Higgs boson compositeness: from $e^+e^-\to ZH$ to $e^+e^-\to Z_L,W_L +anything $

We assume that the Higgs doublet has a composite structure, respecting the main standard model properties, and therefore called Composite Standard Model (CSM), but leading (through Goldstone equivalence) to $Z_L$ and $W_L$ form factors. We illustrate how such a form factor affecting the $ZZ_LH$ coupling will be directly observable in $e^+e^-\to ZH$. We then show the spectacular consequences which would appear in the inclusive processes $e^+e^-\to Z_L+anything$. Such a form factor could also affect the $\gamma W^+_LW^-_L$ and $Z W^+_LW^-_L$ vertices and we show what effects this would generate in $e^+e^-\to W^+W^-$ (especially in $e^+e^-_R\to W^+_LW^-_L$) and in $e^+e^-\to W_L+anything$. We finally mention the $\gamma\gamma\to W^+W^-$ process and several other processes in hadronic collisions which could be similarly affected.