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

[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" .

 

[arivero]

For the exactly supersymmetric form of the MSSM, reduced to a single line, see page 95 (equation 465) of hep-ph/0505105.

I bought the book!

 

[arivero]

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 hep-th 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.

 

[arivero]

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 three-sphere with the five-sphere. 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 7-dimensional 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 F-theory, 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.

 

[mitchell porter]

I made a https://www.physicsforums.com/showthread.php?p=3423211" for this 12-dimensional idea.

edit: Meanwhile I observe that we can get SO(10) (which contains http://math.ucr.edu/~huerta/guts/guts.html" .

 

[mitchell porter]

With the modern ideas (strings, branes, strings between branes, strings/branes wrapped around noncontractible submanifolds...), you can get Pati-Salam in other ways too. Maybe the boldest neo-Kaluza-Klein hypothesis would be to say that all of these modern possibilities arise from dualities applied to a very-high-dimensional theory that is pure Kaluza-Klein. E.g. T-duality can take a space-filling brane and turn it into a brane of codimension one. But that discussion belongs in the other thread.

In order to relate quark-antiquark 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 http://arxiv.org/abs/hep-th/0207232" , 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 phase-dependent 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 tug-of-war 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 http://www.sciencedirect.com/science/article/pii/0550321384902608" , 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.

 

[arivero]

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.

 

[qsa]

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 phase-dependent 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 tug-of-war 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.)

.

my idea strongly suggests that the above line is the more correct one. if you have one particle its energy is tiny (inverse of the size of the universe) and nothing interesting happens. but as soon as you have two of them then you get all the fireworks like you see in the attachment. but that is done for a small universe, for a bigger universe and more resolution you get more complicated shape in the running phase but always stablazing somewhere about 3* electron compton(those formulas I showed you seem to be related to this). and at distances on the order of bohr radius then I get exactly the hydrogen numbers, energy and all. so, just like the hydogen when the KE and PE have some relation for stable system ,it seem you also have that at shorter distances. i am working on that now. I will PM you soon the details.

 

[qsa]

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.

 

[mitchell porter]

I was looking at notes from http://pyweb.swan.ac.uk/~pyarmoni/oberwolz.pdf" , 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 quark-antiquark" that is stable and is actually a lepton. It's OK if a free "diquark string" is unstable.

http://arxiv.org/abs/0901.4508" goes into further stringy technicalities.

 

[mitchell porter]

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 (quark-quark pair). In practice, what we see are similarities between a meson (quark-antiquark) and a baryon (quark-diquark). 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 quark-antiquark 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 quark-antiquark combinations.

The combination of quark and antiquark is normally a meson. But we see that for quark-diquark 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 quark-diquark 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 meson-baryon 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 quark-antiquark 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 "meson-baryon supersymmetry" actually corresponds to Alejandro's "meson-lepton 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.

 

[mitchell porter]

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 D-branes, 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 left-handed and right-handed 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 color-brane 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 "meson-baryon 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.

 

[arivero]

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, string-wise, 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.

 

[mitchell porter]

A few times I remarked on the fact that work on GUTs didn't concern itself with mesons and baryons. So it's fascinating to see that "holographic QCD" does. In fact, I think the pursuit of holographic QCD within Type 0 string theory offers the best opportunity yet to realize your super-bootstrap.

Standard holographic QCD works in Type II string theory. You have a stack of flavor branes intersecting a stack of color branes; quarks, gluons, and mesons are various open strings between the branes; and baryons are localized branes connected by strings to the color and flavor branes. By the way, this is "top-down" holographic QCD, where you use the full string theory. AdS/QCD usually means "bottom-up" holographic QCD, where you define a five-dimensional AdS geometry but don't necessarily have an embedding into string theory.

Fantastic progress has been made in realizing phenomena of QCD like chiral symmetry breaking and confinement, and in getting predictions for meson and baryon masses, but there still isn't a canonical holographic model of QCD - the top-down constructions are all supersymmetric. Also, one of the frontier problems for holographic QCD is to model the diquark condensate which breaks chiral symmetry in the "color-flavor locking" phase of "three-flavor QCD" (three light flavors, that is). There doesn't seem to be a standard representation of diquarks yet (they feature in some of the bottom-up, AdS/QCD work, but I think more as a numerical factor than a geometric object); though I have run across http://arxiv.org/abs/1101.1120" . The flavor branes are D8-branes (if you work within Type IIA string theory), and the proposal is that the diquark-diquark string is a D6-brane connecting the two flavor branes involved in the diquark condensate, with five of its dimensions compactified on the S^5 factor of the AdS geometry - leaving just one worldvolume dimension uncompactified, so it looks like a string.

http://arxiv.org/abs/0902.4515" "This D4-D8 model was slowly developed over the years, starting with Witten’s initial identification of the dual geometry for D4 branes wrapped on a thermal circle, study of glueball mass spectra of pure QCD without matter, the introduction of mesons via D8 branes, and very recent study of baryons as solitonic objects on D8 branes." The fact that here, quarks are strings, mesons are strings, and there may even be a diquark-diquark "string", should make us very optimistic that hadronic supersymmetry could become a real supersymmetry here, and that it might be extended to include the leptons.

Now let us return to the Type 0 string. This is a nonsupersymmetric string theory, essentially discovered by Sagnotti, which can be obtained from M-theory by an unusual quotient. Everything works a little differently - for example, instead of just having D-branes distinguished by their dimension, the D-branes have the extra property of being "electric" or "magnetic" - but you can do http://arxiv.org/abs/hep-th/0202024" . At least, up to a point. I think the main reason there has been so little work is because the lack of supersymmetry makes it hard to calculate. Nonetheless, there's an echo of supersymmetry, e.g. in the Bose-Fermi mass degeneracy between bosonic and fermionic strings explored by Armoni and Patella. In fact, that echo is potentially all we need to realize the super-bootstrap. Quark-diquark supersymmetry is not dynamical, in the sense of there being gauginos, nor is its extension to the leptons. At this stage, I wouldn't advise to completely forget about the MSSM and related possibilities, but it seems obvious that the Type 0 string has just enough "sub-supersymmetry" to explain all the facts. All that's needed - and this is still not easy! - is to find a Type 0 realization of QCD and the Standard Model with the indicated features.

 

[arivero]

... ... is to find a Type 0 realization of QCD and the Standard Model with the indicated features.

A puzzle, or a hint, is the need of doing QCD, not SU(N). The diquark depends essentially of SU(3) colour, so I am a bit suspicious of any AdS/CFT when they need to have some limit for big N.

And then, the same goes for any attempt to do the trick with strings a la Sagnotti. In 4D space time, SU(3), or even SU(3) colour times U(1) electromagnetic, should appear.

 

[mitchell porter]

How is http://blog.vixra.org/2011/08/13/has-the-lhc-seen-the-higgs-boson-at-144-gev/#comment-9775" which posits that both Higgs and top are composites, and claims to get the Higgs values currently under consideration at vixra.) Leptons as mesinos - I can imagine that working - but it becomes a little paradoxical to say that quarks are fermion-string "diquarkinos", at least when you talk about the quarks other than the top, because they are also supposed to be what terminates the strings. That would be the most involuted part of the bootstrap, and I can't quite see how to do it.

edit: Some interconnected observations.

First, let's consider one simple way the superbootstrap might work. We have a few fundamental quarks and antiquarks, they can be held together in bosonic composites by gauge bosons (e.g. gluons), and we can also form fermionic composites in which the gauginos are the intermediate operator. These three-object combinations might be thought of as http://physics.stackexchange.com/questions/13101/is-there-a-sqcd-gluino-string-similar-to-the-gluon-string" - quarks and/or antiquarks at the ends, gaugeons and gauginos along the string - or more neutrally, they might be thought of as ordered products of three field operators.

So, we have quarks and antiquarks. We have quark-quark and quark-antiquark pairings, which we call diquarks and mesons respectively, which have boson statistics, and which are implicitly "quark-gaugeon-quark" and "quark-gaugeon-antiquark". Finally, we have superpartners of these, which take the form "quark-gaugino-quark" and "quark-gaugino-antiquark", and which have fermionic statistics.

The super-bootstrap, interpreted in this framework, says that the leptons are actually "quark-gaugino-antiquarks", i.e. mesinos. OK, it remains to be demonstrated that this is viable, but there's no overt paradox so far. But the other part of the scheme, inherited from hadronic supersymmetry, is that quarks themselves are "quark-gaugino-quarks" - a quark is a "diquarkino". This is paradoxical because of its recursion. The numerology of the scheme assumes that u,c,d,s,b are fundamental, so there's no paradox for the top; but how are we to understand the mutual compositeness of the other five quarks? Can you "substitute" one diquarkino into another diquarkino? Or can the recursive relations posited to connect the quarks be realized in terms of further, non-recursive, fundamental compositeness? (i.e. preons)

The other factor I have to mention here is the role of http://physics.stackexchange.com/questions/5232/what-restricts-the-value-of-weak-hypercharge-from-being-5-3" . This could certainly cause problems for the scheme, but I also wonder if you couldn't try to tie those values of 4/3 to the problematic uu, uc, cc pairings.

 

[MTd2]

How do we know that the top quark is actually a quark? It has no time to form a bound stat e so it actually displays a non confined color. How do we know it is not something else?

 

[arivero]

How do we know that the top quark is actually a quark? It has no time to form a bound stat e so it actually displays a non confined color. How do we know it is not something else?

't Hooft, anomalies.

And speaking of 't Hoft, we also guess that there is something more, if we use the naturalness principle; in some limit where the mass of the top is, say, 1, and all the other are zero, a symmetry should cover all the other fermions except the top. Time ago I was intrigued because "all the other fermions" means 84 helicities, a pretty number.

 

[arivero]

The other factor I have to mention here is the role of http://physics.stackexchange.com/questions/5232/what-restricts-the-value-of-weak-hypercharge-from-being-5-3" . This could certainly cause problems for the scheme, but I also wonder if you couldn't try to tie those values of 4/3 to the problematic uu, uc, cc pairings.

Yes! The guiding principle should be that while the uc and dd pairs can be organised in three generations of Dirac supermultiplets, the uu only can do three generations of purely chiral supermultiplets. So uc and dd types are able to "see" the vector charges, colour SU(3) and electromagnetic U(1), but uu type can not. So they (the uu type combinations) should be considered "neutral", with no tree level coupling to the gluons, from the point of view of SU(3), even if they are the combination of two charged objects... And even something more strange with photons, I have not worked it out.

 

[MTd2]

't Hooft, anomalies.

What I mean is the Top being something other than a quark. That is, a top is a quark and also something else.

 

[mitchell porter]

What I mean is the Top being something other than a quark. That is, a top is a quark and also something else.

That's an interesting idea. See http://profmattstrassler.com/articles-and-posts/particle-physics-basics/how-to-look-for-supersymmetry-at-the-lhc/" ... in the MSSM, there are all those other heavy particles; how would you know that the phenomenological top isn't really a top plus a squark, for example?

The top has been heavily studied at the Tevatron, I imagine there would be answers to this question somewhere in the literature.

edit: http://www.phy.bnl.gov/~partsem/fy09/TTait_Talk_06_19_09.pdf" says the best opportunities for something more than pure top to show up, is in the vertex for four right-handed tops.

 

[mitchell porter]

Yes! The guiding principle should be that while the uc and dd pairs can be organised in three generations of Dirac supermultiplets, the uu only can do three generations of purely chiral supermultiplets. So uc and dd types are able to "see" the vector charges, colour SU(3) and electromagnetic U(1), but uu type can not. So they (the uu type combinations) should be considered "neutral", with no tree level coupling to the gluons, from the point of view of SU(3), even if they are the combination of two charged objects... And even something more strange with photons, I have not worked it out.

I guess you mean "ud and dd", not uc?

Also, a "Dirac supermultiplet" is a type of supermultiplet peculiar to AdS space, made of a pair of "singleton" representations which only live on the boundary. It was the subject of a paper by Fronsdal, and Michael Duff even employed in a bootstrap conjecture (see "Supermembranes: the first fifteen weeks"). But I assume you just mean a vector supermultiplet containing Dirac fermions?

 

[mitchell porter]

For reference, I'll link to some earlier discussions: https://www.physicsforums.com/showthread.php?t=457825&page=8#114".

This idea of placing gauge bosons in vector supermultiplets creates another problem/clue for the sbootstrap. The problem is that gauginos transform in the adjoint representation of the gauge group, but Standard Model quarks are in the fundamental representation. The clue: as Armoni and Patella note, for SU(3), and for "two-index" representations, the adjoint representation and the antisymmetric representation are the same. Two-index representations are appropriate for products of two quark operators, such as diquarks or mesons.

I see two ways to go about utilizing this fact. One way is to focus just on color SU(3), the other would be to look at getting the weak interaction from flavor SU(3)^n, n>=1.

edit: If we go to http://physics.stackexchange.com/questions/13629/gut-that-includes-all-3-particle-families-into-a-large-group" .

 

[mitchell porter]

And speaking of 't Hoft, we also guess that there is something more, if we use the naturalness principle; in some limit where the mass of the top is, say, 1, and all the other are zero, a symmetry should cover all the other fermions except the top. Time ago I was intrigued because "all the other fermions" means 84 helicities, a pretty number.

I like this number because it's half of 168, the number of symmetries of the Fano plane i.e. the unit octonions. I should also link back to our https://www.physicsforums.com/showthread.php?t=447612".

At one level, my model of how to think about sbootstrap has been (super)QCD with five massless quarks and one massive quark, the top. But if we consider the posited quark/diquarkino identity, then it seems like the five 'massless' quarks are fundamental and the top is just one among many (super)composites. What could make it special? Well, here I think of http://motls.blogspot.com/2008/12/ckm-matrix-from-f-theory.html" , which as I recall amounts to showing that a generic sort of geometry will produce a preferred direction in CKM matrix space. Perhaps one could do the same for the top. In other words, it's not that there is something special about the top, but rather, there will inevitably be a heavier quark, and the top happens to be it. Though one might still want to know why it's a +2/3 rather than a -1/3.

Anyway, the idea is that then, the other 84 degrees of freedom possesses a residual symmetry, resulting from "dividing out" by the top in a larger symmetry. And the 168-element symmetry group of the Fano plane, http://en.wikipedia.org/wiki/PSL%282,7%29" . (In the literature, it's often called "Delta(168)".)

 

[arivero]

I guess you mean "ud and dd", not uc?

Also, a "Dirac supermultiplet" is a type of supermultiplet peculiar to AdS space, made of a pair of "singleton" representations which only live on the boundary. It was the subject of a paper by Fronsdal, and Michael Duff even employed in a bootstrap conjecture (see "Supermembranes: the first fifteen weeks"). But I assume you just mean a vector supermultiplet containing Dirac fermions?

Yes to both... I am very sloopy, you see But yep, it is "ud and dd", and it is just a supermultiplet (this should be more generic that vector, even if in this case is a massive vector one) containing Dirac fermions.

 

[MTd2]

That's an interesting idea. See http://profmattstrassler.com/articles-and-posts/particle-physics-basics/how-to-look-for-supersymmetry-at-the-lhc/" ... in the MSSM, there are all those other heavy particles; how would you know that the phenomenological top isn't really a top plus a squark, for example?

I was not really thinking about the compositeness of the top quark. I was thinking if the top quark could be something else like a 4th generation lepton besides being also a quark.

 

[arivero]

I was not really thinking about the compositeness of the top quark. I was thinking if the top quark could be something else like a 4th generation lepton besides being also a quark.

I still don't get it. Do you mean the *signal* of the top in accelerators, to be really a mix of two signals? Surely this is mostly ruled out by secondary observables.

 

[MTd2]

Not a signal. I am brainstorming here about the nature of the top quark. It doesn't have a half life long enough to hydronize. But colors are confined, so a top quark must be bound to an anti color gluon, right?

 

[mitchell porter]

Every hadronization event (jet) starts with a quasi-free quark. But the top changes flavor before hadronization can occur. So this issue isn't specific to the top.

I can see two ways to think about it. Jets don't occur in isolation; top quarks are always produced along with other (anti)quarks. So it could be that, even though these quasi-free quarks - parents of the jets - aren't bound to each other, their total wavefunction may be color-neutral.

Alternatively, it may just be a matter of scale (length and time). Confinement - of color, of quarks - sets in somewhere above 10^-15 m. The top quark decays in 10^-25 s. Maybe it just doesn't live long enough for confining dynamics to matter.

Just from skimming the literature, I can't see that one concept or the other is favored. But then I cannot see a rigorous dynamical explanation of hadronization in the literature, just various rival models. There may be something of a "plasma of models" here. :-)

 

[MTd2]

Every hadronization event (jet) starts with a quasi-free quark.

What do you mean by quasi-free?

 

[mitchell porter]

What do you mean by quasi-free?

I just mean, not currently part of a hadron. How that works depends on the model of hadronization. The Lund model (http://arxiv.org/abs/hep-ph/0212122" ) provides a useful example because of its simplicity. In the Lund model, you have a string that stretches and breaks into a sort of discretized spacelike hyperbola, the elements of which are the outgoing hadrons. Now consider a point in the history of one of the quarks terminating the original string, when it is far away from its partner but before the fragmentation which creates the outgoing hadron to which it belongs. At this time, when the quark is between hadrons, it's not exactly free, but it isn't confined either.

edit: The Lund model is just something I came across while answering your question, but it turns out to have a http://arxiv.org/abs/1007.4313" ! This is very cool because it's a QCD string model, containing diquarks, that is used to describe the difficult dynamics of hadronization. It's great to have a potential bridge between Alejandro's correspondence and something as concrete as a scattering process.

 

[mitchell porter]

After staring at the http://math.ucr.edu/~huerta/guts/node11.html" assignments for a while, I have devised a new approach to this whole idea. I haven't even tried to get the right numbers of particles, I just want to mention it as a mutant form of the hypothesis which might assist its analysis.

Alejandro's idea involves pairing (anti)quarks, adding the electric charges, and then supposing that these pairings have superpartners, and is called the super-bootstrap. I do the same, except that I add the ordered pairs (weak hypercharge, weak isospin), so I call it the "hyper-bootstrap".

To add ordered pairs, the rule is (a0,b0)+(a1,b1)=(a0+a1,b0+b1). There is also a secondary "rule" that you can add two ordered pairs which both have nonzero weak isospin, only if one has isospin +1/2 and the other has isospin -1/2. Also, you only add quarks; leptons are an exit point. (This is "because" only quarks feel color, and the strong force is the rationale for all the pairings.) And finally, you only add two ordered pairs at a time.

To begin with, we suppose we only have left-handed quarks and right-handed antiquarks to work with; so we have ordered pairs of the form (+/- 1/3, +/- 1/2). Because of the secondary rule about only adding nonzero isospins of opposite signs, the only ordered pairs we can make from these are (0,0) and (+/- 2/3, 0). That is, left-handed neutrino / right-handed antineutrino, and left-handed down-type antiquark / right-handed down-type quark.

Next, suppose we are adding ordered pairs of the form (+/- 2/3, 0). From this we can again get (0,0), and we can also now get (+/- 4/3, 0), i.e. right-handed up-type quark / left-handed up-type antiquark.

Next, suppose we are adding ordered pairs (+/- 2/3, 0) and (+/- 4/3, 0). This allows us to get (+/- 2/3, 0) and (+/- 2, 0). So here the hyper-bootstrap offers an additional way to obtain (+/- 2/3, 0), as well as putting right-handed electrons / left-handed positrons (and their muon and tauon counterparts) within reach.

Finally, suppose we add (+/- 1/3, +/- 1/2) and (+/- 2/3, 0). This allows us to obtain (+/- 1, +/- 1/2) ... left-handed leptons and right-handed antileptons ... and (+/- 1/3, +/- 1/2) ... left-handed quarks and right-handed antiquarks again, the hyper-bootstrap feeding into itself again.

As happens for Alejandro, I don't have a rule that prevents me from combining (+/- 4/3, 0) with itself, so I also get the annoying extra combination (+/- 8/3, 0). edit: Nor do I have a rule against adding (+/- 4/3, 0) with (+/- 1/3, +/- 1/2), which produces (+/- 1, +/- 1/2) as above, and another nonexistent assignment (+/- 5/3, +/- 1/2).

Obviously the hyper-bootstrap and the super-bootstrap have considerable similarities - including the leftover at the end! And we need to examine whether the actual multiplicities, of quark fields and their combinations, work at all. But it's interesting that even at the slightly finer-grained level which considers isospin and hypercharge quantum numbers separately, you can still define a similar scheme.

 

[mitchell porter]

A sketch is attached.

 

[arivero]

There is also a secondary "rule" that you can add two ordered pairs which both have nonzero weak isospin, only if one has isospin +1/2 and the other has isospin -1/2.

It seems reasonable, as then we can look for some symmetrization argument to justify the idea. But is is also peculiar. It means that the uu and dd combinations only happen for R type quarks.

Looking at the reference of Huerta, I note that in http://math.ucr.edu/~huerta/guts/node10.html the previous section he takes some pains to discuss the adjoint representation of U(1) and its role in the hypercharge. A subltle point here is that U(1)-hypercharge is still chiral (as Distler likes to stress) and then it needs complex representations, while U(1) electromagnetism is not.

 

[mitchell porter]

I've counted up the combinations, see attachment.

As input, I've taken every ordered pair (weak hypercharge, weak isospin) that is actually realized by a quark in the standard model. In the table I list every possible summation of two such ordered pairs (I have dropped the "secondary rule" which excluded outcomes with a "weak isospin of +/- 1"). Finally, I calculate multiplicities (represented in the table by subscripts) by assuming that I'm just working with udscb.

For example, in adding (-1/3,1/2) and (1/3,-1/2) to get (0,0), there are nine combinations, because the inputs correspond to an electric charge of magnitude 1/3, so there are three flavor options for each. Whereas, in adding (1/3,1/2) and (2/3,0) to get (1,1/2), we are adding an electric charge of magnitude 2/3 to an electric charge of magnitude 1/3, so (by the rules of the game) we have two flavor options for the first (no top) and three flavor options for the second. Everywhere in the table, to get the multiplicity, I just multiply two numbers in this fashion, except along the diagonal, where we are pairing elements of the same set. So three flavors gives six possibilities (dd ss bb ds sb bd), two flavors gives three possibilities (uu uc cc).

Each ingredient of each combination is specified by a handedness, a flavor, and whether it's a quark or an antiquark. So we are talking about pairings of the form "left-handed bottom antiquark + right-handed charm quark".

In making sense of the resulting table, I have excluded from consideration (for now) any combination of isospin/hypercharge quantum numbers which does not correspond to a standard model particle. These are labeled "exotics" and crossed out. We are therefore left with an enumeration of "how many ways to reproduce the weak quantum numbers of any standard model fermion, by pairing quarks other than the top".

For the quarks, for all but two outcomes, there are six ways to do it. What we really want is three (the number of generations), but perhaps we can think of pairing the six off in superposition. For (1/3,1/2) and (-1/3,-1/2), there are nine options, as if we want three elements in superposition per flavor, rather than two. Curiously, these are states with electric charge of magnitude 2/3, so maybe we should group them into superpositions with two, two, and five elements, with the five-part superposition being the top.

For the leptons, characteristically there are 12 (6+6) or 13 (4+9) ways to obtain any given outcome. The exceptions are (+/-2,0), but these can be paired up with half the (0,0)s - we have 26 of those. Anyway, here it seems we want four elements in a superposition corresponding to a single standard model species of fermion (specified at the flavor, handedness, (anti)particle level), rather than two.

And then there are all the exotics, the pairings that don't obviously correspond to anything. Some of these have the electric charge of a quark, but the hypercharge and isospin are wrong.

 

[mitchell porter]

You could say that this "hyper-bootstrap" is the super-bootstrap at four times the resolution. Where previously we just combined quarks and antiquarks (e.g. as described https://www.physicsforums.com/showthread.php?t=457825&page=8#127".

As a statement about actual physics, my tabulation of combinations is about as naive as it could get without being completely irrelevant to the real world. All the inputs, at least, are real. Unrestricted combination of left quarks and right quarks is probably wrong, but we do have to take chirality into account eventually, since left and right have different electroweak quantum numbers. I also haven't taken any representation theory into account. If someone just told you that gluons have the form "color-anticolor", where color is RGB, you would assume that there were 9 gluons, but in fact there's only 8. The multiplicities in my table may be reduced or altered by similar considerations. Also, we know that the actual QCD spectrum is http://physics.stackexchange.com/questions/13458/what-the-heck-is-the-sigma-f0-600" . At this point, in the quest for a hidden supersymmetry in the standard model, we still don't know whether it's better to look at the physical hadron spectrum or at the algebra of composite operators.

So this table at least illustrates the idea - that by pairing up quarks, you get combinations with the quantum numbers of all the standard model elementary fermions. But the exact principles on which the table was assembled are very naive, and its properties may change considerably as it become more physical. That is, we could construct an extension of Miyazawa's original hadronic supersymmetry scheme, or an electroweak extension of a dual resonance model, and then see what the tabulation of composite states/operators looks like.

 

[arivero]

I will crosscheck the hyper-bootstrap pairings during the week end, at a first glance they seem to be working well? Have you taken care of separating the I=1 and I=0 weak isospin combinations, for the L-L sector?

The reading of Huerta is interesting. It is clear that there are some differences between u-type and d-type, so we can expect uu to have different role than, say, dd. I am thinking that some detail about being in the fundamental or the adjoint representatios should emerge somewhere, after all we are expecting dd and ud to partner with particles in the fundamental representation of the gauge group, while uu should parnert with particles in the adjoint of the unbroken gauge group (and on the other hand, charged under electromagnetism, so somehow in a fundamental repr of U(1))

Also, which is the difference, Huerta-wise, between electromagnetism and hypercharge? Does the former use real representations, while the later uses real ones? Could it be relevant?

 

[arivero]

Working a little bit with the table, it seems that substituting the naive symmetrisation by a better one will save the day. For quarks, the d comes in packages of 6 and 6, and then u comes in 9 plus 6. But the later 6 is in the diagonal, so the full, unsymmetrised, box actually "12 and 12" for the d and "18 and 6" for the u, which restores the counting and your previous statement where the hyperbootstrap is four times the superbootstrap.

I guess that what we want to go down fro 24 to six is to use the traditional spin sum for 1/2 particles 2x2=3+1 and reject the triplet, isolating the scalar singlet. Some similar trick could be worked out for isospin, but here the it makes sense to use the real thing. Still, it will be amusing in the up sector.

For the charged leptons, some extra work seems to be required: we have (6+6)+6, or if we consider the full box, (12+12)+12. Perhaps the first sum must be symmetrised on its own, reducing to one half. This extra work is strange, because in the superbootstrap the charged lepton sector is similar to the d sector. It could be related to the point of having particle-antiparticle here, and then it is always possible to distinguish each particle, while in the quark sector we can have undistinguible particles.

For the quarks, for all but two outcomes, there are six ways to do it. What we really want is three (the number of generations), but perhaps we can think of pairing the six off in superposition. For (1/3,1/2) and (-1/3,-1/2), there are nine options, as if we want three elements in superposition per flavor, rather than two. Curiously, these are states with electric charge of magnitude 2/3, so maybe we should group them into superpositions with two, two, and five elements, with the five-part superposition being the top.

For the leptons, characteristically there are 12 (6+6) or 13 (4+9) ways to obtain any given outcome. The exceptions are (+/-2,0), but these can be paired up with half the (0,0)s - we have 26 of those. Anyway, here it seems we want four elements in a superposition corresponding to a single standard model species of fermion (specified at the flavor, handedness, (anti)particle level), rather than two.

 

[mitchell porter]

Some more attachments which should make it easier to compare super and hyper...

I have some new thoughts about how to make this work in field theory. The important point is that, along with the option of simply identifying leptons as mesinos and quarks as diquarkinos, one may also regard mesinos and diquarkinos as extra states which mix with fundamental quarks and/or leptons, with which they share electroweak quantum numbers. This appears to require terms in the Lagrangian that combine a chiral fundamental field with a composite of the opposite chirality. That is, together with, or instead of, ordinary mass terms like "qbar_L q_R", one also has "qbar_L D_R", where "D" is the composite which mimics the quark "q". This is a way for the diquarkinos corresponding to udscb to mix with them, contributing some or all of their mass. (In the simplest scenario, the top and all the leptons are wholly composite.)

 

[arivero]

Going to mesinos and diquarkinos has the advantage that we don't worry anymore that the supersymmetry generator violates the barion number (actually, B-L). On the other hand, the fundamental view induces to go even beyond the hyper-bootstrap to the, er, LR-bootstrap?, using B-L, I3R and I3L as the quantum numbers. In this case the electric charge formula is, if I recall correctly

Q= 1/2 (B-L) + I3R + I3L.

Where for instance a uR quark has B=1/3, I3R=+1/2, I3L=0. While a, say, eL lepton has L=1, I3R=0 and I3L=+1/2.

Some more attachments which should make it easier to compare super and hyper...

Yup, it is clear now. As expected, the down squark and charged slepton sectors are way less problematic, sneutrinos are midly problematic (they are off diagonal, so it only happens that you get some extras if you do not use the decomposition 24+1 of SU(5) irreps) and the diagonal sector, the really intriguing one, is the up squark and the extra, "H" sector.

 

[arivero]

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.

I have looked again the article of Csaki, Shirman, Terning, as well as Terning textbook --which I happened to buy randomly in January, in a generic library (!) in Paris-- chapters about duality. I am very surprised that they have not found the sBootstrap effect; even in some cases it is reasonable, in their context, to separate a particular quark from the rest, as we do. Same worry with Luty, and with other people who were taking some advanced look to composites: Alex Pomarol, Flip Tanedo,...