Constraining the SMEFT at Present and Future Colliders

Technical Summary: Constraining the SMEFT at Present and Future Colliders

Problem and Motivation
The conclusion of LHC Run II has yielded a vast array of new measurements, while the upcoming High-Luminosity (HL-LHC) phase and proposed future circular electron-positron colliders (FCC-ee and CEPC) promise significantly increased integrated luminosities and precision. Interpreting this expanding dataset requires a global analysis framework capable of testing the validity of the Standard Model (SM) at the TeV scale and characterizing potential extensions. The Standard Model Effective Field Theory (SMEFT) serves as the primary tool for this purpose, parametrizing high-energy physics effects through low-energy precision measurements. The challenge lies in performing a rigorous global fit that incorporates the latest differential and inclusive measurements, treats electroweak precision observables (EWPOs) exactly rather than approximately, and projects the constraining power of future facilities on SMEFT parameters.

Methodology
This work presents results from SMEFIT3.0, an updated global SMEFT fit utilizing the SMEFIT framework. The analysis considers 50 dimension-6 operators in the Warsaw basis, categorized into five classes: two-fermion (2F), four-heavy-fermion (4H), two-light-two-heavy-fermion (2L2H), purely bosonic (B), and the four-lepton operator ($O_{\ell\ell}$).

The methodology involves three distinct stages:

1. Baseline Fit (Run II): The authors perform a global fit to LHC Run II data at both linear and quadratic orders in the EFT expansion. Experimental inputs include updated Simplified Template Cross Section (STXS) measurements, the $p_T^Z$ differential distribution in $WZ$ production, and recent top quark production measurements from ATLAS and CMS. Crucially, this version implements an exact treatment of EWPOs from LEP and SLD, replacing the approximations used in previous versions.
2. HL-LHC Projections: The baseline fit is extended by adding projections for the HL-LHC. These projections are generated by fluctuating central values around SM predictions within experimental uncertainties. Statistical uncertainties are rescaled by the luminosity increase, while systematic uncertainties are rescaled by a factor of 2.
3. Future Collider Projections: The analysis further incorporates projections for the FCC-ee (used as a representative example for both FCC-ee and CEPC due to similar results). Four running scenarios are considered, ranging from the Z-pole to $\sqrt{s} = 365$ GeV. Observables include EWPOs, light fermion pair production, Higgs production ($hZ$ and $h\nu\nu$ channels), gauge boson pair production, and top quark pair production.

The impact of these future datasets is quantified using the ratio of uncertainties, $R_{\delta c_i}$, comparing the 95% credible intervals (CI) of the baseline fit against those including future projections.

Key Contributions and Results

• Current Constraints (SMEFIT3.0):

  • Quadratic Terms: The inclusion of quadratic terms in the marginalised fit is shown to be generally important, improving bounds and breaking degeneracies (flat directions) present in linear fits, particularly for 4H and 2L2H operators.
  • Operator Bounds: Most coefficients are constrained to order $O(1)$ in units of $1/\text{TeV}^2$. However, 4H operators remain the least constrained, with bounds ranging from order 1 to 10.
  • Fit Residuals: The fit shows good agreement with SM expectations. Notable deviations include $c_{tG}$ (in the quadratic fit only, driven by tension between CMS 8 TeV double-differential distributions and other $t\bar{t}$ data) and coefficients $c_{\phi q}^{(3)}$ and $c_{\phi d}$ (driven by correlations with other parameters).
  • Data Impact: The strongest improvement in the updated analysis comes from recent $\bar{t}t$ production measurements, which reduce bounds on 2L2H operators by a factor of 2 to 3.

• HL-LHC Prospects:

  • Adding HL-LHC projections to the baseline improves the marginalised quadratic bounds by 20% to a factor of 3.
  • The analysis notes that individual parameter fits often show significantly better sensitivity (sometimes by an order of magnitude) compared to global marginalised fits.
  • The authors acknowledge that further improvements could be achieved through finer binning and extended differential distributions, which were not optimized in this specific analysis.

• FCC-ee Prospects:

  • The inclusion of FCC-ee projections following the HL-LHC yields substantial improvements, particularly for bosonic and two-fermion operators, where bounds improve by a factor of 30 to 50 (up to two orders of magnitude).
  • In contrast, the improvement for the four-quark sector is limited. This is because the observables considered for the FCC-ee are insensitive to these operators at Leading Order (LO); the observed minor improvements arise solely from marginalisation effects. The inclusion of Next-to-Leading Order (NLO) effects for these operators is identified as future work.

Significance and Future Outlook
The paper establishes SMEFIT3.0 as a robust baseline for interpreting current and future collider data. It demonstrates that quadratic SMEFT effects are fundamental for reducing parameter space and breaking correlations. While the HL-LHC offers moderate improvements, the FCC-ee is projected to provide a transformative increase in precision for bosonic and two-fermion operators.

The authors conclude by outlining several modest extensions for future work:

• Refining HL-LHC projections through dedicated binning strategies.
• Extending the analysis to include other proposed colliders, specifically the ILC, CLIC, and high-energy muon colliders, to provide a complete comparison of their constraining power.
• Investigating the impact of coefficient mixing due to Renormalization Group Equation (RGE) running.