Why am I posting this in the thread of preons? Well, because, as veteran readers of PF know, I got the idea last year of having the preons directly from quarks: a pair of quarks would compose a boson, and then this boson is supersymmetrically transfomed to the fermion we are aiming for. Sort of bootstrap.
I described the idea one year ago in
hep-ph/0512065. It is not bad, it produces only a extra degree of freedom in the neutrino sector and six horrible 4/3 coloured degrees of freedom in a quark/antiquark sector, but I would hope they can be eliminated on the grounds of representation theory.
It has the adventage that we know the masses of the, er, subquarks, and also we know how they bind: with SU(3) colour. The binding via SU(3) colour gives some substance to infrarred mass relationships, as Koide's, that are troublesome to be planted in the GUT scale (albeit some people do). Ideally the IR limit of QCD explodes the coupling constant, and then justifies the trick.
But the problem is that we already have the "susyleptonic" sector of this theory, and they are the charged mesons of the previous post. It is not a badly broken thing, because the pion has more of less the same mass than muon and the D particles are about the same mass than the tau. But the electron has no partner near, neither the B particles.
So here is why I think it is unlikely to find Koide relationships for mesons: because I think that in the limit of unbroken supersymmetry, leptons would derive Koide relationship from the fact they are partners of sleptons, which happen to be mesons, thus composites. In this limit, then, mesons also meet Koide relationships, and furthermore they are degenerated in pairs. But I find unlikely that Koide can survive in both sectors after symmetry breaking, and if it survives in leptons, my guess is that it will break in the mesonic part.
Telling this, and against myself, I can not but notice that besides the obvious triplets (0, m_\pi, m_{D_s}) and (0, m_\pi, m_{D}), also the triplet (0, m_k, m_{B_c}) is, unexpectedly,very Koide-like. Moreover, when the 0 is substituted by another of the particles, D or B, it counterweights nicely, climbing Koide's relation from 2:3 to 2:5.