Equations 3.2-3.4 in that paper are something to stare at, especially if you're a supersymmetry novice. But let's try to interpret them with some very basic help
. All the "F"s are complex scalar auxiliary fields which allow the supersymmetry algebra to close off-shell (see chapter 3 here
). One normally considers only "phi" to be the scalar superpartner of the fermionic "psi", with "F" left out in the cold, but here the physical meson fields are being found inside an "F". Also, the plan in the paper is to completely decouple the superpartners of the known particles, leaving just QCD, so they want everything except the third term of equation 3.4 to drop out. But our objective is to identify some of the leptons
with superpartners of those mesons, so presumably we want to keep some or all of "psiT
". What if we get "FQ
" to drop out? "psiT
" is "quark times antisquark plus antiquark times squark", and we also still have scalar squark-antisquark composites in the picture, alongside the mesons. It seems a little messy. But if we boldly ignore all the details, the message seems to be that a lepton, in this scheme of things, will be "quark times squark".
Now maybe that particular approach makes no sense in any possible world. But I can begin to imagine that, in a more complicated scheme, such considerations would allow you to construct a working preonic model, in which leptons are composite and their superpartners are mesons or diquarks.
Meanwhile, let me also note the existence of some papers by Kyianov-Charsky (also spelt Kiyanov-Charsky and Kiyanov-Charskii), in which QCD mesons and baryons are similarly derived from super-QCD, with the explicit intention of realizing hadronic supersymmetry: 1 2 3