Same-sign WW scattering at the LHC: can we discover BSM effects before discovering new states?

It is possible that measurements of vector boson scattering (VBS) at the LHC will reveal disagreement with Standard Model predictions, but no new particles will be observed directly. The task is then to learn as much as possible about the new physics from a VBS analysis carried within the framework of the Effective Field Theory (EFT). In this paper we discuss issues related to the correct usage of the EFT when the WW invariant mass is not directly accessible experimentally, as in purely leptonic W decay channels. The strategies for future data analyses in case such scenario indeed occurs are proposed.