ATLAS global dimension-six SMEFT fit

The ATLAS collaboration combines previously measured Higgs and simplified-template-cross-section observables, di-Higgs, diboson, vector-boson-fusion $Zjj$, high-mass Drell–Yan, top-quark distributions, and electroweak precision inputs. The proton-proton LHC inputs use 13 TeV Run 2 data and input-specific integrated luminosities spanning about $36$–$140{\mathrm{f}\mathrm{b}}^{-1}$; the combined electroweak precision inputs also include LEP and SLD data. Integrated luminosity is the calibrated exposure assigned to a data sample, not a count of selected events. The input measurements retain their own observable definitions and selections.

The fit uses the Standard Model effective field theory (SMEFT): the Standard Model field content is supplemented by higher-dimension gauge-invariant operators. It fits 48 dimension-six Warsaw-basis coefficients or coefficient combinations. The reference normalization $\mathrm{\Lambda }=1\mathrm{T}\mathrm{e}\mathrm{V}$ fixes how the reported coefficients are quoted; it is not a measured new-particle mass.

Adopted SMEFT field content and operator-expansion conventions

Warsaw-basis operator and coefficient conventions

ATLAS global SMEFT fit, full article

The collaboration constructs a joint likelihood from the input analyses, using Poisson terms for event-count inputs and Gaussian terms for measurement inputs where specified. It checks overlaps among event-based inputs using event identifiers, bootstrap studies, and selections; identified overlaps are removed or handled as stated in the article. Experimental and theoretical nuisance parameters encode systematic and theory uncertainties and are profiled subject to the source's constraints and correlation scheme. Profiling means maximizing the likelihood over nuisance parameters at each fixed coefficient value; the resulting profile-likelihood ratio compares that constrained maximum with the unrestricted maximum. For coefficient intervals, §4.2 uses the one-dimensional profile-likelihood statistic with the Wilks chi-square calibration and discusses checks on its applicability. The separate 99% compatibility p-value is reported in §5.3.1 for the linear fit without di-Higgs measurements, but that result section does not identify a global test statistic or its null calibration; this item does not reconstruct either or infer them from the coefficient-interval calibration. These are source-reported analysis choices, not a reconstruction of the component likelihoods.

Likelihoods as functions of parameters for observed data

Profile likelihood ratios with nuisance parameters

P-values under an explicit null calibration

ATLAS global SMEFT fit, overlap, likelihood, and calibration sections

The collaboration reports no statistically significant overall deviation from the Standard Model. Its $99\mathrm{\%}$ compatibility $p$-value is reported in §5.3.1 for the linear fit without di-Higgs measurements: 47 fit-basis coefficients are shown and the other 39 directions are fixed to their Standard Model value of zero. The result is not assigned the one-dimensional Wilks calibration used for coefficient intervals; the global test statistic and null calibration are not reconstructed here. The article also identifies an electroweak-precision coefficient direction, denoted $c_{HVV,Vff}^{[19]}$, as pulled by the known tension between the measured $A_{\mathrm{F}\mathrm{B}}^{b,c}$ asymmetries and the Standard Model prediction. The overall fit statement therefore does not mean that every coefficient is individually within two standard deviations. A $p$-value is a tail probability under its stated null calibration, not the probability that the Standard Model is true.

Null-calibrated tail probability and its interpretation

ATLAS global SMEFT fit, results and electroweak-pull discussion

Wasserman, statistical interpretation of p-values, full textbook §10.2

The reported likelihood carries statistical, detector, theory, and other systematic uncertainties with the correlations adopted for the input measurements. The article describes checks and special handling for shared-event inputs. This item does not recreate the raw-event record, rerun detector reconstruction, validate every input calibration, or independently estimate a covariance matrix. The reported $p$-value and intervals inherit those source-level assumptions.

ATLAS global SMEFT fit, systematic uncertainties and correlation treatment

The result is a source-defined constraint on the selected 48 coefficient directions and data inputs. The reported parameterization retains linear and quadratic dimension-six contributions while omitting dimension-eight interference terms at order ${\mathrm{\Lambda }}^{-4}$; its quadratic fit is therefore not a complete expansion to that order. The fit neither proves the SMEFT model nor establishes or excludes new physics in general. Its statistical conclusions remain conditional on the chosen observables, input likelihoods, nuisance model, coefficient truncation, and stated asymptotic calibration.

Page-level scope and prerequisite interface

ATLAS global SMEFT fit, coefficient truncation and result qualifications