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

arivero

It could be. I am also curious about Gribov ideas for point-like pions; Humanino mentioned this line of research some weaks ago.

arivero

http://arxiv.org/abs/1111.0477 Scalar diquark in t tbar production and constraints on Yukawa sector of grand unified theories

So even direct observation of +4/3 scalars is not discarded? But, colored and +4/3 instead of singlet and +1? After so much work, is it just the plain version?

mitchell porter

I thought the real "4/3" problem for the sbootstrap is, where are the fermion partners of the charge 4/3 diquarks?

arivero

Well, yes, if the 4/3 diquarks do exist as real particles, and no just uu QCD pairs, it goes against the sBootstrap because we are postulating that all the scalars do not exist fundamentally, that they are just QCD strings.

But it should be also a partial success because any supersymmetric theory providing these quarks would actually have the flavour SU(5) symmetry of the sBootstrap in the scalar sector.

And I guess that such susy theory would have the same problems that the sBootstrap to understand the fermion partners of these particles. To me, the best candidate is still that they are undressed of colour and B-L charges and then they are eaten by the SU(2) winos to build the massive gauge supermultiplets.

arivero

This susy composite that Lubos is speaking about, has it got squarks and sleptons, or is it about spreons?

mitchell porter

It has both. The right-handed stop and the left-handed stop-sbottom doublet are composite, but the other squarks are elementary.

The model is quite complex. It contains the MSSM minus those particles and the Higgs, a new strongly coupled SU(4) sector which gives rise to composite t and H superfields, and also to composite W and Z which mix with the elementary W and Z, and it also has to contain a third, susy-breaking sector which they have not bothered to specify.

Hopefully such models can be made better and more elegant by trying to build them around the sbootstrap and the extended Koide relations...

mitchell porter

I'd like to revisit the recent idea (comment #121, arxiv:1111.7230) that a "sBootstrap diquark" with (hyper)charge 4/3 could explain the t-tbar asymmetry. I'm rather skeptical about the idea, and we don't even know that the t-tbar asymmetry is real, but it's a good opportunity to concretize certain issues:

• The top has a special status in the sBootstrap (it's only an output of the combinatorics, not an input)
• It's difficult to treat top differently from bottom when t_L b_L are a weak doublet
• How to interpret the charge 4/3 diquark pairings

In my opinion, the best way to interpret the sBootstrap is as a Seiberg duality for the standard model, and the time is ripe for such an interpretation. Just this week there has been another major theory paper, "Seiberg duality versus hidden local symmetry", indicating major conceptual progress. Especially see pages 42 to 44, where they discuss Higgs versus technicolor models of EWSB as ends of a continuum.

Elsewhere, I've noticed this seminar by Florian Hartmann, which looks at Higgs and flavons in (Pati-Salam x family SU(3)). Getting Higgs yukawas from flavon VEVs is the Koide-Sumino approach to explaining the Koide relation, and an extra U(1) family gauge boson would give us Sumino's U(3) family symmetry. Meanwhile, L-R extensions of the sBootstrap were considered a while back, and the "charge 4/3 scalar diquark" explanation for the t-tbar asymmetry looks at couplings between the scalar diquark, and u_R and t_R.

So I see a nexus here that's worth investigating. Maybe the way to proceed is to look at the "diquark models of t-tbar asymmetry" that have been proposed - the specific field-theoretic models - and then to see if they can be hybridized with one of the many ideas about how to realize the sBootstrap within a concrete theory.

mitchell porter

I have kept thinking about how this could work in conjunction with the Koide relations for quarks. Sevral ideas:

1) The flavor symmetry of the sBootstrap, if gauged, could be the Sumino family symmetry that protects the Koide relations.

2) Get the GUT group and the gauged family symmetry group from an extra dimension, possibly deconstructed.

3) The overall theory is a supersymmetric extended technicolor theory in which the techniquarks are the electric quarks of a Seiberg duality. The magnetic theory is to be a Koide-Sumino model in which the yukawas come from flavon VEVs - but the flavons are actually condensates from the electric theory.

arivero

It could be better to think not of the flavour symmetry of "the sBootstrap" but of the "flavour symmetry of the scalar sector of susy", or even of the "composite flavour symmetry", because it is always 5x5 and a 5x5+5x5. This fact is independent of the sBootstrap hypothesis and in this way it could be more palatable.

Just in case that some newcomer reaches this thread, let me reminder that S(5x5) is a 24, for the sleptons, and that, with some abuse of notation, S(5x5+5x5) is a 30, from which a 24 are the usual squarks of a given colour charge, and the extant 6 are the problematic, or intriguing, +- 4/3 scalar pests.

arivero

Been speculative, I wonder if a gauge of the SU(5) should produce something as SO(2^5). It is known that the gauge group in string theory comes from half the number of dimensions (so SO(8192) is a relevant group for the bosonic string), and Bailin and Love shown, or hinted, that this number can be also related to a Chan Paton charge for fermions in the 1+1 surface.

mitchell porter

Two papers today which fit the agenda of comment #127 (points 1 and 3): "Family Gauge Bosons with an Inverted Mass Hierarchy" and "Scalar Mesons in Holographic Walking Technicolor". The first paper, coauthored by Koide, adapts the Sumino mechanism to a supersymmetric theory. The second paper looks at the spectrum of composite scalars in a strongly coupled supersymmetric technicolor theory - so it's relevant for understanding how a theory like that in the first paper (which accounts for Koide-like relationships among particle masses by positing a set of scalar "flavons" or "yukawaons") could emerge from a sBootstrap-like model.

mitchell porter

Looking back over a year of speculation in this thread, I am alarmed by how little I really knew about the topics under discussion (e.g. standard model, supersymmetry). I don't think I said many false things, but I was really flying blind a lot of the time. I say this because, having attained to some relatively sober and at least superficially plausible ideas in recent comments, I want to sketch another big-picture approach, and that means a return to going far beyond what I know about.

I'll start with Strassler's review of Seiberg duality. I have thought for a long time that the case of interest for the sBootstrap is SQCD, with Nc = 3 colors and Nf = 6 flavors, and N=1 or 2 supersymmetry. The N=2 case is self-dual; the N=1 case has a dual which also has 3 colors and 6 flavors, but in addition there is a new meson superfield.

For the sBootstrap to work, the quarks have to have the appropriate charges. So we might imagine the N=2 case with an extra U(1) gauged. Also, we give the top a large mass while keeping all the others massless (because the sBootstrap involves the combinatorics of five quarks, not six). Let us suppose we have gone from N=2 to N=1 supersymmetry along the way. Now suppose we take the Seiberg dual of this N=1 theory. The idea is that the leptons will emerge as part of the meson superfield, and the other five quarks will also acquire nonzero masses in the dual picture.

This picture is missing certain details. How exactly is supersymmetry broken? Where do weak interactions and parity violation come from? What about the Higgs? In recent comments I've speculated about getting scalars (Higgses, flavons) from composites. It may be possible to break an N=2 theory to get parity violation, but apparently it's challenging to do so in a way consistent with experiment. The origin of fermion masses has to be more complicated than in the standard model because the usual mass-generating terms don't exist.

Without having shown that any of this really can work, I now want to add two further speculations to the mix.

First, Alejandro has pointed out that the top quark Yukawa is unnaturally close to 1. It's not just of order 1, which would be technically natural; it's within less than 1% of being exactly 1. In my recent response to his observation (see preceding link), I've outlined the barest beginnings of a strategy for explaining this observation, in the light of new calculations by Rodejohann and Zhang. This could be added as a further epicycle on the "3-color, 6-flavor" approach to the sBootstrap that I just outlined (according to which there is a Seiberg duality, on one side of which the top Yukawa is "large" and the other Yukawas are zero, and on the other side of which is the standard model, with all quark Yukawas nonzero).

Second, way back in comment #110 (page 7) I mentioned that N=2 Nc=3 Nf=6 SQCD (with all quarks massless) has a twistor-string representation. The twistor space employed to define this twistor string with flavor is very similar to the one used by Witten in his 2003 paper, it just has slightly different branes and boundary conditions. What I would like to know is whether one can reproduce Heckman and Verlinde's recent construction using hits twistor space, in order to produce the N=2 theory coupled to gravity in a cosmologically realistic space. It's just an idea about what the ultimate context of a "3-color 6-flavor sBootstrap" might be.

Finally, I have to wonder if some version of my "N=8 cosmology" could apply here. The idea there is to take a particular AdS4/CFT3 model with an impressionistic resemblance to reality, and then to use gravitino condensates to uplift it to positive spatial curvature. The model in question has an SU(3) x U(1) local symmetry, and under SU(3), the eight gravitinos of d=4 maximal supergravity form a triplet, an antitriplet, and two singlets. The idea is that the triplets are the dark energy and the singlets are the dark matter... The "N=2 sBootstrap" above also has SU(3) x U(1) symmetry (the U(1) gives the quarks the charges needed for the sBootstrap combinatorics), so one might hope that an embedding in M-theory could produce the desired gravitino spectrum.

The N=8 cosmology starts from a perturbed version of ABJM theory, while the twistor string (in its unflavored version) gives rise to N=4 Yang-Mills, and there are deep relationships between ABJM (an N=6 theory) and N=4 YM, but they're too deep for me to say anything sensible about how they might relate to this project. The most plausible conclusion of all might be that the theory we're looking for is to be obtained from a string theory construction of conventional intricacy (e.g. compactification on a Calabi-Yau of the sort that phenomenologists already study), and everything I've just discussed is still too simple - though it might be a step towards the real thing.

mitchell porter

Way back in comment #47 (on page 3), when I was still figuring out the difference between a QCD diquark and a GUT diquark, I mentioned a paper from 1990, "Radiative generation of quark and lepton mass hierarchies from a top-quark mass seed" (free copy). I just revisited it, and I am amazed by how many of the properties you're looking for are satisfied by their model.

What took me back to it was the search for an explanation of the chained Koide triplets among the quarks. The Koide triplet for leptons relates corresponding particles in different generations, and this is much friendlier to standard thinking than the sequential quark triplets tbc, bcs,... Eventually I thought to look for models in which all the fermion masses descend from the top, via loop effects. And then I noticed that in the paper above, "We show that the simplest model one can construct has the following cascade: tree level-->top; one loop-->bottom; two loop-->charm, tau; three loop-->strange, mu, up, down; four loop-->electron."

Now suppose for a moment that in some model of this type, masses arising at n, n+1, and n+2 loops (for certain values of n) naturally satisfy the Koide formula for some reason. Then right away not only do we have the tbc, bcs, and tau-mu-e triplets, but tau and mu are also correctly "aligned" with charm and strange, for e.g. a Georgi-Jarlskog explanation of the factor of 3 relating their "Brannen" parameters. Something goes a little wrong with up and down, but their masses show the greatest deviation from the chained Koide ansatz anyway.

The radiative generation of masses is accomplished by having scalar diquarks and scalar leptoquarks which can change the particle species and allow already-massive particles like the top to appear in a loop. (Also one needs a Z3 symmetry to prevent particles other than the top from picking up tree-level masses via the usual couplings to the Higgs.) The couplings of these new scalars are arbitrary; the form of the model is constrained only by the requirement that the rank of the mass matrices grows appropriately, as higher-loop corrections are added. So there is no immediate explanation of Koide formulae here; but that's not a problem. This is really a representative of a whole class of models, and what one should now do is search the class for a specific model in which Koide relations appear.

arivero

It is amusing that in the nine "Citing Articles" catalogued by the PhysRev, three of them are from "usual suspects"; one by Ernest Ma and two by Robert Foot. SPIRES misses some of the citing articles: http://prd.aps.org/abstract/PRD/v43/i1/p225_1 on exotic scalar particles (!), http://prd.aps.org/abstract/PRD/v41/i7/p2283_1 by Foot, and http://prl.aps.org/abstract/PRL/v64/i24/p2866_1 by Ma. Generically, it seems that the concept of a "top quark seed" has not been considered "productive" by the mainstream :-(

Mitchell, let me note that Volkas is still working on diquarks and he lives near your home, so perhaps some friend or even yourself could happen to have attended some lecture of his?

arivero

The problem is, really, that the diquark idea and Koide cascade have still not evidence for a connection. Koide was the motivation for diquarks because Koide model were more easy to understand from compositeness, as in the original papers. But the sBootstrap is not connected (yet?) to Koide cascade.

arivero

Really it would be a real shock if the MSSM sfermion content (which is the one we produce in the sBootstrap) with some extra interaction were able to generate the mass spectrum of the standard model, and in the Koide format. That should be beyond coincidence.

mitchell porter

Other work by Foot suggests an interpretation of the mirror fermions appearing in the N=2 Nc=3 Nf=6 theory: they make up the dark sector! I just found this in Sheppeard's "ribbon dark sector" paper, which ends with some numerology connecting Koide phase parameters, dark sector fractions, and quark-lepton complementarity. Foot wrote a whole book arguing that dark matter is mirror matter... So maybe it's time to unearth Nir Polonsky's papers on N=2 phenomenology, and see if we can't get a Koide cascade and emergent leptons in the visible sector, and everything dark in a mirror sector.

I don't think I ever saw Volkas or Foot talk, by the way.