Polarized-boson pairs at NLO in the SMEFT

We present a computation of diboson production in the $W^\pm Z$ channel at the Large Hadron Collider (LHC), incorporating leptonic decays of the gauge bosons and considering intermediate gauge bosons with definite polarization states. The analysis includes contributions from the Standard Model effective field theory (SMEFT) and is carried out at next-to-leading order accuracy in QCD, matched to a parton-shower simulation. Our implementation allows for the selection of specific helicity configurations, both in the Standard Model and in the presence of dimension-six operators inducing anomalous triple-gauge-boson couplings. This work provides a key ingredient for both polarization-template and quantum-tomography analyses of diboson systems at the LHC within the SMEFT framework.

💡 Research Summary

The paper presents a state‑of‑the‑art theoretical prediction for W±Z diboson production at the LHC, fully differential in the leptonic decay products and including the possibility to select definite polarization states of the intermediate W and Z bosons. The authors work within the Standard Model Effective Field Theory (SMEFT) framework, incorporating a complete set of eight CP‑even dimension‑six operators that modify both Higgs‑gauge couplings (Q_HB, Q_H‹B, Q_HW, Q_HfW, Q_HWB, Q_HfWB) and triple‑gauge‑boson interactions (Q_W, Q_fW).

The calculation is performed at next‑to‑leading order (NLO) in QCD and matched to a parton‑shower (PS) using the POWHEG‑Box‑Res framework. A crucial technical ingredient is the double‑pole approximation (DPA), which isolates the doubly‑resonant contributions (on‑shell W and Z) while preserving gauge invariance. Within the DPA the authors project the resonant amplitude onto on‑shell kinematics, then replace the gauge‑boson propagator numerators with explicit polarization vectors ε(λ)μ(k) (λ = L, +, −). This allows the definition of polarized cross sections at any perturbative order, provided the same DPA and polarization projection are applied to Born, virtual, real and subtraction terms. For real emission contributions the authors boost the partonic centre‑of‑mass frame to the diboson centre‑of‑mass frame before applying the polarization vectors, ensuring a consistent definition of helicities.

Amplitudes containing SMEFT operators are generated automatically with a modified version of Recola 2, which has been extended to handle the chosen set of operators and to output helicity‑specific matrix elements. The resulting fixed‑order NLO predictions are then interfaced with POWHEG‑Box‑Res, which implements the DPA and the polarization projection, and finally matched to a parton‑shower (e.g. Pythia) to obtain realistic event samples.

Phenomenological results are presented for proton‑proton collisions at √s = 13 TeV, using realistic fiducial cuts on the charged leptons (p_T > 25 GeV, |η| < 2.5, etc.). The authors compute (i) the inclusive (unpolarized) cross section, (ii) singly‑polarized observables where only one of the bosons is fixed to a given helicity, and (iii) doubly‑polarized observables where both W and Z are assigned specific helicities. They find that the interference between SM and SMEFT amplitudes is highly polarization‑dependent: longitudinal‑longitudinal (L‑L) configurations are most sensitive to Higgs‑gauge operators, while transverse‑transverse (T‑T) and mixed (L‑T, T‑L) configurations probe the triple‑gauge operators Q_W and Q_fW. At leading order many interference terms are suppressed by helicity selection rules, but NLO QCD corrections partially resurrect these interferences, leading to sizable SMEFT effects even for modest Wilson‑coefficient values.

The impact of the parton shower is examined; while showering smears angular distributions and reduces the purity of polarization tagging, observables based on azimuthal angles (e.g. the φ* variable) retain significant discrimination power. The authors also explore a “quantum tomography” approach, fitting multidimensional angular distributions to extract simultaneous constraints on the full set of Wilson coefficients, thereby providing a model‑independent alternative to traditional template fits.

In conclusion, the work delivers a fully differential NLO+PS tool for polarized W±Z production in the SMEFT, enabling precise studies of anomalous triple‑gauge couplings and Higgs‑gauge interactions. The implementation is publicly available within the POWHEG‑Box‑Res repository, and the authors outline future extensions to include NNLO QCD and NLO electroweak corrections as well as applications to other diboson channels (WW, ZZ). This development is poised to become a key ingredient for the upcoming Run 3 and HL‑LHC analyses that aim to exploit boson polarization as a sensitive probe of physics beyond the Standard Model.