the interpolation formulas for Standard Model predictions and the modular SMEFT parametrizations: no quantitative error budget, residual plots, or direct comparison against independent NLO calculations is provided for the case in which perturbative NLO and SMEFT corrections are applied simultaneously across the five electroweak input schemes. Because the central claim of improved parametric-uncertainty treatment and tighter constraints on muon couplings and A_u/A_d rests on these formulas remaining accurate at the per-mille level demanded by the data, the absence of such validation is load-bearing.

    Authors: We agree that the manuscript does not provide a dedicated quantitative error budget, residual plots, or direct comparisons to independent NLO calculations for the simultaneous application of perturbative NLO and SMEFT corrections across the five input schemes. Separate validations exist for the SM interpolation and for SMEFT corrections, but the combined case is not explicitly demonstrated at the per-mille level. In the revised version we will add a new subsection containing residual plots for representative Wilson coefficient values in multiple schemes, a table of estimated interpolation uncertainties, and comparisons against independent NLO results where available. This directly addresses the load-bearing concern for the accuracy claims. revision: yes

  2. Referee: [Section on the ATLAS Drell-Yan reinterpretation and combination] Analysis combining the EWPD likelihood with the ATLAS Drell-Yan measurement: the text does not specify how correlations between the EWPD observables and the Drell-Yan triple-differential cross sections are propagated when both are expressed in the same SMEFT basis and input scheme; without this information it is impossible to confirm that the reported improvement on muon couplings and the A_u/A_d combination is not inflated by double-counting or inconsistent scheme choices.

    Authors: The manuscript does not explicitly describe the correlation treatment or confirm scheme consistency in the combination. The analysis proceeds under the assumption that the EWPD pole observables and the high-mass Drell-Yan triple-differential cross sections are uncorrelated, as they involve disjoint kinematic regions and independent experimental systematics, while using a single consistent input scheme throughout. We will revise the relevant section to state this assumption explicitly, justify the absence of correlations on kinematic and experimental grounds, and confirm that the same input scheme is employed for both datasets, thereby ruling out double-counting. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper constructs an EWPD SMEFT likelihood directly from external precision measurements of W and Z pole observables, providing interpolation formulas for SM predictions and modular SMEFT parametrizations as computational tools. These elements are presented as derived from theory calculations and data inputs without any reduction to self-definition, fitted parameters renamed as predictions, or load-bearing self-citations. The analysis of input scheme dependence, NLO effects, and combination with ATLAS Drell-Yan data relies on external benchmarks and the supplied code, with no equations or steps shown to be equivalent to their own inputs by construction. The derivation chain remains self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central deliverable is a likelihood function whose numerical values rest on interpolation formulas for SM predictions and on the assumption that NLO SMEFT corrections can be added linearly; no new particles or forces are introduced.

axioms (2)
  • domain assumption Next-to-leading-order perturbative and SMEFT corrections can be included simultaneously without higher-order inconsistencies
    Stated in the description of available SMEFT predictions
  • domain assumption The five electroweak input parameter schemes produce equivalent physics once all observables are expressed in the same scheme
    Invoked when studying scheme dependence of the EWPD fit

pith-pipeline@v0.9.0 · 5851 in / 1474 out tokens · 24048 ms · 2026-05-23T07:04:43.470687+00:00 · methodology

discussion (0)

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Forward citations

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