This is a sequel to an earlier question about Alejandro Rivero's correspondence, the "super-bootstrap".

The correspondence itself was introduced in his "Supersymmetry with composite bosons"; see the tables on page 3. Briefly, we consider all possible pairings of quarks and antiquarks, but only from the first five flavors, "because" the top quark decays too quickly to hadronize. If we add up the electric charges, we get exactly the right number of combinations to get all six flavors of quark and all three charged leptons. There are also enough combinations to match all three neutral leptons (with an extra state left over); and there are also some exotics with charge 4/3. One may repeat the exercise with the full electroweak quantum numbers and it still works, more or less.

We seem to be getting back all the standard model fermions by pairing up five flavors of quark - except that two quarks should create a boson. So in addition we postulate that the standard model fermions are superpartners to these pairings: a lepton is a "mesino", a quark is (or mixes with) a "diquarkino". For months I've been thinking how to obtain this set of relationships within a supersymmetric theory. There are two problems: first, how do you get elementary and composite particles into the same superfield; second, what about gauginos, superpartners of the gauge bosons?

But it has finally occurred to me that maybe you don't need supersymmetry at all - you just need some extra fermionic preons. Suppose there are five fundamental quarks, udscb, and fermionic preons n, n',... which don't feel the strong force. And suppose that there is a new confining force, the ultrastrong force, and that udscb and n, n',... all feel it - they all have ultracolor charge. Then there will be "ultrahadrons", some of the form "qqnn..." or "qbar qnn..", and these can be the diquarkinos and mesinos of the correspondence. Leptons would be mesino-like ultrahadrons, the top quark would be a diquarkino-like ultrahadron, and the udscb quarks might also mix with other diquarkino ultrahadrons.

This seems like a very simple idea, and yet I see no sign of it in the literature on preon models. I would therefore be interested in any anticipation of the idea that does exist, and in any arguments which have a bearing on its viability.

  • $\begingroup$ Hi Mitchell. As I can not see how to advance more in this topic, I am summarizing the result to send it for eventual publication in some minor journal. The draft now is in vixra at vixra.org/abs/1408.0196 and I could benefit of answers in this question doing some constructive criticism and/or proofreading of the paper. $\endgroup$
    – arivero
    Aug 31, 2014 at 0:23

2 Answers 2


Your model is no good for the following reasons:

  • You are using what you call quarks as fundamental building blocks of other particles which are also called quarks. You need to say explicitly what the preons are, and what their gauge charges are.
  • You absolutely can't have 5 flavors of preon quarks, because I presume the left handed part of the preon bottom is an SU(2) doublet.
  • You can't have quarks with the usual quantum numbers without leptons too, because such a theory is anomalous. You need to consider both gauge and gravitational anomalies and show that they vanish, as they do in the standard model.
  • The top quark does not decay too quickly to hadronize if it has a superstrong confining interaction, so I can't make sense of this statement. Anyway, you didn't write down the combinations you believe correspond to the observed particles, and you didn't talk about the condensates in the theory. What is the analog of the pion? Without the superstrong theory, you don't have a model.
  • How do you get massless neutrinos from a superstrong confining interaction? You then have to deal with the fact that the neutrino is not exactly massless.
  • A supersymmetry between bound states can exist, there are such approximate supersymmetries in nuclei, the only observed supersymmetries so far. But in your model, there is no way you will get a low-energy supersymmetric theory without tuning it, and I don't see why you want it anyway.

The whole field of preon models is mostly pointless, because it is so obvious that quarks and leptons are fundamental particles. They are structureless experimentally, and the quarks and leptons are related by anomaly cancellation . They also fall out from an SU(5) or SO(10) gut extremely naturally. Why would anybody think they are composite? If they are composite, you should at least explain their generation structure from your model by having excited states be second generation, third generation leptons. But then it is hard to stop at 3 generations. You didn't do that for sure.

Technicolor theories are completely different--- they postulate that there is a strong interacting sector whose hadrons are responsible for the Higgs mechanism. They are taken seriously because they solve the heirarchy problem without supersymmetry, the mass of the proton is not determined by the Higgs after all, but by the QCD running.


I would question some of these statements. Lepton decay (e.g. muon) would seem to indicate some internal structure. While many have faith in the existence of quarks they have never been directly observed because of 'confinement' and so seem to me to be a mathematical abstraction. And the Standard Model includes 16 fundamental particle (plus 8 gluons), double that if one subscribes to supersymmetry, that's an awful lot of fundamental particles.

  • 2
    $\begingroup$ Welcome to the site. once you gain some points you can comment Now on your comment :a) who decreed that fundamental particles cannot decay into other fundamental particles? b) none of the elementary particles are directly observed: we see their macroscopic tracks and use mathematics to classify the origin of those tracks. Quarks follow the same pattern, except they do no leave tracks in bubble chambers, but measurable interaction effects that are most economically described by the QCD theory. c) who decreed that there should only be one fundamental particle? $\endgroup$
    – anna v
    Apr 12, 2012 at 12:13
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    $\begingroup$ continued: the ongoing research is in the process of discovering and mathematically organizing the microcosm. At the moment the SM reigns supreme, and supersymmetry and string theory might be around the corner at the LHC, as mathematical descriptions. As the pythagorians believed: "god always measures " "θεος αιεν γεωμετρει" . $\endgroup$
    – anna v
    Apr 12, 2012 at 12:17
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    $\begingroup$ If a fundamental particle can decay, this does NOT mean that it is COMPOSED of the decay products ... Prof. Strassler beautifully explains why here, using the higgs decay to two photons ans an example. I too would give you the advice to give some useful answers or ask some useful questions soon, such that you can comment everywhere. You need 50 points of reputation for this. $\endgroup$
    – Dilaton
    Apr 14, 2012 at 12:08
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    $\begingroup$ While quarks have never been seen freed, evidence has been found for them courtesy of deep inelastic scattering. I think a lot of people would say that they aren't merely a "mathematical abstraction". @Dilaton also brings up an excellent point regarding decay. $\endgroup$
    – HDE 226868
    Sep 4, 2014 at 0:03

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