Main Question or Discussion Point
Why was is it needed to include the Z boson along with the W's... is the theory nonrenoramalizable without it?
Right. To have a renormalizable theory, one must have a U(1) x SU(2) gauge invariance. After spontaneous symmetry breaking, two of the gauge fields of the SU(2) symmetry as well as one linear combination of the U(1) generator and tau_3 generator acquire a mass..Those are the Z,W+,W-. The other, orthogonal, linear combination of the generators give the massless photon. If one simply throws in a W+ and W-, there is no gauge symmetry and the theory can't be made renormalizable.Why was is it needed to include the Z boson along with the W's... is the theory nonrenoramalizable without it?
When I referred to unitarity I meant that in the Fermi theory there are cross sections that grow with the energy.You can describe low-energy limit of weak interaction without intermediate bosons, that's called Fermi theory, but it is not renormalizable. A theory with spontaneously broken SU(2) x U(1) symmetry group nicely describes everything, and SU(2) x U(1) just happens to have 4 generators, which become a photon and three new gauge bosons.
I don't think that unitarity enters in any way.