MTd2 said:
This setup! Always this one! :)
Well, what we have got -besides uniqueness- is to obtain, from this hidden SU(5) symmetry, all the non-gauge bosons of the Superymmetric Standard Model.
Of these, the ones related to the electroweak scale are the partners of the top, and the scalar partners of the W+, W- and Z bosons (more precisely, the scalar partners of the chiral fermion that is absorbed by the gauge bosons to get mass).
All of them come in different ways from the 15 +
15 representation of SU(5), which in turn is extracted from 5x5=15+10. In plain words, they are the set of different pairs you can do with u,d,c,s,b, plus the different pairs you can do with
u,
d,
c,
s,
b
Of these, six plus six do the partners of Dirac up quarks:
dd,ds,db,ss,sb,bb,dd,ds,db,ss,sb,bb
six plus six do the partners of Dirac down quarks:
du,dc,su,sc,bu,bc,du,dc,su,sc,bu,bc
and three plus three do the partners of the Chiral (Weyl?) w+,w+,z companions:
uu,uc,cc,uu,uc,cc
The Dirac fermions can see colour, so they triplicate for each colour. The Chiral fermions can not see colour (and they can see electroweak charge, but not pure electromagnetic charge), so their partners do not triplicate neither (the mechanism for it, I do not known yet, it implies to use Super-QCD, surely).
All we can expect is that two special combinations of the first (bi)sextet are related to the top, and then its mass before susy breaking is related to the mass of the chiral companions. Within this setup, I do not see any other exploitable feature, and even this one is unclear, as I do not see what combinations we should select. We could put some more group theory into, namely the decomposition of SU(5) into the subgroup SU(3) x SU(2), and we could also pay attention the left and right chiralities.