Combined EFT interpretation of top quark, Higgs boson, electroweak and QCD measurements at CMS

A recent EFT result from CMS is presented, combining differential cross section and direct EFT measurements performed by the CMS Collaboration across four branches of the Standard Model: top, Higgs, electroweak and QCD physics. To maximize the sensitivity, measurements of electroweak precision observables from LEP and SLC are included as well. 64 Wilson Coefficients (WC) are targeted in this combined measurement, both individually and with a simultaneous fit to 42 linear combinations of the Wilson Coefficients.

💡 Research Summary

The CMS Collaboration has performed a comprehensive global interpretation of the Standard Model Effective Field Theory (SMEFT) by combining a diverse set of measurements spanning four major sectors: top quark physics, Higgs boson production, electroweak vector‑boson processes, and QCD jet production. Using the topU3l basis of SMEFTSim3, the analysis targets 64 independent dimension‑6 operators (Wilson coefficients, WCs). Seven CMS analyses are selected for maximal sensitivity and minimal overlap: (i) differential Higgs →γγ cross sections in the STXS 1.2 binning, (ii) differential Wγ, WW, and Z→νν cross sections, (iii) double‑differential inclusive jet pT‑η spectra, (iv) tt̄ differential cross section in the lepton+jets channel (using the invariant mass of the tt̄ system), and (v) a multilepton top analysis covering same‑sign dilepton and ≥3‑lepton final states, split into 43 exclusive categories and further binned in a high‑pT observable. Electroweak precision observables (EWPO) from LEP and SLC are incorporated to provide complementary low‑energy constraints.
The theoretical predictions for each observable are generated with SMEFTSim3 where possible, and with SMEFT@NLO for loop‑induced processes, allowing both linear (interference) and quadratic (pure‑EFT) contributions in the WCs. Two sets of results are presented. First, a “single‑parameter” fit varies one WC at a time while fixing the others to zero, yielding 68 % and 95 % confidence intervals with and without quadratic terms. These limits, displayed in Figure 2, typically reach the O(1 TeV⁻²) level. Second, a simultaneous fit of all 64 WCs is attempted. Because many operators affect the same observables, the full likelihood exhibits strong degeneracies. To isolate the constrained directions, a principal‑component analysis (PCA) of the Hessian matrix (constructed from the linear‑term likelihood) is performed. Only eigenvectors with eigenvalues larger than 0.04 are retained, resulting in 42 well‑constrained linear combinations of WCs, whose limits are shown in Figure 3. The contribution of each individual measurement to each WC (or principal component) is also quantified, highlighting, for example, the dominant role of high‑mass tt̄ bins for top‑related operators and the multilepton categories for mixed electroweak‑top operators.
No statistically significant deviation from the Standard Model is observed in any of the examined directions. The analysis demonstrates the feasibility and power of a full‑likelihood combination within a single experiment, emphasizing the importance of publishing detailed statistical models alongside experimental results. This work sets a solid foundation for future, more precise global SMEFT fits as LHC data accumulate and theoretical predictions improve.