Constraining the SMEFT at Present and Future Colliders

We present results from SMEFiT3.0, a global SMEFT fit of Higgs, top quark, and diboson production data from the LHC. Our updated analysis includes recent inclusive and differential measurements from the LHC Run II, together with the exact implementation of electroweak precision observables (EWPOs) from LEP and SLD. We then analyse the impact of HL-LHC measurements by adding to SMEFiT3.0 the projections obtained by extrapolating from Run II data. Finally we estimate the potential of two proposed high-energy circular $e^+e^-$ colliders, the FCC-ee and the CEPC, in further improving the bounds on the SMEFT parameters.

💡 Research Summary

The paper presents SMEFiT 3.0, an updated global fit of the Standard Model Effective Field Theory (SMEFT) using the latest LHC Run II measurements together with precise electroweak precision observables (EWPO) from LEP and SLD. The authors consider a complete set of 50 dimension‑6 operators in the Warsaw basis, grouped into two‑fermion, four‑fermion (four‑heavy and two‑light‑two‑heavy), purely bosonic, and four‑lepton categories. Experimental inputs include recent Simplified Template Cross Section (STXS) Higgs data, differential WZ pT distributions, and new top‑quark production measurements from ATLAS and CMS. Crucially, EWPO are now treated exactly rather than approximated, improving the overall constraint power.

The fit is performed both at linear order (keeping only interference terms) and at quadratic order (including squared dimension‑6 contributions). Marginalised 95 % credible intervals are reported in units of 1/TeV². Most operator coefficients are bounded below unity, indicating that the current data already probe new‑physics scales of order a few TeV. Four‑fermion operators involving only heavy quarks (the “4H” class) remain the least constrained, with bounds ranging from O(1) to O(10), because linear fits exhibit flat directions that are only lifted by quadratic terms. Two‑light‑two‑heavy operators (2L2H) see the strongest improvement, with uncertainties reduced by factors of two to three thanks to recent tt̄ measurements. Fit residuals, defined as the distance of the posterior mean from the SM value in units of the 68 % interval, show overall good agreement with the SM; only a few coefficients (c_{tG}, c_{ϕq}^{(3)}, c_{ϕd}) display pulls above the 2‑σ level, the former driven by a tension between CMS 8 TeV double‑differential tt̄ data and other top measurements.

Future projections are then examined. For the High‑Luminosity LHC (HL‑LHC) the authors assume a total integrated luminosity of 3 ab⁻¹ per experiment, scale statistical uncertainties accordingly, and halve systematic uncertainties. Adding these projected measurements to the baseline SMEFiT 3.0 fit improves the quadratic marginalised bounds by 20 % up to a factor of three, depending on the operator. Individual (one‑parameter) fits would achieve even stronger limits, often an order of magnitude better than the global fit, highlighting the impact of correlations among operators.

The impact of a future circular electron‑positron collider, represented by the FCC‑ee (with results shown also for the CEPC), is evaluated using four running scenarios from the Z‑pole up to 365 GeV, covering Z‑pole EWPO, light‑fermion pair production, Higgsstrahlung (hZ) and vector‑boson‑fusion (hνν) processes, diboson production, and top‑pair production above threshold. When FCC‑ee observables are added on top of the HL‑LHC projections, the uncertainties on bosonic operators (e.g., c_{ϕD}, c_{ϕW}, c_{ϕB}) and two‑fermion operators (e.g., c_{tZ}, c_{tW}) shrink by factors of 30–50, corresponding to improvements of up to two orders of magnitude relative to the current LHC‑only fit. Four‑quark operators see only modest gains because the FCC‑ee observables are insensitive to them at leading order; inclusion of NLO effects is left for future work.

In conclusion, the authors demonstrate that the current LHC Run II data already provide O(1) constraints on most SMEFT coefficients, and that quadratic effects are essential for breaking degeneracies, especially in the four‑fermion sector. The HL‑LHC will modestly tighten these bounds, while a high‑energy circular e⁺e⁻ collider like the FCC‑ee can dramatically improve sensitivity to bosonic and two‑fermion operators, reaching precision levels that would probe new‑physics scales well beyond the TeV range. Planned future extensions include refined HL‑LHC binning strategies, inclusion of other proposed facilities (ILC, CLIC, high‑energy muon colliders), and the treatment of renormalisation‑group mixing among SMEFT coefficients.