  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.
