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

[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]

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

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]

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

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]

"Radiative generation of quark and lepton mass hierarchies from a top-quark mass seed" (free copy). I just revisited it...

"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."

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.

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.

 

[arivero]

In any case, I agree that the "seed top" idea is interesting. The squarks we have are different, as they change barion number. But the diagram at the end of the paper almost fits with the chains from koide, we have also a t-->b-->c and then a b-->c--->s, and the point of having the lepton sector hanging separately b--->tau c--->mu s--->e could be similar to the orthogonality.

 

[mitchell porter]

I have been reluctant to play the game of conventional MSSM phenomenology - too many possibilities, too much history of "this time, it's just around the corner" - but I have found a psychological starting-point from which to approach this exercise: think in terms of starting with a "supersplit" spectrum in which all the superpartners are at some ultra-high scale. You don't start out with the assumption that supersymmetry is the answer to the hierarchy problem or to anything else, and you are spared all the further problems-to-be-solved that are caused by assuming low-scale supersymmetry. Initially you regard it just as a feature of final-stage unification, extremely remote from experiment...

Then you think "what if one, two, or a few of these particles have small enough masses to be relevant to observable physics after all", and e.g. try to construct a Koide cascade from a He-Volkas-Wu-type theory. And only then do you start thinking about how to get your Koide-MSSM from a GUT, from the heterotic string, etc. (The idea of gauge-top unification, or even gauge-Higgs-top unification, looks interesting.) If it's worth it, you're even "allowed" to include ideas from conventional super-phenomenology, in a specific Koide-MSSM model. But in constructing a Koide-MSSM, I think it's imperative to start philosophically as if you were just extending the SM, and not the MSSM as conventionally conceived.

 

[mitchell porter]

We may have our first step in a MSSM top-seeded mass cascade: a right-handed down-type squark. Dobrescu and Fox (2008) present a model somewhat in the spirit of He, Volkas, and Wu, in which a leptoquark scalar they call "r", and a color-octet weak-doublet scalar, and some vectorlike fermions, produce a mass cascade in which, starting with a tree-level mass for the top, they obtain bottom and tau at one loop, charm at two loops, and strange at three loops; and muon at three loops and electron at four loops. On pages 9-10 they note that the down-type squark could play the same role as the "r" - "in supersymmetric models with R-parity violation the squarks may have leptoquark couplings" - though with differences in the details.

There has been a lot of work on radiative generation of SM fermion masses in the MSSM - e.g. hep-ph/9601262, hep-ph/9902443, hep-ph/0107147, arxiv:1108.2424 - but it's focused on other sources of mass, e.g. massive gauginos. Nonetheless I think all that work offers a useful context for a detailed development of MSSM top-cascade models, e.g. Crivellin (arxiv:1105.2818). There's work on starting just with top, bottom, and tau masses, so if we cut that back to just top, and then put in place a modified Dobrescu-Fox cascade, we might get somewhere.

Of course, since we're ultimately trying to explain a cascade of Koide relations, just parameter-fitting and showing the phenomenological viability of such a model would not be enough. If this really is how things work, one has to suppose that the Koide relations have an origin outside the MSSM. I suppose it would be convenient if e.g. one introduced extra symmetries to the MSSM just to set non-top yukawas to zero and to get the right structure of couplings for the cascade, and those extra symmetries alone were sufficient to produce Koide relations. But I wouldn't be surprised if we have to go very deep. For example, think of the topological expansion in string theory, in which e.g. a tree-level scattering of n open strings becomes a disk with n insertions on its boundary, and the k-loop correction is a disk with k holes. It's conceivable that the Koide relations have their origins in the properties of amplitudes at such a remote level of description.

 

[arivero]

About the point of "Assuming that the leptons and quarks other than top are massless at tree level", I still kept a thinking that the M2-brane and M5-branes should have a role to justify this masslessness. Either that, or something having an 84 irrepr.

 

[mitchell porter]

Gauge-top unification occurs in six dimensions. t_R, Q3_L (i.e. the third-generation weak doublet of quarks), and the Higgs all live in the bulk, and the top yukawa coupling is just the unified six-dimensional gauge coupling connecting those fields. (The other SM fermions are all confined to submanifolds.)

Meanwhile, the recently notorious M5-brane worldvolume theory is holographically dual to M-theory (and is thus approximated by d=11 supergravity) on a 7+4 dimensional manifold. The 7 large dimensions are the 5+1 of the M5-brane volume plus the usual AdS dimension that is emergent from RG flow. As described on Urs Schreiber's site, this theory also has a description in terms of a 7-dimensional Chern-Simons theory that can be obtained by truncating the supergravity C-field for this geometry.

It is not beyond imagining that there is a realization of gauge-top unification in terms of M5-branes compactified on a particular space, with all the non-top SM fermions being related to the C-field by a special supersymmetry transformation, as we have discussed before. I don't know if it's at all likely that this is so, but it is a scenario one can imagine and explore. There even seems to be a realization of what I want to call the "(2,3,6) theory" (N=2 susy, 3 colors, 6 flavors) in such a compactification, but I haven't looked into it yet.

 

[arivero]

Not that the blogsphere (ie Dorigo Matt Motl) is burning about non-detection of SuSy, I wonder what are the implications of the wrong-turn here. For instance if gluinos decay to quark squark, and squarks are diquarks.

 

[mitchell porter]

Well, let's think about what the "wrong turn" idea is. I've focused mostly on the sBootstrap, which is just a pattern, and in principle that pattern might be realized in a theory completely consistent with conventional thought about SUSY, or it might show up in some strange SUSY theory - maybe high-scale SUSY, maybe some peculiar alternative math like Sultan Catto's work.

The idea of the "wrong turn", as I understand it, is alternative historiography which says that string theorists might have figured everything out if they had continued on a path of the very early 1970s. Now what happened is that you had the original constructions of fermionic strings, e.g. by Ramond, you had a few of the basics figured out, and then the standard model revived QFT and almost everyone left strings. Meanwhile Scherk and Schwarz came up with the idea that strings are a theory of everything, which required that the string tension be Planck scale rather than QCD scale.

So despite the title of this thread, the "turn" in string theory was not about the scale at which SUSY holds, but about the string scale... I can think of two ways in which bringing the string scale down again might be motivated. One is the large-extra-dimension models that talk about TeV-scale gravity. The other is the revival of "strings for QCD" via AdS/CFT, holographic QCD, and the quest for a string dual of QCD. Also you get the occasional paper talking about TeV-scale conformal symmetry, though I don't understand that stuff enough to know whether it's sensible.

My attitude to the main line of research since the standard model is that it might be right and it might be wrong. We really could be living in a Calabi-Yau compactification of the heterotic string. Or we could be living in some different sort of physics that no-one thought of yet. Combining a few buzzwords, imagine a twistorial, conformal, noncommutative, asymptotically safe standard-model-plus-gravity based on division algebras. :-) I think string theory has tapped into math so deep that surely it's relevant to real physics. But the strings we know about might not be the only possible manifestation of that math.

So in your question, I think you're asking us to think about the MSSM as if it were 1972, and we had the simple early ideas about dual resonance models, and we had the sBootstrap pattern... what might we come up with.

 

[mitchell porter]

You were asking what high-scale supersymmetry might imply for the sBootstrap... One implication of high-scale supersymmetry is that SUSY doesn't stabilize the weak scale. But as pointed out here:

What is the minimal set of new particles that must appear below 1 TeV to avoid fine-tuning? It is well known that the only SM contribution to the Higgs mass that must be modified at sub-TeV scales is the one-loop correction from the top sector. All other SM loops are numerically suppressed by either gauge or non-top Yukawa couplings, by extra loop factors, or both. As a result, the states responsible for cutting off these loops can lie above 1 TeV with no loss of naturalness. Thus, the sub-TeV particles that soften the divergence in the top loop, the "top partners," provide a uniquely well-motivated target for searches at the LHC, and it must be ensured that a comprehensive, careful search for such partners is conducted.

It would be very nice if the charge ±4/3 particles could play this role!

But there's still a conceptual problem here: among the motivations for the sBootstrap, beyond the basic pattern of charge pairings, are a few mass coincidences like pion and muon. The dare is to think that these mass scales actually have a cause, e.g. that the muon is a hypercolor mesino whose mass is almost degenerate with the mass of the pion for a reason. The existence of crypto-susy near-degeneracies of mass is at odds with the idea of high-scale SUSY; or at least it would imply that SUSY is "broken" in a peculiarly irregular fashion. Then again, this was always so, even before weak-scale SUSY began to look problematic.

I have a lot more confidence in the meaningfulness of the Koide relations than any of this (like, 99% confidence versus 1% confidence), but the muon/pion and tauon/glueball coincidences are still fascinatingly suggestive, especially if you're looking to obtain the leptons from SQCD mesinos. The heavy charged leptons look like a "collapsed" hadronic sector with only one "meson" (and it's a fermion), and only one baryon.

And since the tauon "corresponds" to a three-quark object, and the muon to a two-quark object, the electron presumably "corresponds" (in the same dreamlike way) to a single quark. It vaguely reminds me of the difference between ordinary numbers and Grassmann numbers: the ordinary hadrons exist in infinite towers of resonances, but there's just one of each type of charged lepton.

Before you dismiss this as sounding too bizarre and arbitrary, consider figure 6 (on page 10) in "Twistor String Theory and QCD", in which the spectra of "ordinary" string theory and twistor string theory are compared. Ironically for the present discussion, Dixon wants to say that the spectrum on the left (with its infinite tower of higher states) doesn't resemble QCD; whereas what I want to say is that the spectrum on the left does look like QCD, and the spectrum on the right looks like the charged leptons, as I have just been describing them! If this was taken seriously, in the context of the sBootstrap, it would suggest that the leptons emerge from a "topological sector" of an SQCD-like theory.

 

[mitchell porter]

More on the theme that the charge ±4/3 "diquarks" and "diquarkinos" could be "top-partners": this paper runs through a whole series of scenarios in which the higgs -> gamma gamma branching ratio is enhanced by the existence of new, heavy, "highly-charged" quarks, which appear at one loop. Combined with the idea that the top-antitop "forward backward asymmetry" is due to a charge 4/3 scalar diquark, and it seems like we have something for all the problematic sBootstrap combinations to do.

 

[arivero]

More on the theme that the charge ±4/3 "diquarks" and "diquarkinos" could be "top-partners": this paper runs through a whole series of scenarios in which the higgs -> gamma gamma branching ratio is enhanced by the existence of new, heavy, "highly-charged" quarks, which appear at one loop. Combined with the idea that the top-antitop "forward backward asymmetry" is due to a charge 4/3 scalar diquark, and it seems like we have something for all the problematic sBootstrap combinations to do.

Aghh, 8/3 or -7/3 ! It is clear that people is very courageus, out there.

I think, speaking generically and nor for a particular theory, that the real trick is that the exotic charge comes partly from B-L and partly from the chiral part of the gauge group. The fractionary part is only the U(1) B-L contribution. In most cases, B-L is peculiar, we are not even sure if it is a local gauge or not.

 

[arivero]

I had some hope that the three 4/3 diquarks (and three -4/3) could be somehow undressed of its vector like charge, and then become an alternative to the Higgs mechanism. Or course such alternative implies the W and Z eat three, and still three are out there to detect.

A completely independent argument, not sBootstrap related, was SSM, the minimal susy standard model. There each W and Z just go to a supermultiplet, and imply they have a massive scalar partner. Call them H0, H+, H- if you want.

 

[mitchell porter]

Crazy idea of the day... Rodejohann and Zhang write that the large third neutrino mixing angle can be explained by "a 23-rotation appearing to the right of a tri-bimaximal mixing matrix". Meanwhile, it's a fact that mesons and glueballs mix, e.g. see these remarks about mass of the eta prime meson. In the sbootstrap it's postulated that the muon mass and pion mass, and perhaps the tauon mass and a fundamental baryonic mass scale close to that of the 0++ glueball, are related for a reason. So... what if that "23-rotation" is the manifestation of meson-glueball mixing, supersymmetrically transmitted to an emergent electroweak sector where mixing is otherwise described by the Koide-friendly TBM ansatz?

Also of definite interest: "Partially Composite Higgs in Supersymmetry" by Kitano, Luty, and Nakai. Kitano and Luty have been mentioned previously, and one could imagine that they've been reading the thread :-) given that the paper talks about a "Higgs bootstrap" relating [strike]QCD[/strike] a QCD-like scale and Higgs VEV, and a few other sbootstrap-like ideas.

 

[mitchell porter]

Bruno Machet (1 2) has an idea that is complementary to the sbootstrap: that the Higgs is formed from quark bilinear condensates. As was discussed in this recent thread, even if the Higgs VEV were zero, the W and Z would still get a mass by absorbing the pion (but it would be a MeV mass, not GeV). Machet is considering a 2HDM (2-Higgs doublet model) in which the Higgses look like pions by design, I suppose as a step towards eventually deriving a Higgs from within QCD. (In this regard, one might also want to consider Wetterich's gluon-meson duality.)

Independently we may observe that there is a history of trying to employ a slepton as a Higgs (see first page here), and there has been a minor comeback of this idea recently. Let me add that in the MSSM context, an up-type Higgs should probably be a mirror slepton, which would fit the N=2 supersymmetry theme I have sometimes promoted in this thread. The only problem with that idea is that N=2 theories don't have chiral interactions, so it all looks conceptually incoherent. But it could be that we just haven't found the right perspective, e.g. a way of breaking N=2 to N=1 in which Higgs-like effective interactions show up.

In the sbootstrap, the sleptons are supposed to be something like mesons, perhaps mesons for a new confining interaction, and the leptons are mesino superpartners of these mesons. I also think it's very interesting that there are three generations of them, and that Adler obtained circulant mass matrices from 3- and 6-higgs models. So one could suppose that a greatly extended version of Machet's idea is at work: an SQCD gives rise to leptons and sleptons, and the emergent sleptons produce a Koide-Higgs mechanism.

 

[lpetrich]

In a theory without Higgs particles or alternatives to them, the elementary fermions would be massless.

That would mean that QCD would not have chiral symmetry breaking, and thus that W's and Z would not get masses from massive pions.

However, if the quarks, at least, get masses from some source that does not couple to the W's and Z, then the W's and Z would indeed get masses from pions. That is rather unlikely from gauge symmetry, however. Whatever effect makes the masses of the elementary fermions must have weak isospin 1/2 and weak hypercharge +-1/2. That means coupling to the W's and Z also.