Dimension-8 SMEFT contact-terms for vector-pair production via on-shell Higgsing

We derive the dimension-8 standard-model effective theory (SMEFT) contact terms relevant for vector-pair production at the LHC and lepton colliders. We first list the relevant dimension-8 massless SMEFT amplitudes, and then obtain the low-energy amplitudes using on-shell Higgsing. In all cases, the contributions we calculate are the leading-order contributions to 4-point contact-terms; the dimension-6 SMEFT merely corrects the three-point couplings entering the amplitudes. Since they are given in terms of physical quantities, namely momenta and polarizations, the results allow for a direct mapping of EFT effects to low-energy observables. The vector amplitudes are sensitive to both anomalous vector couplings and Higgs self-couplings. The left-handed fermion amplitudes feature SU(2) violating effects first generated at dimension-8. We also compare our results to HEFT predictions. Interestingly, the dimension-8 SMEFT populates almost all the novel structures generated by the dimension-8 HEFT.