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

arivero

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

I am downloading them for the weekend!

mitchell porter

I want to tackle your idea, alluded to in comment #7, that the QCD string could be the Type I fundamental string; an idea arising from the 1987 paper by Marcus and Sagnotti, in which the SO(32) group of the Type I theory is derived by placing 5 "quarks" (and their antiquarks) at the endpoints of the string. For anyone just tuning in, the logic of the idea, explained in the first link above, is that the top quark decays too quickly to form hadrons, so all the mesons we know about are only formed from the first five flavors. Although the idea of weak-scale superstrings exists, I think this is the least likely avenue (mentioned so far) towards a realization of very-low-energy supersymmetry. But it might be instructive to walk a short distance down this road, and see what there is to discover.

So, to begin, here's a modern exposition of Type I string theory by Lubos. The Type I theory is just Type IIB with a space-filling orientifold plane, and then you also need 16 space-filling D-branes and their images reflected in the O9-plane in order to cancel anomalies. 16+16=32 and you can almost see where SO(32) comes from (and a similar relation holds in the S-dual heterotic SO(32) theory). I say "almost" because I'm used to a stack of n D-branes giving rise to a SU(n) theory, not a SO(n) theory; I suppose the O-plane has something to do with the latter.

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

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

mitchell porter

Alejandro, what's your philosophy regarding the Higgs?

arivero

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

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

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

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

arivero

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

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

mitchell porter

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

Here's what they (Sannino and Schechter) say: "Mesonic superfields" show up in Part III. This seems really promising, because it's an analysis at the level of a Lagrangian, and not just talking about quantum numbers.

mitchell porter

Equations 3.2-3.4 in that paper are something to stare at, especially if you're a supersymmetry novice. But let's try to interpret them with some very basic help. All the "F"s are complex scalar auxiliary fields which allow the supersymmetry algebra to close off-shell (see chapter 3 here). One normally considers only "phi" to be the scalar superpartner of the fermionic "psi", with "F" left out in the cold, but here the physical meson fields are being found inside an "F". Also, the plan in the paper is to completely decouple the superpartners of the known particles, leaving just QCD, so they want everything except the third term of equation 3.4 to drop out. But our objective is to identify some of the leptons with superpartners of those mesons, so presumably we want to keep some or all of "psi_T". What if we get "F_Q" to drop out? "psi_T" is "quark times antisquark plus antiquark times squark", and we also still have scalar squark-antisquark composites in the picture, alongside the mesons. It seems a little messy. But if we boldly ignore all the details, the message seems to be that a lepton, in this scheme of things, will be "quark times squark".

Now maybe that particular approach makes no sense in any possible world. But I can begin to imagine that, in a more complicated scheme, such considerations would allow you to construct a working preonic model, in which leptons are composite and their superpartners are mesons or diquarks.

Meanwhile, let me also note the existence of some papers by Kyianov-Charsky (also spelt Kiyanov-Charsky and Kiyanov-Charskii), in which QCD mesons and baryons are similarly derived from super-QCD, with the explicit intention of realizing hadronic supersymmetry: 1 2 3.

arivero

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

mitchell porter

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

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

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

mitchell porter

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

1) There are a number of papers on expressing the Nambu-Jona-Lasinio model (1 2) in terms of diquark and meson variables. Perhaps see especially "PNJL", the combination of NJL with the "Polyakov loop". There is also a supersymmetric version (sometimes called super-NJL), which one could try to re-express in this way. Also, early papers of Tomohiro Matsuda try to apply NJL to SQCD.

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

(Also see NJL from branes. Can it be combined with holographic diquarks?)

arivero

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

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

qsa

Hi Arivero,

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

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

mitchell porter

The paper where I first came across "diquark coupling" vs "leptoquark coupling" as a model-building choice was "Radiative generation of quark and lepton mass hierarchies from a top-quark mass seed" (1990). "We envisage a cascade mechanism, whereby quarks and leptons gain mass at various orders of perturbation theory from masses induced at the preceding order of approximation. In this way we hope to explain at least some of the qualitative features of the observed mass spectrum."

It has very few citations, especially in the past decade, but there is a recent one, "A Domino Theory of Flavor" (2009; talk). "Radiative models of flavor have a long history...", and to prove their point, they list 17 papers (refs 19-35), starting with Weinberg in 1972.

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

mitchell porter

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

Electron, muon, and tauon masses satisfy Koide's formula to high precision. Pion, kaon, and eta-meson masses satisfy a Gell-Mann–Okubo mass formula, but only approximately. I don't understand the derivation of the GMO formula, but apparently it's a standard thing in chiral perturbation theory, descended from QCD. The only field-theoretic explanations for the Koide formula that I know are those proposed by Sumino and by Koide himself. So there's the challenge: integrate these two mechanisms into one. This 2009 paper tries to do so.

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

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

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

hep-ph/0501200:

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

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

mitchell porter

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

arivero

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

mitchell porter

It needs more work.