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

By including the recently discovered Higgs-like scalar $φ$ in the Electroweak Chiral Lagrangian, and using the Equivalence Theorem, we carry out the complete one-loop computation of the elastic scattering amplitude for the longitudinal components of the gauge bosons $V=W, Z$ at high energy. We also compute $φφ\rightarrow φφ$ and the inelastic process $VV\rightarrow φφ$, and identify the counterterms needed to cancel the divergences, namely the well known $a_4$ and $a_5$ chiral parameters plus three additional ones only superficially treated in the literature because of their dimension 8. Finally we compute all the partial waves and discuss the limitations of the one-loop computation due to only approximate unitarity.