Effective field theory versus UV-complete model: vector boson scattering as a case study

Effective field theories (EFT) are commonly used to parameterize effects of BSM physics in vector boson scattering (VBS). For Wilson coefficients which are large enough to produce presently observable effects, the validity range of the EFT represents only a fraction of the energy range covered by the LHC, however. In order to shed light on possible extrapolations into the high energy region, a class of UV-complete toy models, with extra SU(2) multiplets of scalars or of fermions with vector-like weak couplings, is considered. By calculating the Wilson coefficients up to energy-dimension eight, and full one-loop contributions to VBS due to the heavy multiplets, the EFT approach, with and without unitarization at high energy, is compared to the perturbative prediction. For high multiplicities, e.g. nonets of fermions, the toy models predict sizable effects in transversely polarized VBS, but only outside the validity range of the EFT. At lower energies, dimension-eight operators are needed for an adequate description of the models, providing another example that dimension-eight can be more important than dimension-six operators. A simplified VBFNLO implementation is used to estimate sensitivity of VBS to such BSM effects at the LHC. Unitarization captures qualitative features of the toy models at high energy but significantly underestimates signal cross sections in the threshold region of the new particles.