Probing EFT breakdown in the tails of $W^+ W^-$ observables

TL;DR

The paper tackles the challenge of ensuring EFT validity in high-energy tails of $WW$ production, where the unobservable $M_{WW}$ complicates enforcing the expansion parameter $E/\Lambda$ to be small. It systematically compares three approaches—Clipping on Simulation ($M_{WW}<\Lambda$ at generator level), bin-by-bin hierarchy checks between dimension-6 and dimension-8 contributions, and data cuts using proxies like $M_{T3}$—and assesses their effectiveness using bosonic dimension-6 and dimension-8 operators in the $gg$ channel. The study finds that naive generator-level clipping fails to guarantee the operator hierarchy and that $M_{e\mu}$ is a poor proxy for $M_{WW}$, whereas the $M_{T3}$ observable provides the strongest correlation with $M_{WW}$, enabling a robust data-level EFT-valid region. Sensitivity analyses at the HL-LHC show that data-cut approaches with $M_{T3}$ can approach the constraining power of generator-level clipping, while bin-by-bin methods can be more stringent but require detailed knowledge of higher-order contributions; overall, the results advocate using $M_{T3}$-based data cuts to maintain EFT validity and maximize sensitivity to higher-dimension operators. The work informs practical EFT fits in diboson channels by clarifying the tradeoffs between validity enforcement and experimental implementability, and cautions against form-factor-like generator cuts that could undermine model-independence.

Abstract

In this letter, we test clipping effective field theory (EFT) simulations as a method of ensuring EFT validity. The procedure imposes that, at the level of the simulation, the invariant mass of a $W^+W^-$ pair $M_{WW}$ is less than the new physics scale $Λ$. We compare this to two other methods, comparison bin by bin of dimension-6 and dimension-8 squared contributions and implementing a cut on data. We find that setting $M_{WW} < Λ$ is not strict enough to ensure that the hierarchy of EFT operators is respected for dimension-6 and dimension-8 contributions. We also show that, even when using a stricter cut on $M_{WW}$, due to different correlations between $M_{WW}$ and $M_{eμ}$ at different EFT orders, the bins in $M_{eμ}$ (the invariant mass of the leptons originating from $W$ decays) used in an EFT fit may not truly be in the regime of EFT validity when performing a dimension-6 fit with $M_{WW} < Λ$. We also explore the correlations of three transverse mass observables: $M_{T1}, M_{T2}$ and $M_{T3}$, finding that $M_{T1}$ and $M_{T3}$ follow the $M_{WW}$ distribution more closely than $M_{eμ}$. We present sensitivity studies using both the $M_{T3}$ distribution and $M_{eμ}$ distribution. We test implementing an experimental cut on $M_{T3}$ in place of clipping the EFT simulation at $M_{WW} < Λ$. We finally comment that adding $M_{WW} < Λ$ cuts only to the EFT simulation could be interpreted as modifying the SMEFT expansion by a form factor and could therefore impact the model independence of EFT fits under this procedure.

Figures (7)

• Figure 1: Comparison of the full dimension-6 (black), dimension-6 subject to the cut $M_{WW} < 1\,$TeV (blue), and dimension-8 (green) contributions to the $M_{e\mu}$ (left) and $M_{WW}$ (right) distributions. The upper panels are for $\Lambda = 1\,$TeV, the lower panels for $\Lambda = 1.65\,$TeV.
• Figure 2: The conditional expectation value of $M_{WW}$ for each bin of the $M_{e\mu}$ (top left), $M_{T1}$ (bottom left), $M_{T2}$ (bottom right), and $M_{T3}$ (top right) distributions, for the SM (black), dimension-6 squared (blue), and dimension-8 squared (green) contributions. The error is given by calculating the asymmetric variance from the expectation value.
• Figure 3: Comparison of the ratio of dimension-8 squared and dimension-6 squared contributions to the theoretical value from the EFT (for the $M_{WW}$ distribution). This theoretical value is given as $\frac{M^4}{\Lambda^4}$, $M=\{M_{WW} ,\,M_{T1},\,M_{T2},\,M_{T3},\,M_{e\mu}\}$.
• Figure 4: Comparison of $M_{T3}$ and $M_{e\mu}$ distributions of SM (black) with SM theoretical uncertainty (shaded area), dimension-6 squared contribution (blue) and dimension-8 squared (green) and SM interference (yellow) contributions, for $\Lambda=3\,$TeV.
• Figure 5: Comparison of the cut on simulation (CoS) approach (left) with the cut on data (CoD) approach (right). The CoD approach includes an extra fiducial cut of $M_{T3} < 0.75\,$TeV whereas the CoS approach applies a cut of $M_{WW} < 0.75\,$TeV only to the generation of dimension-6 EFT contributions. The dimension-6 contribution without CoS is shown in black. The dimension-6 contribution with CoS is shown in blue. Dimension-8 squared (green) and interference (yellow) contributions are also shown without a CoS.