Isolating Vector Boson Scattering at the LHC: gauge cancellations and the Equivalent Vector Boson Approximation vs complete calculations

We have studied the possibility of extracting the $W^+W^-\to W^+W^-$ signal using the process $us\to cd W^+W^-$ as a test case. We have investigated numerically the strong gauge cancellations between signal and irreducible background, analysing critically the reliability of the Equivalent Vector Boson Approximation which is commonly used to define the signal. Complete matrix elements are necessary to study Electro--Weak Symmetry Breaking effects at high $WW$ invariant mass