
#55
Jun2911, 11:43 PM

P: 748

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 "Seibergdual" description in terms of an SQCDlike 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 Luty and Terning and collaborators, to the present context. 



#56
Jul311, 06:40 PM

PF Gold
P: 2,884





#57
Jul711, 04:39 AM

P: 748

I hope to have something to say soon about where the constituent quark mass scale comes from, but meanwhile, "AdS/CFT & Compositeness in the SM" has a nice basic explanation of the idea of "partial compositeness" which features in these Seiberglike models.




#58
Jul2211, 05:15 AM

P: 748

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 "Riverocorrespondence 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. 



#59
Jul2211, 10:28 PM

P: 362

here is the chart I promised you. 



#60
Jul2511, 12:54 AM

P: 748

Something which has previously bothered me is that, if you were trying to make a "quarkdiquark superfield" or a "leptonmeson 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 quarkdiquark 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 alreadysupersymmetric 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 quarkdiquark supersymmetry is an emergent extra supersymmetry, in addition to quarksquark supersymmetry, or else the squarks are really the diquarks of a simpler, SQCDlike underlying theory. The idea of a "quantum constrained MSSM"  not to be confused with the parameterconstrained 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 quarkdiquark supersymmetry emerging within the MSSM is curious. On the one hand, it seems like it ought to be wellfounded, because QCD does unquestionably exhibit an emergent approximate quarkdiquark 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! (1 2 comment). Possibly in the context of a dual for susy SU(5) GUT. That is, you'd find a dual theory for susySU(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 when you include gravity, 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 hepph/0505105. 



#61
Jul2511, 10:51 AM

PF Gold
P: 2,884





#62
Jul2511, 06:01 PM

PF Gold
P: 2,884

I just read the last confrontation between Motl and Woit... It is not worthwhile to try to comment on this at either blog (Woit actually censurates me and Motl allows posting but well, surely he just prefers to make fun of people instead of actually censurating, at least in my case). But it is worthwhile to read them, specially if you have in mind the perspective of the "wrong turn"... and that we know that the argument about the purity of hepth fails, because it is almost impossible to find papers with an unbroken or midly unbroken susy, and well, Mitchell has practically revised all the arxiv for papers useful here, and only got a handful of them.




#63
Jul2611, 01:37 PM

PF Gold
P: 2,884

After all this LHC excitation, I am afraid i could go into hibernation for some period, but I want to say some words about this 313 GeV thing and how, to my regret, it could relate to extra dimensions. The point is that if we want quarks and leptons to stand in some symmetry group, the smaller candidate is SU(4), "Lepton number as the fourth color". The full group Pati Salam thing, SU(4)xSU(2)xS(2), is known to appear with 8 extra dimensions: it is the group of isometries of the manifold S5xS3, the product of the threesphere with the fivesphere. It was argued by Bailin and Love that 8 extra dimensions are needed to get the charge assignmens of the standard model, but I am not sure if this manifold was used. Its role was stressed by Witten, who pointed out that the family of 7dimensional manifolds that you get by quotienting this one via an U(1) action have the isometry group SU(3)xSU(2)xU(1).
I liked to think of this compactification as an infinitesimal extra dimension, partly because of the hint of Ftheory, partly because thile the SU(4) group seems a need, I don't like to look at it as a local gauge group. Again, this was well known lore of supergravity (and even in string theory) in the early eighties, but in the same way that the first revolution wiped gluons away, the second string revolution killed the research on realistic Kaluza Klein theories. 



#64
Jul2611, 10:42 PM

P: 748

I made a new thread for this 12dimensional idea.
edit: Meanwhile I observe that we can get SO(10) (which contains both SU(5) and PatiSalam) from 13 dimensions, as in Stheory. 



#65
Jul2711, 03:52 AM

P: 748

With the modern ideas (strings, branes, strings between branes, strings/branes wrapped around noncontractible submanifolds...), you can get PatiSalam in other ways too. Maybe the boldest neoKaluzaKlein hypothesis would be to say that all of these modern possibilities arise from dualities applied to a veryhighdimensional theory that is pure KaluzaKlein. E.g. Tduality can take a spacefilling brane and turn it into a brane of codimension one. But that discussion belongs in the other thread.
In order to relate quarkantiquark and lepton supersymmetrically, I have also been looking at another idea from the Time Before Arxiv: supersymmetric preon theories. This is because it is quite difficult to get elementary and composite fields into the same supermultiplet. I know of one example of emergent supersymmetry involving composite fields, but all the components of the supermultiplet are composite. So it might be easier to have quarks and leptons already composite. There is a big literature on supersymmetric preon models, again from the 1980s. I won't list individual papers, but reviews by Volkas look useful. A more concrete form of guidance, complementary to the Koide formula, is the fact that the pion mass is about the square root of the constituent quark mass. (I believe this has a derivation in terms of chiral perturbation theory, and also a holographic derivation.) The way I think about this is as follows. Suppose we consider the hypothetical "exactly supersymmetric" realization of the correspondence, in which particles and their superpartners are the same mass. So a lepton is trying to be the same mass as a meson, which has two constituent quarks, implying a natural mass scale of 626 GeV  and as I pointed out, you can rewrite the Koide formula so it's 626 GeV multipled by a phasedependent factor (thanks to basic trigonometric identities). But at the same time, a quark is trying to be the same mass as a diquark  and here we get a direct contradiction, or a tension that has to be resolved. I'm thinking that this pion mass relation is a clue to how the tugofwar on that side is resolved, even though a pion should supposedly pair up with a lepton. (I suspect the basic relations are actually between "operators" or "currents", e.g. that there's a relation between a quark current and a diquark current, and that the properties of the physical particles, like pion, eta meson, kaon, only exhibit an echo of the basic relations.) I also found work on the idea that particle masses might be due to hypercolor instantons, which dates back to a paper by Weinberg, and which has contemporary correlates in string theory. This is what the reference to "technicolor instantons" in comment #55 was about; the idea is that the nucleons get their mass from QCD instantons, so if the Koide mass scale of the leptons is the same thing, there should be a picture in which the leptons are also getting their mass that way. 



#66
Jul2711, 03:52 AM

PF Gold
P: 2,884

A new thread can be a good thing.
13 dimensions? Yep I noticed it was needed for SO(10) and I will not ask for manifolds whose isometry group is E6,E7 or E8 and I was very afraid of this overplus of dimensions. :( Perhaps the rule that limits the max dimension to 11 applies only to the production of the gauge group. IE, we can put more dimensions but in order to produce a gauge group we are limited, from some consistency rule somewhere, to choose eleven of them. 



#67
Jul2711, 11:16 AM

P: 362





#68
Jul2711, 12:13 PM

P: 362

this is the most beautiful chart ever. no matter what compton(172,182,364,1000) you always end up at interaction distance of 5468 with the energy of .00054858 . that is what is so special about the mass of the electron.




#69
Jul3111, 06:54 AM

P: 748

I was looking at notes from a recent talk by Adi Armoni, and nearly fell over when something extremely simple jumped out at me. See pages 25 and 26. He's talking about work by Sagnotti on "Type 0 string theory". Apparently it offers a realization of hadronic supersymmetry in which a meson is a bosonic oriented string connecting a quark and an antiquark, and a baryon is a fermionic unoriented string connecting a quark and a quark; there is some sort of fermionic field along the length of the string.
So then it hit me: could such a model then incorporate a diquark as a bosonic oriented string connecting a quark and a quark? And what about its "partner", an unoriented string connecting a quark and an antiquark, with a fermionic field running between them? Would that offer a way to place the leptons in a Type 0 string theory, in a way that extends hadronic supersymmetry?! Having stated the very attractive idea, now let me state a few problems. First, it's unclear to what extent this model of open strings can possibly reproduce all the observed complexities of hadronic physics. Also, we don't see free diquarks in reality. But then, maybe we don't have to; what we need is a "fermionic quarkantiquark" that is stable and is actually a lepton. It's OK if a free "diquark string" is unstable. arxiv:0901.4508 might be the best place to start, especially for the references  the two papers by Sagnotti, and also CorriganRamond. arxiv:hepth/9906055 goes into further stringy technicalities. 



#70
Jul3111, 09:57 PM

P: 748

My remarks were a little confused. But it's one of the confusing things about Alejandro's correspondence.
In theory, hadronic supersymmetry relates an antiquark and a diquark (quarkquark pair). In practice, what we see are similarities between a meson (quarkantiquark) and a baryon (quarkdiquark). To obtain the baryon from the meson, we substitute the diquark for the antiquark. Alejandro's extension of hadronic supersymmetry relates a lepton to a quarkantiquark pair. Unlike hadronic supersymmetry, there's no known dynamical significance to this correspondence (but this is why we are talking about the similarity between the constituent quark mass scale and the mass scale appearing in the Koide relation). It's just that the electromagnetic charges match up; by pairing quarks with antiquarks, you can make composites with charge 1, 0, and +1, which matches the charges one sees in the elementary leptons, "as if" they were superpartners to these quarkantiquark combinations. The combination of quark and antiquark is normally a meson. But we see that for quarkdiquark symmetry, we can't speak of it as true in all imaginable contexts. For example, I don't think you can "substitute a diquark for a quark" in any meaningful way, if the quark is already part of a diquark. Indeed, hadronic supersymmetry is usually said to be an emergent symmetry, true because diquarks resemble quarks under certain circumstances (as substructures of a hadron), not because the fundamental theory is supersymmetric. It's only a very rare theorist like Sultan Catto who is trying to explain hadronic supersymmetry as a manifestation of a fundamental supersymmetry. So the posited relationship between "mesons" and leptons is even more tenuous. As I said a few comments back, I suspect that if such a relation exists, it's fundamentally algebraic, and may be obscured to the point of invisibility in the actual mesons. Furthermore, the observable mesons already play a role in quarkdiquark symmetry  you can substitute a diquark for one of their constituent quarks, and get a baryon with similar properties. This was the genesis of my confusion about Armoni's talk. The "orientifold field theories", which arise from certain models in Type 0 string theory, exhibit a supersymmetry between a bosonic "meson" string and a fermionic "baryon" string. The mesonbaryon relationship exists in hadronic supersymmetry, so I jumped to the conclusion that if we changed the sign of one of the quarks terminating these Type 0 strings, we could implement Alejandro's idea. But in fact, Alejandro's idea applies directly to "mesons", i.e. to quarkantiquark strings, such as exist in "orientifold planar equivalence". So really, the more logical way to employ planar equivalence here would be to say that its "mesonbaryon supersymmetry" actually corresponds to Alejandro's "mesonlepton supersymmetry"; and then we should seek to extend planar equivalence so as to include bosonic "diquark strings" which will be dual to fermionic "quark strings". This last step sounds problematic, to put it mildly. Maybe there's some other way to proceed. But I had to make this clarification. 



#71
Jul3111, 10:46 PM

P: 748

I also want to make some remarks about hadrons from the perspective of contemporary string theory.
Consider a stringy standard model such as appears in Barton Zwiebach's textbook. Other string models work differently to this, but this one allows me to make my point. There are several intersecting stacks of Dbranes, and all the fundamental particles are open strings running between the brane stacks. There is a stack of 3 branes, one for each color in QCD. Strings between these branes are the gluons. There are also separate stacks of "left branes" and "right branes". Quarks are strings that connect a color brane with a left brane or a right brane. (There are also lepton branes, and leptons are strings connecting lepton branes with a left brane or a right brane.) Having left branes and right branes, and thus different strings for lefthanded and righthanded quarks, is a way to have them behave differently, as in the real world. Now consider what a hadron is. It's a bunch of quarks, bound together by the exchange of gluons. In the string model above, gluons are strings interior to the stack of color branes, and quarks are strings stretching from the color branes to the "handedness" branes. A hadron, therefore, is a "bundle" of two or three (or more) "quark strings", stretching between color branes and handedness branes, exchanging a lot of "gluon strings" at the colorbrane end of the "bundle". A very approximate image might be a bouquet of flowers; each flower is a quark, the petals are at the "left brane" or "right brane", and the stems stretch down to the color branes  and that's where the bouquet is tied together, by the gluons. The important part of this image is the idea that a hadron is a bundle of quark strings, tied together at the color end. This is a rather more complex model of a hadron than in the Type 0 string model discussed by Armoni. There, a meson is a single string, connecting two "quark branes", and not a bundle of two strings, connecting two separate brane stacks. This is more akin to the way mesons were described in the "dual resonance models" which ultimately gave rise to string theory. This has big implications for how one might seek to realize hadronic supersymmetry, and its generalization to leptons, within string theory. The strings in the model from Zwiebach's textbook are superstrings, so at the particle level they correspond to superfields. That is, the "quark strings" that I mentioned, actually describe quarks and squarks. It's only when supersymmetry is broken that the bosonic and fermionic aspects of the string acquire different masses, and all those different classes of string become identifiable, at low energies, with just one or the other. I haven't really studied Type 0 string theory yet, but although it's technically not supersymmetric, I get the impression that a sort of residual supersymmetry exists, and that the "mesonbaryon supersymmetry" discussed by Armoni is pretty much the same thing as the coexistence of boson and fermion within a single string in ordinary supersymmetric string theory. The "baryon" is just the fermionic counterpart of the "meson" string. But if we consider the "bundle" model of hadrons that arises in conventional string phenomenology, it's clear that the superpartner of the bundle is a much more complicated entity  that is, if it can be said to exist at all. The bottom line is that the implementation of hadronic supersymmetry, and hence of its extension to the leptons, is potentially much more economical in Type 0 string theory than in conventional string phenomenology, because mesons and baryons could themselves be fundamental strings, and not "bundles" of fundamental strings. That perspective is part of what was abandoned by the "turn" of string theory mentioned in the title of this thread. 



#72
Aug111, 05:44 PM

PF Gold
P: 2,884

Still, I remember I visited works similar to Armoni's time ago. An idea was to get leptons via transitions between hadronic states, but lepton and baryon numbers get involved and block the way. Another was to think that this "1/2 spin in the string" of some models of baryons was to be interpreted not a a third quark, but as the superpartner, stringwise, of the spin 1 gluon. But then one needs to explain how two spin 1/2 particles get to exchange another spin 1/2 particle: fields must be always bosonics. On the other hand, just this problem could explain why the leptons are points: a spin 1/2 open string should always be a point, because only boson fields can be extended in space.
Sagnotti seems always to be near of something, but then he jumps elsewhere. I was very excited with his work with Marcus, where he got the SO(32) group as a consequence of open strings in the worldsheet, before the advent of the tadpole interpretation. 


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