Weak isospin 1/2 vector bosons

Question

The weak vector bosons are spacetime vectors (spin 1) and also incidentally weak isospin vector components (-1, 0, +1). I understand why that is required from nucleon beta decay and other weak interaction decays.   Experimentally there are no weak interactions that I'm aware of that require a weak boson field that is a spacetime vector but a weak isospin spinor  (weak isospins of +-1/2). Is there a sound theoretical reason to exclude such a field from the interaction Lagrangian density, e.g. no suitable term can be made? I have not seen it discussed anywhere, but perhaps just haven't found the right reference yet.

Jim Eshelman · Answer

Thanks for the advice. @TwoB, re the initial reply I believe that the requirement for the gauge bosons to transform as the adjoint rep comes from the need to end up with a scalar lagrangian density, and the fact that normally there is a product of the field with the su(2) (lie alg) generators to cause this. So I guess the question is in those terms whether any other reasonable way to create a scalar term from SU(2) or su(2) and the field reps exists, although, as we all agree, the current one has been pretty well verified by experiment. Possibly something considered by Pauli, Yang and Mills and the others when the theory was forming but discarded by them. Apparently not considered in print so far as I've found. And yes, as someone noticed the motivation is to see if some valid possibility has been overlooked that might help get us out of the tight corner we've painted ourselves into with the SM.

Answered by Jim Eshelman on November 19, 2020

Weak isospin 1/2 vector bosons

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