If susy were unbroken, should we need a higgs?

[arivero]

reading the light-heart book of Aitchison, "an informal intro...", we see that the problem with mass terms in the electroweak bosons is not that they spoil gauge invariance, but that they spoil gauge invariance in a way that it is not recovered when their mass goes to zero.

After one has been forced to introduce these auxiliary scalar fields, it seems that they only way to organize them is via the Higgs field.

Now, in susy, the scalar fields are not an extra. They come included, via the susy generators, in any massive vector multiplet. So they natural... do they need to come from a higgs, at all. I mean, it seems that the limit M--->0 works perfectly in this case, just separating the massive multiplet in a massless vector plus a massless chiral.

 

[fzero]

Trying to accomplish realistic EWSB with an adjoint Higgs seems a bit unlikely. There are no gauge invariant Yukawa couplings between the left and right-handed fermions (assuming the usual chiral $$SU(2)_W$$ charges) so fermion masses don't appear to be generated naturally. To maintain the SUSY of the massive supermultiplet, the scalar field can only couple to the fermions the same way that the gauge bosons do, namely left to left and right to right.

A much bigger problem is that you can never get a massless photon from a component of a massive vector superfield.

 

[arivero]

Trying to accomplish realistic EWSB (...)

Well, of course, to consider SUSY unbroken at EW scale is not a realistic scenary (it is for my own purposals, as I do not believe on fundamentel squarks and sfermions... but in general we can consider it a theoretical exercise) . Similarly, fermion mases are not a requisite in this scenary. One could consider a plus if some mechanism incorporates a mass for the top.

with an adjoint Higgs seems a bit unlikely.

So my first bet was "no higgs at all", but yes, possibly we can consider the winos and their partners as a kind of adjoint higgs.

A much bigger problem is that you can never get a massless photon from a component of a massive vector superfield.

Hmm I had not though on the mixing, damn!