
#37
Apr2411, 12:39 AM

P: 748

Alejandro, what's your philosophy regarding the Higgs?




#38
Apr2411, 09:41 AM

PF Gold
P: 2,884

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. 



#39
Apr2411, 04:29 PM

PF Gold
P: 2,884





#40
Apr2911, 02:21 AM

P: 748

With respect to my comments #29 and #32, this paper 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 superQCD, 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: 



#41
Apr3011, 04:44 AM

P: 748

Equations 3.23.4 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 offshell (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 "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 squarkantisquark 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 KyianovCharsky (also spelt KiyanovCharsky and KiyanovCharskii), in which QCD mesons and baryons are similarly derived from superQCD, with the explicit intention of realizing hadronic supersymmetry: 1 2 3. 



#42
May1011, 05:46 PM

PF Gold
P: 2,884

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.




#43
May1611, 01:38 AM

P: 748

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 symmetrybreaking and massgenerating 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 realworld 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 lowenergy 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 beyondSM 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 SUSYGUT.) 



#44
Jun1511, 02:43 AM

P: 748

Update on the bottomup and topdown strategies:
1) There are a number of papers on expressing the NambuJonaLasinio model (1 2) in terms of diquark and meson variables. Perhaps see especially "PNJL", the combination of NJL with the "Polyakov loop". There is also a supersymmetric version (sometimes called superNJL), which one could try to reexpress in this way. Also, early papers of Tomohiro Matsuda 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 review article on string E6 models (still frequently cited), and view the discussion on pages 199200, about leptoquark, diquark, and quark couplings in the superpotential... there might be some guidance there, for how, say, a superNJL model might embed into a theory with leptons. (Also see NJL from branes. Can it be combined with holographic diquarks?) 



#45
Jun1511, 12:25 PM

PF Gold
P: 2,884

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. 



#46
Jun1511, 05:19 PM

P: 362

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 recieving the info. Mitchelle has been kind and has taken a look at them. http://www.physicsforums.com/showthread.php?t=46055 



#47
Jun1611, 01:43 AM

P: 748

The paper where I first came across "diquark coupling" vs "leptoquark coupling" as a modelbuilding choice was "Radiative generation of quark and lepton mass hierarchies from a topquark mass seed" (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, "A Domino Theory of Flavor" (2009; talk). "Radiative models of flavor have a long history...", and to prove their point, they list 17 papers (refs 1935), 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 leptonmeson multiplet involves composite particles on both sides. But maybe it requires something more subtle, like Seiberg duality or holographic cascades. 



#48
Jun1711, 03:31 AM

P: 748

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 etameson masses satisfy a GellMann–Okubo mass formula, but only approximately. I don't understand the derivation of the GMO formula, but apparently it's a standard thing in chiral perturbation theory, descended from QCD. The only fieldtheoretic explanations for the Koide formula that I know are those proposed by Sumino and by Koide himself. So there's the challenge: integrate these two mechanisms into one. This 2009 paper tries to do so. Also, today's Seiberg dual for the MSSM 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: 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? hepph/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 welldefined gaugeinvariant objects, which share with pions a twocomponent structure with a relatively shortrange 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 instantonbased 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. 



#49
Jun1811, 10:55 PM

P: 748

Now getting very close to a coherent fieldtheoretic 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!




#50
Jun2111, 07:49 PM

PF Gold
P: 2,884

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




#51
Jun2211, 04:39 AM

P: 748

It needs more work.




#53
Jun2211, 03:51 PM

PF Gold
P: 2,884

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). 



#54
Jun2811, 01:19 AM

P: 748

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  spinflavor symmetry (see comment #18 in this thread)  to 5 or 6 flavors. I can find precisely one paper talking (page 9) about SU(12) spinflavor wavefunctions, and noone 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) quarkspectatordiquark model, so the road ahead is mapped out for us... 


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