Anomalous Triple Gauge Couplings in the Effective Field Theory Approach at the LHC

TL;DR

The paper investigates how to extract anomalous triple gauge couplings within the SMEFT framework using LHC diboson data, emphasizing consistency by retaining only ${\mathcal{O}}(\Lambda^{-2})$ interference terms and examining the impact of ${\mathcal{O}}(\Lambda^{-4})$ dim-6 squared contributions. It analyzes EFT validity, including how cross sections depend on aTGCs and the role of the energy scale $\hat{s}$, and develops conservative strategies when $m_{VV}$ cannot be reconstructed, such as applying EFT cuts only to BSM simulations. Through recasts of CMS $WW$ and ATLAS $WZ$ analyses at 8 and 13 TeV, the study demonstrates that current LHC bounds on aTGC are often dominated by quadratic dim-6 terms and are compatible with, or stronger than, Higgs+LEP-2 constraints for certain UV scenarios. An explicit UV model with vector resonances is used to illustrate the matching to SMEFT and to quantify the EFT validity range, finding agreement between EFT and direct bounds for $m_V \gtrsim 3$ TeV and conservative bounds otherwise. The work highlights practical guidance for interpreting LHC diboson searches in SMEFT, including the importance of publishing full likelihoods and presenting results as a function of the EFT validity cut $m_{VV}^{\max}$, to enable accurate translations to UV theories.

Abstract

We discuss how to perform consistent extractions of anomalous triple gauge couplings (aTGC) from electroweak boson pair production at the LHC in the Standard Model Effective Field Theory (SMEFT). After recasting recent ATLAS and CMS searches in $pp\to WZ (WW) \to \ell' ν\ell^+\ell^- (ν_{\ell})$ channels, we find that: (a) working consistently at order $Λ^{-2}$ in the SMEFT expansion the existing aTGC bounds from Higgs and LEP-2 data are not improved, (b) the strong limits quoted by the experimental collaboration are due to the partial $Λ^{-4}$ corrections (dimension-6 squared contributions). Using helicity selection rule arguments we are able to explain the suppression in some of the interference terms, and discuss conditions on New Physics (NP) models that can benefit from such LHC analyses. Furthermore, standard analyses assume implicitly a quite large NP scale, an assumption that can be relaxed by imposing cuts on the underlying scale of the process ($\sqrt{\hat{s}}$). In practice, we find almost no correlation between $\sqrt{\hat{s}}$ and the experimentally accessible quantities, which complicates the SMEFT interpretation. Nevertheless, we provide a method to set (conservative) aTGC bounds in this situation, and recast the present searches accordingly. Finally, we introduce a simple NP model for aTGC to compare the bounds obtained directly in the model with those from the SMEFT analysis.

Figures (13)

• Figure 1: Dependence of the $\sigma(pp\rightarrow WW)$ (left) and $\sigma(pp\rightarrow WZ)$ (middle) on the aTGC, $\lambda_z$ (black), $\delta g_{1,z}$ (blue), and $\delta \kappa_\gamma$ (red). One parameter is varied at a time while the other two are set to zero. In the left and center panels the solid (dashed) lines correspond to the cases with $m_{VV} (\equiv\sqrt{\hat{s}}) < \infty$ (600 GeV). In the right panel, instead, only high energy events ($m_{VV} > 600$ GeV) are shown, using solid (dotted) lines for $pp\rightarrow WZ (WW)$.
• Figure 2: Left: Event distribution in the plane of the invariant mass of dilepton system, $m_{\ell\ell}$ (which is reported by the experiment) versus $m_{WW}$ (which corresponds to $\sqrt{\hat{s}}$.). Right: Similar plot for $m_T^{WZ}$ vs $m_{WZ}$. Both histograms are based on $5\times 10^5$ events.
• Figure 3: $68\%$ CL region from 8 TeV CMS $pp \to W^+W^-$ searches for different $m_{WW}$ cuts.
• Figure 4: Recast of the CMS analysis of $W^+W^-\rightarrow l\nu l\nu$ process at $\sqrt{s} = 8$ TeV and $19.4~\mathrm{fb}^{-1}$Khachatryan:2015sga. Bounds on the anomalous triple gauge couplings obtained expressing the signal strengths in each bin up to quadratic (red-filled) and linear (red-dashed) order in aTGC, respectively. No cuts on truth $m_{WW}$ are applied.
• Figure 5: $68\%$ CL region from 8 TeV ATLAS $pp \to W^\pm Z$ searches for different $m_{WZ}$ cuts.