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

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.

💡 Research Summary

In this paper the authors critically examine the common practice of “clipping” effective‑field‑theory (EFT) simulations by imposing the condition (M_{WW}<\Lambda) at generator level, with the aim of guaranteeing that only the dimension‑6 operators are used within their regime of validity. They compare three strategies for ensuring EFT validity in the high‑energy tails of the (W^+W^-) production process at the HL‑LHC:

1. Clipping on Simulation (CoS) – a step‑function (\Theta(1-p^2/\Lambda^2)) is applied only to the BSM (dimension‑6) contribution, leaving the SM and data untouched.
2. Bin‑by‑Bin comparison (CBB) – the size of the dimension‑6 squared term (\sigma^{(6)}) is required to be at least twice that of the dimension‑8 squared term (\sigma^{(8)}) in each bin, i.e. (\sigma^{(6)}\ge2\sigma^{(8)}). This is taken as the most robust definition of the EFT‑valid region.
3. Cut on Data (CoD) – an observable that can be measured experimentally is used to cut away events with energies above (\Lambda). Since the true invariant mass (M_{WW}) is not observable (missing neutrinos), a proxy must be chosen.

The study focuses on the gluon‑fusion channel, which is dominated by two bosonic operators: the dimension‑6 operator (O_{GH}=\phi^\dagger\phi,G_{\mu\nu}^a G^{a\mu\nu}) and the dimension‑8 operator (O_{3}=G_{\mu\nu}^a\tilde G^{a\mu\nu}W_{\rho\sigma}^I\tilde W^{I\rho\sigma}). Using MCFM‑RE at LO and next‑to‑leading‑log (NLL) accuracy, the authors generate differential distributions for the dilepton invariant mass (M_{e\mu}) and the true diboson invariant mass (M_{WW}) under various (\Lambda) choices (1 TeV and 1.65 TeV).

Key findings:

• CoS is insufficient. Even when imposing (M_{WW}<\Lambda), the dimension‑8 squared contribution remains dominant in the (M_{e\mu}>200) GeV region for (\Lambda=1) TeV. A stricter cut ((M_{WW}<1.65) TeV) is needed to suppress dimension‑8, but this still does not guarantee that all bins used in a dimension‑6 fit are free from higher‑order contamination.
• Correlation changes with EFT order. The conditional expectation (E