EFT observable stability under NLO corrections through interference revival

TL;DR

This work examines the stability of EFT observables under NLO corrections for the SMEFT operator $O_W$, demonstrating that interference between SM and SMEFT amplitudes can be revived by selecting phase-space variables that separate opposite-sign interference contributions. Using three LHC processes—EW $Zjj$ via VBF, fully leptonic $WZ$, and leptonic $W\gamma$—the authors compare LO and NLO differential cross sections and $K$-factors for linear and quadratic SMEFT terms, showing that appropriate observables yield more reliable predictions and controlled perturbative expansions. They derive bounds on $C_W/\Lambda^2$ from these observables and find bounds comparable in strength to those obtained from quadratic terms or related measurements, with the strongest sensitivity in $Zjj$ and $W\gamma$ when interference-revival observables are used. The results underscore the generality of the method and its compatibility with data, uncertainty treatments, and even machine-learning approaches to optimize interference restoration across EFT analyses.

Abstract

We illustrate the importance of interference revival, when higher-order corrections are included, by presenting LO and NLO differential cross sections and $K$-factors for three processes that are sensitive to the dimension-6 SMEFT operator $O_W$ : $Z$-plus-two-jets ($Zjj$) through VBF, leptonic diboson $WZ$ and $Wγ$ production. We show how lifting the interference suppression at LO, through suitable variables and cuts, is necessary to get reliable predictions at NLO. We also present bounds on $C_W /Λ^2$ obtained from these observables

Figures (11)

• Figure 1: NLO SM differential distributions for the azimuthal distance between jets in EW Zjj, at FO and matched with Pythia8 and Herwig7 showers. Numerical and scale-variation uncertainties are shown, and the experimental data as well
• Figure 2: Differential cross section for the signed azimuthal distance between jets in Zjj, at LO without PS. The black line reproduces the SM distribution divided by 10, while the red (blue) one the positive- (negative-) weigthed contribution to the linear term. The orange line is the difference of the last two, namely the interference differential cross section. The uncertainties are not shown
• Figure 4: WZ interference cross section per bin at LO without PS, as a function of p_T^Z and ϕ_{WZ}, in the two cases in which the Z leptons have helicities ± 1 and ∓ 1. Red (blue) areas mark where the cross section is positive (negative), as the positive- (negative-) weighted contribution dominates there. The black dashed lines separate the phase-space areas in \ref{['cuts']}. The uncertainties are not shown
• Figure 5: LO and NLO differential cross-section distributions for ϕ_{WZ}, over all the phase space (top) and when specific cuts on p_T^Z and ϕ_{WZ} are applied (centre and bottom). The black (orange, green) line represents the SM, divided by 50 (interference, quadratic correction divided by 4). The K-factors are also shown, together with their numerical and scale uncertainties. For each case, the relative cancellation for LO interference is plotted. Note the different variable range in the central plot, due to the cuts
• Figure 6: FO LO and NLO differential cross-section distributions for the transverse mass of the WZ system, over all the phase space (top) and when cuts on p_T^Z and ϕ_{WZ} are applied (centre and bottom). The black (orange, green) line represents the SM, divided by 50 (interference, quadratic). The K-factors are also shown, together with the relative cancellation for LO interference. In the first plot, we also report N^2LO results for the SM at FO and the experimental measurements, divided by 50. The last bin contains the overflow