Consistent constraints on the Standard Model Effective Field Theory

TL;DR

This work develops a global constraint framework for the linear SMEFT, integrating 103 observables from LEP-era and low-energy experiments to bound 19 dimension-6 Wilson coefficients while explicitly incorporating a theory-error metric Δ_{SMEFT}(Λ). By constructing a Gaussian likelihood with a comprehensive error budget that includes SMEFT-specific uncertainties (e.g., Δ_{IFI}, Δ_{L8}, Δ_{offshell}) and by profiling across lower-dimensional subspaces, the authors show that SMEFT theory errors significantly relax bounds, challenging the interpretation of per-mille precision bounds as model-independent limits. The global analysis reveals that LEP data dominate the most constrained directions, but the presence of theory errors changes the eigenstructure of the constrained parameter space, underscoring the importance of UV assumptions about the cutoff scale Λ. The results provide a transparent, reproducible framework for SMEFT fits that is essential for robustly interpreting pre-LHC constraints alongside LHC results, and they argue against setting individual Wilson coefficients to zero in LHC analyses without accounting for theory errors. Overall, the paper demonstrates that consistent SMEFT fits require explicit theory-error treatment to avoid overstating sensitivity to new physics in the dimension-6 sector.

Abstract

We develop the global constraint picture in the (linear) effective field theory generalisation of the Standard Model, incorporating data from detectors that operated at PEP, PETRA, TRISTAN, SpS, Tevatron, SLAC, LEPI and LEP II, as well as low energy precision data. We fit one hundred and three observables. We develop a theory error metric for this effective field theory, which is required when constraints on parameters at leading order in the power counting are to be pushed to the percent level, or beyond, unless the cut off scale is assumed to be large, $Λ\gtrsim \, 3 \, {\rm TeV}$. We more consistently incorporate theoretical errors in this work, avoiding this assumption, and as a direct consequence bounds on some leading parameters are relaxed. We show how an $\rm S,T$ analysis is modified by the theory errors we include as an illustrative example.

Figures (9)

• Figure 1: The effect of neglecting $\Delta_{SMEFT}$ on extracted constraints. $\Delta O/O$ is the experimental precision of a measurement in percent. The [solid,dashed,dot-dashed,dotted] curves correspond to $(\sqrt{N_8} \, x_i, \sqrt{N_6} \, y_i)$ values of $(1,1)$, $(\sqrt{10},\sqrt{10})$, $(3 \, \sqrt{10},0)$,$(0, 3 \, \sqrt{10})$ in the simplified theory error metric. The left plot shows the generic impact on percent and per-mille bounds experimentally, while the right shows specific LEPI observables compared to theory error. The actual impact of neglected terms depends strongly on the particular UV scenario integrated out. It seems reasonable to neglect $\Delta^i_{SMEFT}$ when considering LEPI data only when very large cut off scales are implicitly assumed. The SMEFT is not currently developed to a level that allows a consistent incorporation of LEPI data if the SMEFT theory error is not included, for cut off scales $\Lambda \lesssim 3 \, {\rm TeV}$.
• Figure 2: The effect of varying $\Delta_{SMEFT}$ on an oblique analysis. The green, yellow, grey regions correspond to the $68 \%, 95\%$ and $99.9 \%$ CL regions for a two parameter fit around the minimum of the $\chi^2$ distribution. The regions correspond to $\chi^2 = \chi^2_{min}+ \Delta \chi^2$ with $\Delta \chi^2 = 2.30$ ($1 \sigma$, green), $6.18$ ($2 \sigma$,yellow), $11.83$ ($3 \sigma$, grey) defined via the Cummulative Distribution function for a two parameter fit. The left plot does not include any theory error for the EFT, the middle sets $\Delta_{SMEFT} \sim 0.3 \%$, the right sets $\Delta_{SMEFT} \sim 1 \%$.
• Figure 3: This figure shows directly that per-mille bounds on $Z$ couplings (in this case $C_{He} \bar{v}_T^2/\Lambda^2$ and $C_{Hq}^{(3)} \bar{v}_T^2/\Lambda^2$) to fermions can be relaxed to $\sim \%$ constraints when considering the effect of $\Delta_{SMEFT,i}$. Conventions for the confidence regions as in the previous figure.
• Figure 4: The effect of varying $\Delta_{SMEFT}$ on an oblique analysis, when the remaining parameters are profiled over and not set to zero. Constraints are relaxed essentially by a loop factor $\sim 16 \pi^2$. Conventions for the confidence regions as in the previous figures. The interpretation of this result requires some care, see the text. We stress that this figure should not be interpreted as directly comparable to Fig. \ref{['Fig;LEPyay']} as the assumptions of the two analyses fundamentally differ.
• Figure 5: The fit space for $C_{He} \bar{v}_T^2/\Lambda^2$ and $C_{Hq}^{(3)} \bar{v}_T^2/\Lambda^2$ when the remaining parameters are profiled away. Conventions for the confidence regions as in the previous figures. Note the impact of profiling on the correlations in this case.