# Alejandro Rivero's correspondence: diquarks and mesons as superpartners of quarks and leptons

The idea of “hadronic supersymmetry” originated in the mid-1960s and derives from the observation that baryons and mesons have similar Regge slopes, as if antiquarks and diquarks are superpartners. This is most efficiently explained by supposing a QCD string model of baryons in which a diquark substitutes for an antiquark at one end of the string, but there are superstring models in which the baryon-meson relationship is a genuine supersymmetry.

In 2005, Alejandro Rivero proposed that mesons are to leptons as diquarks are to quarks. If the top quark is excluded from consideration, as too heavy to hadronize, then one has enough quark-antiquark pairings to match the electromagnetic charges of all the leptons, with a few leftover u,c pairings with charge ±4/3.

The construction is a little complicated, but the possibility that supersymmetry is already right in front of us is so amazing that it just cries out to be investigated. I have an ongoing discussion with Rivero, about whether his correspondence might be realized in a preon model, or a "partially composite" model, or a sophisticated string-theory construction.

Meanwhile, I'd like to know, is there some reason why this can't be realized? The closest thing to such a reason that I've seen is found in comment #11 in that thread: "For a SUSY theory, not just the spectrum must be supersymmetric, but also the interactions between the particles." So far, all Rivero has is the observation that some quantum numbers of diquarks/mesons can be correlated with some quantum numbers of fundamental quarks/leptons, just as if they were elements of a single superfield. I suspect (but I'm such a susy newbie that I can't even confirm this) that you could realize the correspondence in a QCD-like supersymmetric theory, if it was first expressed in terms of meson and diquark variables, and then supersymmetry was completely broken (see comments #40 through #44), but that this would somehow be trivial.

Nonetheless, I think the possibility that supersymmetry is already right in front of us would be important enough, that someone should investigate even such a "trivial" realization of Rivero's correspondence, with a view to understanding (i) whether such a "hard" form of susy breaking might realistically occur (ii) how it would affect the various roles and problems associated with supersymmetry in contemporary physical thought (protect the Higgs mass, supply dark matter candidates; technical model-building issues like "the supersymmetric flavor problem, the gaugino mass problem, the supersymmetric CP problem, and the mu-problem"...).

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When I first met supersymmetry, decades ago, I was surprised to learn that it is used in nuclear physics models: iopscience.iop.org/1742-6596/237/1/012005 as an example. Whenever bosons and fermions gather together supersymmetry can be invoked. ( similar as with SU(2)..SU(N) when the conditions allow). –  anna v Jun 20 '11 at 5:51

I will expand on my comment here, which is an answer to part of the question:

Nonetheless, I think the possibility that supersymmetry is already right in front of us would be important enough, that someone should investigate even such a "trivial" realization of Rivero's correspondence,

I said above : When I first met super-symmetry, decades ago, I was surprised to learn that it is used in nuclear physics models. Whenever bosons and fermions gather together super-symmetry can be invoked.

I am old enough to have started particle physics with the tau/theta puzzle and to have been entranced by the eightfold way, when it was clearly presented to us. That was the way we met SU(3). Meeting SU(3) as the symmetry governing the strong interaction, at a later date, opened my perception that in a similar way that when one has a complicated crystal structure, various symmetries can be found, but there is one basic symmetry of the crystal, in the symmetries involved in elementary particles various groups can be expressed as a consequence, as projections/consequences without being the fundamental symmetry underlying the physics.

The poetic "eightfold way" is just a " cute" projection of deeper underlying symmetries, which depend on similar groups.

Now super-symmetry is a symmetry between bosons and fermions. As my link shows this exists in nuclear physics states too, and actually I have the impression that that is where super-symmetry usage originated in physics, when they were trying to organize nuclear levels and their similarities and differences.

If you have found super-symmetric groupingss between diquarks and mesons, it is interesting, but unless it addresses fundamental questions of model building, one would tend to see it as an interesting analog super-symmetric eightfold way representation, showing nothing more fundamental than that super-symmetry is a viable representation for elementary particles. IMO ofcourse.

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In other words, you are just saying that this symmetry is probably approximate. But that makes it no less useful... In fact, as one digs deeper most of the symmetries are only approximate. Real crystals are never perfectly symmetric, $U(1)$ in QED is just a special case of $U(1)_w \times SU(2)$ and likewise $SU(3)$ is probably a special part of something GUT-ish broken down... –  Marek Jun 24 '11 at 14:52
@marek not particularly approximate, but a projection/confluence of the basic symmetry in the TOE, broken or not.Yes it could be useful, even if it is not TOE. –  anna v Jun 24 '11 at 16:07
Do you have some reminiscences of the S-Matrix democracy and bootstrap ideas? They started the long detour of string theory, but I am under the impression that this symmetry somehow vindicates the bootstrap. –  arivero Jun 25 '11 at 20:21
@arivero My thesis was on k_p scattering at 7GeV/c and the Reggie poles observed :). I do remember the bootstrap model but my knowledge is not deep enough to see if your supersymmetric observations tie up with it. It is good that you report them as part of the jigsaw puzzle. –  anna v Jun 26 '11 at 8:09

Ha, by opening a huge bounty (which I promise I will concede if there is at least an answer beyond mine) I have lost all my privileges, including to do comments (EDIT: I recovered most, thanks everyone :-D Now please give a nice pretty answer so I will be able to pay the bounty happyly) So take this as a note of extra information:

• First, I am not Mitchell, of course :-D I thank him the interest on the issue.
• arxiv:hep-ph/0512065, named in the question. is only a piece of a saga, the "sBootstrap", with different ideas in each preprint, not everything at the same "confidence degree". By the way, already this preprint worries about a scalar with charge 4/3, very like the ones used to explain the $t \bar t$ CDF asymmetry.
• Besides the named preprint, see arXiv:0910.4793 arXiv:0710.1526, as well as the PF threads mentioned by Mitchell, and even a brief note at Vixra :-)
• It is not only that, as Mitchell says, " one has enough quark-antiquark pairings ". With three generations, one has exactly the needed number of pairings, not more not less. In some sense the idea predicts three generations, as it only works nicely with them.

While the main argument is the algebraic match, I have collected too a lot of collateral evidence that seems to indicate that some connections do exist between electroweak and QCD mass scale. Some of them are well known (eg, why the yukawa of the top quark is equal to one? Why do the muon and the tau lurk in the QCD natural and chiral scales?) and others are surprising: the equality between the decay width of pions and Z0 particles, when scaled via the cube of the mass (arXiv:hep-ph/0603145,arXiv:hep-ph/0507144). Or the coincidende that the basic mass scale of Koide formula is 313 MeV, equal to the constituient mass of QCD.

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really great question –  lurscher Jun 23 '11 at 16:13
So, can you use these correspondences to make some guesses about gaps, i.e. try to predict some new particles? –  Raskolnikov Jun 23 '11 at 16:33
@Raskolnikov gaps between known particles, that should be the final goal. New particles nope, only three spin 1/2 "higgsino" (really the partners of W and Z when massive) are expected to be new, all the others are accounted for. –  arivero Jun 24 '11 at 0:27
This last reference to Koide's could deserve further explanation. Koide formula for leptons can be written also as $m_l= m_0 ( 1 + \sqrt 2 \cos(\phi_l))^2$, with $m_0=313.1885 MeV$ and the angles $\phi_l$ required to be separated 120 degrees. –  arivero Jun 24 '11 at 23:43
@riemannium from the formula, given that the angles are separated 120 degrees, the sum $m_1+m_2+m_3$ is equal to $6m_0$ –  arivero Aug 16 '13 at 1:10