The wrong turn of string theory: our world is SUSY at low energies

[tom.stoer]

Sorry to say that, but I still don't understand why the SUSY explanation shall provide any benefit. It adds new and un-observed particles (and perhaps resonances / bound states). It adds new questions and nearly no answers. It seems to be a solution hunting for a problem b/c there is no problem in QCD, we perfectly understand its structure.

 

[mitchell porter]

Sorry to say that, but I still don't understand why the SUSY explanation shall provide any benefit.

As far as I'm concerned, the question is: Is there a supersymmetric theory which gives us the standard model, and in which the numerical coincidences which Alejandro has noted, actually arise from supersymmetry? Alternatively, can we prove that no such theory exists? If it can't be done, it would be good to understand why.

Can we find a superpartner to the QCD string?

This is a basic question about how supersymmetry works in theories like super-QCD, to which I do not know the answer. Supersymmetric theories are diverse and very complex. For example, my earlier remark about "gluinos bound by squarks" was rather naive; it looks like the most important interactions of gluinos are with gluons. In discussions of MSSM, you will find people saying that the superparticles will in any case decay to ordinary particles, so composites would not be stable, but that is under the usual assumption that they must be too heavy to have been seen already. So among other things, one should probably look at the behavior of massless super-QCD first - a theory which already comes in many forms: "pure SQCD" with no quarks; SQCD with adjoint quarks, SQCD with quarks in the fundamental representation; SQCD with various numbers of flavors and colors. The 1990s results of Seiberg on electric-magnetic duality look to be of basic importance in understanding these theories.

In all these theories, massless and massive, the elementary fields can be arranged into superfields. But what about composite objects like mesons and baryons - are they generically part of supermultiplets as well? This is what I don't understand. By the way, http://en.wikipedia.org/wiki/Seiberg_duality" involves the appearance of an extra meson superfield on one side.

Back in comment #18, I mentioned a minor research program from string theory - "orientifold planar equivalence" - in which meson strings have baryon strings as superpartners. In the baryon string, the third quark is smeared along the length of the string. See these http://physik.uni-graz.at/itp/iutp/iutp_09/welcome.php?sf=13", but not on the arxiv). In the third lecture, pages 12-13, Armoni actually mentions quark-diquark supersymmetry (Lichtenberg's hadronic supersymmetry), and says this is an alternative explanation (he explicitly says that a certain fermion in N=1 SYM becomes superpartner of the meson). Though I wonder if this picture, with the third quark smeared along the string, might arise from a symmetrized version of the quark-diquark string.

Anyway, obviously we need to look at this and see if it can be extended to include your extension of hadronic supersymmetry to leptons. The framework is unfamiliar to me ("type 0' string theory") so I don't know what pitfalls lie ahead.

 

[arivero]

Sorry to say that, but I still don't understand why the SUSY explanation shall provide any benefit. It adds new and un-observed particles (and perhaps resonances / bound states). It adds new questions and nearly no answers. It seems to be a solution hunting for a problem b/c there is no problem in QCD, we perfectly understand its structure.

The whole "program" is to have less un-observed particles that in standard susy (as in the MSSM). On one side, you know that the the minimal SSM is smaller that the MSSM by two scalars, at the cost of not having a higgs mechanism. On other side, you can arrange all the scalars of this SSM using a SU(5) based flavour symmetry with seems very much as QCD with five flavours. The goal is not to understand QCD, the goal is to understand this flavour and see if it allows a formulation in terms of gluon-like composites, so that the total of particles in the "sBootstrapped SM" is still less than in the SSM.

Even if we understand QCD, we don't understand yet ETC, ie the multiple reincarnations of topcolor and extendedtechnicolor that could be still around the corner in CERN (and Fermilab!). So there is a benefit even if you don't buy the whole program.

 

[tom.stoer]

OK, I'll try to get that

 

[arivero]

A problem I still don't get about relating gluons to strings is that the QCD string is not a single gluon state... the QCD string appears at long distances and intuitively it seems as a "classic field". But a classic field is a collective of elementary excitations; it is because of it that force fields are always bosons, is it not? It is not easy to build a collective field out of fermions (note that a fermionic field, at least in 3d, is proportional to hbar: it dissapears in the classical limit).

So among other things, one should probably look at the behavior of massless super-QCD first - a theory which already comes in many forms: "pure SQCD" with no quarks; SQCD with adjoint quarks, SQCD with quarks in the fundamental representation; SQCD with various numbers of flavors and colors. The 1990s results of Seiberg on electric-magnetic duality look to be of basic importance in understanding these theories.

(...) By the way, http://en.wikipedia.org/wiki/Seiberg_duality" involves the appearance of an extra meson superfield on one side.

Back in comment #18, I mentioned a minor research program from string theory - "orientifold planar equivalence" - in which meson strings have baryon strings as superpartners. In the baryon string, the third quark is smeared along the length of the string. See these http://physik.uni-graz.at/itp/iutp/iutp_09/welcome.php?sf=13", but not on the arxiv). In the third lecture, pages 12-13, Armoni actually mentions quark-diquark supersymmetry (Lichtenberg's hadronic supersymmetry), and says this is an alternative explanation (he explicitly says that a certain fermion in N=1 SYM becomes superpartner of the meson). Though I wonder if this picture, with the third quark smeared along the string, might arise from a symmetrized version of the quark-diquark string.

I am downloading them for the weekend!

 

[mitchell porter]

I want to tackle https://www.physicsforums.com/showthread.php?t=180275" exists, I think this is the least likely avenue (mentioned so far) towards a realization of very-low-energy supersymmetry. But it might be instructive to walk a short distance down this road, and see what there is to discover.

So, to begin, here's http://physics.stackexchange.com/questions/3342/space-time-filling-d-branes-in-type-i-superstring-theory" ). I say "almost" because I'm used to a stack of n D-branes giving rise to a SU(n) theory, not a SO(n) theory; I suppose the O-plane has something to do with the latter.

So what's going on in Marcus and Sagnotti's paper? I have put together an explanation, a crucial part of which came from section 3.3 of http://gradworks.umi.com/32/71/3271005.html" ). The fundamental issue is how to obtain the "Chan-Paton factors" which contribute to the amplitude when you have strings ending on branes. When M&S wrote their paper, it wasn't even understood that there are branes in the Type I theory, so they came by their construction another way. But in Rinke I read that, normally, the Chan-Paton factor is obtained from a Wilson line in the worldsheet theory of the brane(s) to which the string is attached, a Wilson line which follows the path of the string endpoint. The method of M&S is an alternative, in which you have fields living on the endpoints and the Chan-Paton factor comes from including them in the path integral. They are called boundary fermions and they have had a revival in recent years, including an application in Berkovits's pure spinor formalism.

Along with the space-filling D9-branes, the only stable branes in Type I string theory are D1-branes and D5-branes. I had thought that maybe I could find a braney explanation of why M&S needed five pairs of boundary fermions (quark, antiquark being one pair) in the D5-branes: open strings in Type I can end on the D1s and D5s as well as on the D9s, so there's a calculus of Chan-Paton bookkeeping which extends to those lower branes as well. But I haven't done the work to understand it yet. You can read about some of it in section 14.3 of Polchinski volume 2.

 

[mitchell porter]

Alejandro, what's your philosophy regarding the Higgs?

 

[arivero]

Alejandro, what's your philosophy regarding the Higgs?

That the Higgses coming from the algebra are reasonable, but the ones coming from the dynamics are dubious.

If you look at the SUSY algebra, you will see that in order to build massive supermultiplets, one must add an extra scalar for each massive particle. This can be seen by construction with the susy operator, but you can also check it directly by counting: get a massless Z0; it can be partnered with a Weyl spin 1/2 fermion and it makes a fine gauge massless supermultiplet. But now if you want the Z0 massive, you have an extra bosonic helicity, you need to counterweight in the fermion side and the minimal thing you can do is to add another Weyl spin 1/2 fermion (I guess you could also try to go up to spin 3/2, in any case the counting is the same), but then you have added two fermionic degrees of freedom, so now you must add an extra scalar in order to counterweight exactly.

So a massive Z0 implies an extra scalar, and same for massive W+, W-. That comes from the algebra, it is true for any SUSY setup, and I think that these "higgses" should be there in some disguise. Now, the minimal dynamics of MSSM goes further: it needs to use full SU(2) Higgs multiplets. so it adds another two bosons to the total count. These bosons are, in my opinion, not a real requisite, they come from a very particular model.

As for the "disguise" of the higgses in my own construct, we can discuss it, if you want. But note that the above applies to any SUSY model, not just mine.

 

[arivero]

(I guess you could also try to go up to spin 3/2, in any case the counting is the same)

Well, not exactly the same. If you want the 3/2 fermion to be massive, you need double again, while in the other case you can use both Weyl 1/2 to build the massive dirac fermion. But I mentioned it because the solution where two d.o.f come from an 1/2 and the other two come from a 3/2 has a peculiar content, close to some compactifications of maximal sugra.

As for the "disguise" of the higgses in my own construct, we can discuss it, if you want.

Really, the only idea is that you could have noticed that after the full (and exact) pairing for \pm 1,0, \pm 2/3 and \pm 1/3, there are still six combinations left, uu, uc, cc and their antiparticle versions. I can not use them to make Dirac fermions, and then I suspect that these combinations are chiral in a way that they can only couple in an axial way: they can not see QCD, and they can only see EM in the way it comes from SU(2) and hypercharge.

 

[mitchell porter]

With respect to my comments #29 and #32, http://arxiv.org/abs/hep-th/9708113" looks exciting (I haven't read it yet, and I'm posting about it, that's how exciting): It's about how to obtain QCD as a limit of super-QCD, and it actually talks about the meson states of QCD. This is what's missing in all the literature on supersymmetric preon models. Over 100 papers talk about "composite superfield" or "composite supermultiplet", but they never bring standard model mesons into these supermultiplets, they only talk about quarks and leptons.

Here's what they (Sannino and Schechter) say:

At the fundamental gauge theory level the supersymmetric theories contain gluinos and squarks in addition to the ordinary gluons and quarks. At the effective supersymmetric Lagrangian level, all of the physical fields are composites involving at least one gluino and one squark. This means that none of them should appear in an effective Lagrangian for ordinary QCD. Where the mesons and glueballs, which are the appropriate fields for an effective QCD Lagrangian, actually do appear are in the auxiliary fields of the supermultiplets, which get eliminated from the theory...

The simplest approach to relate the supersymmetric (SUSY) effective theories to the ordinary ones is to add suitable supersymmetry breaking terms... The standard procedure assumes the breaking terms to be ‘‘soft’’ in order to keep the theory close to the supersymmetric one. Indications were that the soft symmetry breaking was beginning to push the models in the direction of the ordinary gauge field cases. However the resulting effective Lagrangians were not written in terms of QCD fields.

In this paper we will provide a toy model for expressing the ‘‘completely broken’’ Lagrangian in terms of the desired ordinary QCD fields. Since we will no longer be working close to the supersymmetric theory we will not have the protection of supersymmetry for deriving ‘‘exact results.’’ In practice this means a greater arbitrariness in the choice of the supersymmetry breaking terms. The advantage of our approach is that we end up with an actual QCD effective Lagrangian.

"Mesonic superfields" show up in Part III. This seems really promising, because it's an analysis at the level of a Lagrangian, and not just talking about quantum numbers.

 

[mitchell porter]

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 http://www.phys.columbia.edu/~kabat/susy/3plus1susy.pdf" ). 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 "psi_T". What if we get "F_Q" to drop out? "psi_T" 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: http://arxiv.org/abs/hep-ph/9501412" .

 

[arivero]

A differente venue: http://arxiv.org/abs/0909.5430 "SUSY Splits, But Then Returns", by Sundrum, refers to some previous works (ref 12, 13) on emergent supersymmetry. It would be very surprising if some of these models, which are proposed at the level of toy models, at the end happen to be so accuratelly reflected in Nature.

 

[mitchell porter]

Two more ideas on how to construct a theory realizing "hadronic supersymmetry extended to leptons":

1) Do what Sannino and Schechter did (comment #40), but in reverse. That is, instead of beginning with a supersymmetric Lagrangian and judiciously adding symmetry-breaking and mass-generating terms until you get the standard model, start with the standard model and add terms until you have a broken supersymmetric Lagrangian. The tricky part is once again the aspect of this idea which is unconventional: the mesons and diquarks are the degrees of freedom which must enter into supermultiplets, so we may need to start with an effective field theory (for the whole standard model, not just for QCD) in which they appear directly in the Lagrangian.

2) Look for a realization of hadronic supersymmetry in a string phenomenological model, and then see if it can be extended to the leptons. The papers on "orientifold planar equivalence" that I cited earlier (comments #18, #32)) don't quite work here, because as I understand it they are just illustrative toy models, not real-world models. What I'm thinking here is that string phenomenology (so far as I can see) mostly contents itself with obtaining states which can correspond to free quarks and gluons at high energies. Mesons and baryons are a low-energy phenomenon and are left for field theorists to derive from QCD. But what do the existing accounts of hadronic supersymmetry look like if we restate them within the framework of a beyond-SM theory? We might get some clues for the extension to the leptons. (I suppose one could do this, not just for string models, but also for MSSM and SUSY-GUT.)

 

[mitchell porter]

Update on the bottom-up and top-down strategies:

1) There are a number of papers on expressing the Nambu-Jona-Lasinio model (http://en.wikipedia.org/wiki/Nambu%E2%80%93Jona-Lasinio_model" try to apply NJL to SQCD.

2) "E6 diquarks" are one of the exotic particles that have failed to turn up at the LHC - but I think these are vector diquarks. Nonetheless, if you visit the 1989 http://www.sciencedirect.com/science/article/pii/0370157389900719" (still frequently cited), and view the discussion on pages 199-200, about leptoquark, diquark, and quark couplings in the superpotential... there might be some guidance there, for how, say, a super-NJL model might embed into a theory with leptons.

(Also see http://arxiv.org/abs/hep-th/0604017" ?)

 

[arivero]

I got an email from Bernard Riley telling that also him, back in http://vixra.org/pdf/1004.0101v1.pdf, got worried about the point of having spin 1/2 and spin 0 particles with very near masses, say muon and pion etc.

Again, it is beyond all belief that two different mechanism of mass generation (SU(3) colour versus Yukawian Higgs) without any relationship between them, and coming down from mass Planck scale, at the end produce a value with a difference not beyond a 10%. The problem is that there is no dynamics unifying both mechanism... So the reports of Mitchell are interesting, they indicate that is could be possible to build some mechanism, after all.

 

[qsa]

I got an email from Bernard Riley telling that also him, back in http://vixra.org/pdf/1004.0101v1.pdf, got worried about the point of having spin 1/2 and spin 0 particles with very near masses, say muon and pion etc.

Again, it is beyond all belief that two different mechanism of mass generation (SU(3) colour versus Yukawian Higgs) without any relationship between them, and coming down from mass Planck scale, at the end produce a value with a difference not beyond a 10%. The problem is that there is no dynamics unifying both mechanism... So the reports of Mitchell are interesting, they indicate that is could be possible to build some mechanism, after all.

Hi Arivero,

Good, you are back again. I send you a PM (some days back)regarding the mass of the proton and electron and they are linked to a thread you started. the equations almost look identical to the one you posted, so they must be related. I don't mind if you don't see any value in them but I will be just happy with a two letter word ,like ok, reply to acknowledge receiving the info. Mitchelle has been kind and has taken a look at them.

https://www.physicsforums.com/showthread.php?t=46055

 

[mitchell porter]

The paper where I first came across "diquark coupling" vs "leptoquark coupling" as a model-building choice was http://prd.aps.org/abstract/PRD/v41/i5/p1630_1" (1990). "We envisage a cascade mechanism, whereby quarks and leptons gain mass at various orders of perturbation theory from masses induced at the preceding order of approximation. In this way we hope to explain at least some of the qualitative features of the observed mass spectrum."

It has very few citations, especially in the past decade, but there is a recent one, http://arxiv.org/abs/0906.4657" ). "Radiative models of flavor have a long history...", and to prove their point, they list 17 papers (refs 19-35), starting with Weinberg in 1972.

At this stage, I have no idea whether such models provide guidance in the search for a theory realizing Rivero supersymmetry ;-) or whether the details of the masses is just a distracting complication. My basic notion of how to make it work is still SQCD with preons, so that e.g. the lepton-meson multiplet involves composite particles on both sides. But maybe it requires something more subtle, like Seiberg duality or holographic cascades.

 

[mitchell porter]

OK, I'm sold, it would be extremely stupid to be thinking about how to realize supersymmetry in this way, and to ignore the similarity of the pion mass and the muon mass. Instead, it's absolutely the best clue about how to do it, for the very reason you (Alejandro) state: the method of mass generation is supposed to be completely different.

Electron, muon, and tauon masses satisfy Koide's formula to high precision. Pion, kaon, and eta-meson masses satisfy a Gell-Mann–Okubo mass formula, but only approximately. I don't understand the https://www.physicsforums.com/showthread.php?p=1451883#post1451883" tries to do so.

Also, today's http://arxiv.org/abs/1106.3074" looks important. There is a good chance that we should be trying to take advantage of such relationships (e.g. as in the paper by Sundrum). But in all cases, the authors think of the superpartners as something additional to all the known particles. We need to somehow retrace their steps, but with the role played by supersymmetry entirely folded into the known, Standard Model particles.

edit: http://arxiv.org/abs/1010.4105" - a theory paper, which inspired the Seiberg dual for the MSSM, and which connects the chiral effective theory for QCD to Seiberg duality for SQCD - looks supremely important.

edit#2: How many supremely important papers can there be, I wonder?

http://arxiv.org/abs/hep-ph/0501200" :

"This paper could have been called 'Connecting Diquarks to Pions'"... The most solid consideration, albeit somewhat remote from bona fide QCD, is that based on SU(2)color. Reducing the gauge group from SU(3) to SU(2) allows one to relate diquarks and pions through a global symmetry which exists only for SU(2)color. Diquarks become well-defined gauge-invariant objects, which share with pions a two-component structure with a relatively short-range core. Then one can speculate, qualitatively or, with luck, semiquantitatively on what remains of this symmetry upon lifting SU(2)color to SU(3)color. It is worth noting that all instanton-based calculations carry a strong imprint of the above symmetry since basic instantons are, in essence, SU(2)color objects."

So here we have a symmetry connecting diquarks to mesons. Earlier, we had an interpretation of QCD mesons in terms of a supersymmetric duality. We also have a realization of this supersymmetric duality for the MSSM, in a way which extends to the W and Z. It remains only to decisively fold the leptons themselves into this circle of relationships.

 

[mitchell porter]

Now getting very close to a coherent field-theoretic thesis: We should be trying to generate the masses through a superconformal anomaly. The idea is that the pion mass is generated by a conformal anomaly (or at least breaks conformal symmetry in the chiral effective theory); and in "anomaly mediated supersymmetry breaking", squarks and sleptons acquire their masses from a superconformal anomaly; but in the scenario here, squarks are diquarks and sleptons are mesons. Maybe the answer is just SQCD + AMSB!

 

[arivero]

Mitchell, did you got your preprint online? If you wish, I can upload it somewhere, if only for google to find it...

 

[mitchell porter]

It needs more work.

 

[arivero]

btw I like the SQCD + AMSB line.

 

[arivero]

If Koide is a serious thing, then the clue is the value of the constituent quark mass, 313 MeV. The same mechanism that produces the mass of leptons should produce this mass,

Koide rule is that the mass of leptons is

313.188449 MeV ( 1 + sqrt(2) cos(phase))^2

The square is also inspiring, it seems as if the interesting quantity is actuall sqrt(mass).

 

[mitchell porter]

To make further progress, I feel the need to now return to the original hadronic supersymmetry, which is the prototype. The proposed correspondence for the leptons is just a matter of matching up the charges, but hadronic supersymmetry has a dynamical content, as requested by suprised in comment #11. It would be a big advance to embed the leptons in an extension of one of the effective theories with hadronic susy, even if the extension is dynamically trivial.

In comments #13 and #18, I mentioned Sultan Catto as offering a sophisticated approach to hadronic susy, and he's written some more in the past two years, though for some reason it's not on arxiv (you can find it at inspirebeta). I believe it's an extension of work with Feza Gursey from 1985 and 1988, on an octonionic superalgebra which contains baryons, mesons, diquarks, and quarks. The 1980s version also contained exotic hadrons (like tetraquarks, I guess), the new version does not.

At a more elementary level, I don't see Catto (or other advocates of hadronic susy) working with more than three flavors. So before we extend hadronic susy to the leptons, we may have to extend it to all the hadrons! And the first step in that direction may be to extend the purely bosonic part of hadronic susy - spin-flavor symmetry (see comment #18 in this thread) - to 5 or 6 flavors. I can find precisely http://arxiv.org/abs/hep-ph/0107205" talking (page 9) about SU(12) spin-flavor wavefunctions, and no-one at all talking about SU(10) (five flavors). These wavefunctions are employed in a "naive spectator quark model", and B.Q. Ma has a SU(6) quark-spectator-diquark model, so the road ahead is mapped out for us...

 

[mitchell porter]

Current thoughts: Mass is generated by anomalous breaking of superconformal symmetry in the strong interactions, which is then transmitted to the charged leptons (origin of the shared 313 MeV scale) and also to the electroweak gauge bosons. The whole standard model may have a "Seiberg-dual" description in terms of an SQCD-like theory with a single strongly coupled sector, with the electroweak bosons being the dual "magnetic gauge fields", and lepton mass coming from "technicolor instantons" in the electric gauge fields (analogous to the origin of nucleon mass in QCD).

This is a transposition of recent ideas, due to http://arxiv.org/abs/1106.4815" and collaborators, to the present context.

 

[arivero]

This is a transposition of recent ideas, due to http://arxiv.org/abs/1106.4815" and collaborators, to the present context.

Luty and Terning are doing a good work, at least preparing powerful tools... and students brainy enough to use them qhen they become needed after the runs of the LHC. I am sorry I am already old to retake all of these.

 

[mitchell porter]

I hope to have something to say soon about where the constituent quark mass scale comes from, but meanwhile, http://bajnok.web.elte.hu/JHW/programme.html#pomarol" has a nice basic explanation of the idea of "partial compositeness" which features in these Seiberg-like models.

 

[mitchell porter]

If Koide is a serious thing, then the clue is the value of the constituent quark mass, 313 MeV. The same mechanism that produces the mass of leptons should produce this mass,

Koide rule is that the mass of leptons is

313.188449 MeV ( 1 + sqrt(2) cos(phase))^2

The square is also inspiring, it seems as if the interesting quantity is actuall sqrt(mass).

The constituent quark mass scale is still the same (to within 5-10%) even in what Frank Wilczek calls "QCD Lite" - just two quark flavors with no current mass. So undoubtedly this mass scale is produced within QCD. So far I don't have a simple explanation for its value; we can only hope that there's some simpler way to get it, other than long lattice calculations.

Assuming the connection between the constituent quark mass scale and the Koide relation scale factor is real, it is surely being produced within QCD and transmitted to the leptons. And consider this: simple algebraic transformations of the formula above can bring a factor of 2 out of the squared term, so now we have "mass(lepton) = 2 . mass(constit.quark.) . (new squared term)". In your correspondence, the leptons pair supersymmetrically with mesons, i.e. a quark and an antiquark. So the "naive meson mass", assuming the u/d constituent quark mass scale, is of the order of 2 x 313 MeV.

In other words, one can imagine a sort of "Rivero-correspondence Standard Model Lite", in which all flavors of quark have zero current mass, in which they take on the 313 MeV constituent mass (because of QCD effects) in mesons and baryons, and in which the 625 MeV "naive meson mass scale" gets transmitted to the lepton "superpartners" of the mesons. If such a field theory existed, we could then think about modifying it so that the quarks have nonzero current masses, and so that the charged lepton masses are altered by the extra factor appearing in the Koide formula above.

 

[qsa]

The constituent quark mass scale...

here is the chart I promised you.

 

[mitchell porter]

Something which has previously bothered me is that, if you were trying to make a "quark-diquark superfield" or a "lepton-meson superfield" - that is, if you were trying to apply the standard superfield formalism to this idea - it shouldn't make sense, because the two "components" (at least, in the quark-diquark case) aren't independent degrees of freedom.

But I wonder if you can get around this by just pretending that they are independent, and later imposing a quantum constraint? In fact, I wonder if this could be done to the MSSM? Until this point, I thought there were only two ways to realize this correspondence in terms of the MSSM: Either you have the MSSM emerging from something like SQCD, or you have an extra emergent supersymmetry within the already-supersymmetric MSSM. The reason is, once again, that quarks and squarks are independent degrees of freedom in the MSSM, but quarks and diquarks are not. So either quark-diquark supersymmetry is an emergent extra supersymmetry, in addition to quark-squark supersymmetry, or else the squarks are really the diquarks of a simpler, SQCD-like underlying theory. The idea of a "quantum constrained MSSM" - not to be confused with the parameter-constrained MSSM that is usually denoted by CMSSM; I mean a constraint whereby we project out part of the Hilbert space - would have to be a version of the latter possibility.

But the idea of quark-diquark supersymmetry emerging within the MSSM is curious. On the one hand, it seems like it ought to be well-founded, because QCD does unquestionably exhibit an emergent approximate quark-diquark supersymmetry - this is where the idea of hadronic supersymmetry came from. But adding another supersymmetry to the N=1 supersymmetry of the MSSM should produce N=2 supersymmetry - shouldn't it? - and N=2 theories can't be chiral. This seems like a question of authentic theoretical interest, independent of phenomenology: What happens when you examine hadronic supersymmetry in the context of the MSSM? Does it just break down because of the extra states?

edit: This is not exactly the same thing, but wow: Two papers on finding a Seiberg dual for the MSSM! (http://arxiv.org/abs/0809.5262" ). Possibly in the context of a dual for susy SU(5) GUT. That is, you'd find a dual theory for susy-SU(5), and I guess you'd also find a dual description for breaking it down to MSSM.

The MSSM is criticized for having 120 parameters, but http://golem.ph.utexas.edu/~distler/blog/archives/000681.html" , most possible values of those parameters will probably prove to be unrealizable. So one might hope for a unique mechanism explaining the deformation away from exact supersymmetry (in which e.g. lepton masses would equal diquark masses, see comment #58) which may underlie the Koide formula.

edit #2: For the exactly supersymmetric form of the MSSM, reduced to a single line, see page 95 (equation 465) of http://arxiv.org/abs/hep-ph/0505105" .