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By including the recently discovered Higgs-like scalar $\varphi$ in theElectroweak Chiral Lagrangian, and using the Equivalence Theorem, we carry outthe complete one-loop computation of the elastic scattering amplitude for thelongitudinal components of the gauge bosons $V=W, Z$ at high energy. We alsocompute $\varphi\varphi \rightarrow \varphi\varphi$ and the inelastic process$VV\rightarrow \varphi\varphi$, and identify the counterterms needed to cancelthe divergences, namely the well known $a_4$ and $a_5$ chiral parameters plusthree additional ones only superficially treated in the literature because oftheir dimension 8. Finally we compute all the partial waves and discuss thelimitations of the one-loop computation due to only approximate unitarity.

One-loop $W_L W_L$ and $Z_L Z_L$ scattering from the Electroweak Chiral Lagrangian with a light Higgs-like scalar