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

Understand

By including the recently discovered Higgs-like scalar $\varphi$ 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 $\varphi\varphi \rightarrow \varphi\varphi$ and the inelastic process $VV\rightarrow \varphi\varphi$, 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.