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

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 one paper 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 Luty and Terning and collaborators, to the present context.

arivero

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, "AdS/CFT & Compositeness in the SM" has a nice basic explanation of the idea of "partial compositeness" which features in these Seiberg-like models.

mitchell porter

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

here is the chart I promised you.

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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! (1 2 comment). 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 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 hep-ph/0505105.

arivero

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 new thread for this 12-dimensional idea.

edit: Meanwhile I observe that we can get SO(10) (which contains both SU(5) and Pati-Salam) from 13 dimensions, as in S-theory.

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 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 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 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.

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

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.

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