Recovering the $ SU(2)$ unbroken limit by taking $m_W, m_Z \to 0$ I'm trying to compute the tree-level scattering amplitude for $e^+e^- \to q \overline{q}$ and $e^+e^- \to W^+W^-$ in unitary gauge. Both processes go through an $s$-channel photon, $Z$ and Higgs while the second process also has a $t$-channel neutrino exchange. I would like to check these results with results in the unbroken $SU(2)$ limit, where the $SU(2)$ gauge bosons are massless. Should I expect to recover the result in the unbroken limit by taking all of the gauge boson masses to zero? Or is there something extra that I have to do? 
 A: Your question (if I understand correctly) can be summarized with:

Are the amplitudes computed in the Standard Model in the limit where the Higg's vacuum expectation value (VEV) $\rightarrow 0$ equal to those computed in the Standard Model without spontaneous symmetry breaking (i.e., either without a Higgs at all or with a Higgs but with the Higgs mass parameter $\mu^2>0$)? 

Indeed such amplitudes are equivalent to those in another theory but its not quite either of the theories you proposed. Just removing the Higgs gives the wrong answers for processes involving the longitudinal modes of the vector bosons. Having the Higgs but swapping its mass parameter, doesn't by itself make much sense (what do you mean by the different components of the Higgs then?). However, the amplitudes are equivalent to those computed in the "Goldstone Boson Equivalent" theory. 
In this theory you identify the longitudinal modes of the vector bosons with the different components of the Higgs (the ones that get "eaten" in the Unitarity gauge). Then the amplitudes are given by those computed by this ``unbroken symmetry'' theory in the limit that the VEV approaches zero. More formally, the amplitudes are equal to those computed in the full theory up to $ {\cal O}({\rm energy} / m _{W,Z})  $ corrections. 
