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

[mitchell porter]

I got halfway to a preon model in which leptons and quarks are the hadrons of a new superstrong force. Probably it can't work, but the process is instructive.

The starting point is a reworking of electroweak physics due to http://arxiv.org/abs/hep-ph/0206251" . In his new formulation of the standard model, all the SU(2) singlet fermions are the same, but all the SU(2) doublet fermions actually have a new scalar attached, which I'll call a "prehiggs" boson, because Calmet goes on to build the Higgs (and the Ws) as a bound state of these scalars. This is spelt out on pages 28 and 29 of his thesis. A (weak doublet) lepton is a "leptonic D-quark" plus a prehiggs, a (weak doublet) quark is a "hadronic D-quark" plus a prehiggs, and there are two prehiggses. The leptonic D-quark is just like a standard model lepton; for example, it has integer electric charge.

So what I propose to do, is to apply the ultracolor implementation of Alejandro's correspondence to the elementary fermions of Calmet's dual standard model. As before, we will say that there are five fundamental quarks, udscb, with electric charge (or hypercharge), color charge, and ultracolor charge, and an unspecified number of n quark flavors, "n" for neutral, which have no electric charge and no color charge, but which have ultracolor charge. Ultracolor is a new confining SU(3) force that is stronger than color (so the deconfinement scale is higher than for QCD). Finally, I suppose that Calmet's prehiggs scalars are actually n-quark ultracolor mesons, $n \overline{n}$.

It seems that we end up with something like this (q is an ordinary quark, n is a neutral quark, l is a lepton):

q_R = $qqn$ (baryon)
q_L = $qqnn\overline{n}$ (pentaquark)
l_R = $q\overline{q}nnn$ (pentaquark)
l_L = $q\overline{q}nnnn\overline{n}$ (heptaquark), or maybe some mixture like $q\overline{q}\overline{n}\overline{n}\overline{n}$ + $q\overline{q}nnn$
W+, W-, H = $n\overline{n}n\overline{n}$ (neutral tetraquark)

(edit: slightly modified from original version)

I need to emphasize that these are ultracolor "baryons" and multiquarks, bound by "ultragluons", not by QCD gluons. The composite leptons that result are supposed to be color-neutral and insensitive to the color force except for very weak "color van der Waals forces", while the "composite quarks" do feel QCD (because of the color-charged elementary q-quarks that they contain), and these composite quarks mix with the elementary q-quark fields (except for the top quark, which is entirely composite).

An ultracolor quark-preon model like this might inherit other features of Calmet's scheme. He introduces his version of electroweak unification on page 39. On page 56, he seems to propose that only the top quark has a direct coupling to the Higgs (which in his scheme is a prehiggs composite), with the Yukawas of the other quarks coming from vertices of the form tbW. So there would be plenty to do, if this ultracolor model could get off the ground.

But I don't think it can, for reasons noticed by 't Hooft back at the very beginning of preon models. In this scheme, the composite fermions are baryons and multiquarks of a color-like force, and that means they should be heavy in the same way that nucleons are heavy - not at the exact same scale, we are free to adjust the ultracolor deconfinement scale since ultracolor has its own coupling constant - but it seems to be difficult to reconcile the size of e.g. the electron with the idea that it is an "ultrahadron". I know there was subsequent work (after 't Hooft) exploring ways to get light composite fermions, and it may be worth a look, but for now this is the obvious barrier.

Also, the composite states are very complex, with up to seven constituent quarks (when the n-quarks are also counted). In QCD, the dynamics of such large multiquark aggregates are not well-understood.

But perhaps this foray into preon model-building can serve as preparation for the more difficult task of examining composites in a supersymmetric theory, where, instead of n-quarks, the extra neutral fermionic components are gluinos or ultracolor gauginos. One can imagine studying the http://arxiv.org/abs/hep-th/9807080" in order to have light gluinos / gauginos; and then the quark hypercharges would still need to be introduced...

 

[mitchell porter]

Somehow until now I failed to appreciate figure 1 in http://arxiv.org/abs/hep-ph/0505220" . That web of relationships is one of the most fascinating things I've ever seen. The really amazing thing - given the Koide relation - is the near-coincidence between muon and pion masses, and between tauon and glueball masses.

I can even come up with a handwaving account of what's involved, in terms of the preceding model, which says that leptons are mesinos bound by ultragluons: An electron is a bare mesino, a muon is a mesino dressed with a pion's worth of virtual gluons, and a tauon is a mesino dressed with a glueball's worth of virtual gluons! That is, both the pion and the glueball represent natural bound states of QCD, in which most of the mass comes from virtual particles (though they may organize themselves around "constituent" partons), and we suppose that the three charged leptons somehow instantiate these mass scales for the same reason.

But it's hard to see how this can actually work. If the tauon is a mesino with a QCD glueball attached, then why doesn't it act like a hadron? Well, maybe it's an ultracolor glueball, and the ultracolor coupling constant is the same as the QCD coupling constant (in order to make ultracolor mass scales and color mass scales the same); but then other things ought to go wrong. Still, surely this is yet another big clue regarding how to get the whole standard model from a single, strongly coupled, probably supersymmetric theory.

edit: One more comment about how this could work. Suppose we think of a "bare mesino" as consisting of quark, antiquark, and gaugino (held together by gauge bosons). Then the "pion mesino" might be a mesino in which the quark and antiquark are dressed with virtual gauge bosons as in the pion, and the "glueball mesino" might be a mesino in which the gaugino is also dressed. (I am intrigued by the glueball's proximity in mass to a number of baryons made of three first-generation quarks; it's as if this is the mass scale for three-parton objects - as if the glueball contains three "valence gluons".)

edit #2: Here is an even crisper statement about where this line of thought leads.

According to the formulation of the sbootstrap in e.g. comment #98, leptons are mesinos and quarks mix with diquarkinos. Let us think of these "-inos" as containing three partons: a quark; another quark or an antiquark; and an extra fermion (or extra fermionic ingredient). Let us also suppose, drawing inspiration from QCD, that there are three distinctive wavefunction structures possible for these three-parton objects, and three corresponding mass scales: a wavefunction with no dressed partons, a wavefunction with two dressed partons, and a wavefunction with three dressed partons.

Now refer to figure 1 in the paper cited earlier. In this new language, an electron is a mesino with no dressed partons, a muon is a mesino with two dressed partons, and a tauon is a mesino with three dressed partons. But in the figure we see that all the quarks, except for the top, also cluster around these three energy scales. It is therefore logical to guess that the up and down quarks mix with diquarkinos with no dressed partons, the strange quark mixes with diquarkinos with two dressed partons, and the charm and bottom quark mix with diquarkinos with three dressed partons.

Alejandro has occasionally tried to guess https://www.physicsforums.com/showthread.php?t=457825&page=9#132"; this may be seen as a complementary guess about "wavefunction structure" or "parton distribution functions" for the mesinos and diquarkinos, motivated by the mass scales.

 

[arivero]

Somehow until now I failed to appreciate figure 1 in http://arxiv.org/abs/hep-ph/0505220" .

Not only you... a version of it, without the horizontal reference lines, was removed from the wikipedia entry on elementary particles.

Now you can see how I were framed into this... too many miracles to keep believing that everything here was just a running down from GUT or Planck scales. Some fundamental interplay must be happening between colour and electroweak, and it must be happening here in front of our own noses.

edit: It is funny to use the picture as a reference to speculate with the switch-off of electromagnetic interaction. The electromagnetic coupling is zero if any of the two couplings in SU(2)xU(1) are zero, but the two cases are different, in one case you have MW=MZ, in the other MW goes to zero and MZ keeps finite. The red line seems a hint that the mass of top (and mass of Z and W) should go to infinity when alpha goes to zero.

 

[mitchell porter]

I have two ideas regarding the "~1/alpha, ~14, ~1/alpha" distribution of mass scales in the plot.

First, let me establish some nomenclature. We have a "light" mass scale for the electron and first-generation quarks, a "pion" mass scale for the muon and the strange quark, a "nucleon" mass scale for the charm and bottom quarks, and a "heavy" mass scale for the top quark. (And a superheavy mass scale relevant for neutrino masses if seesaw mechanism applies; it's not on the plot, but it's relevant if we're trying to explain all the masses.) I'll also note as before that a nucleon has three partons, a pion has two partons, and I speculated that the light mass scale corresponds to a "bare" supercomposite (mesino, diquarkino) in which there are no "dressed" partons.

On the plot we see that the step from light mass scale to pion mass scale is a factor of 1/alpha, the step from pion mass scale to nucleon mass scale is a factor of about 14, and the step from nucleon mass scale to heavy mass scale is another factor of 1/alpha. If you note that 14 is close to 1/sqrt(alpha) (certainly much better than order-of-magnitude close), then it's as if the mass scale goes up by one factor of 1/sqrt(alpha) for each extra "dressed parton".

That would imply that the top quark scale is a "five-parton" energy scale, like a pentaquark that binds a meson-like substructure with a baryon-like substructure. Perhaps the W and Z could also be regarded as heavy four-parton objects. This is all reminiscent of the Calmet-inspired preon model I posted earlier, though that model provides no explanation of why each extra charged parton should contribute multiplicatively, rather than additively, to the mass of a bound state.

The other idea is inspired by Jay Yablon, who you say (in the paper) pointed out the 1/alpha size of the step from tauon mass to Fermi scale. http://arxiv.org/abs/hep-ph/0508257" , on "a general upper bound on the strength of gravity relative to gauge forces".

So this other way to interpret the heavy mass scale where the top quark lives, is as the dualon scale, or perhaps as the dualino scale, and to say that the symmetry between the "zero parton scale" and the "five parton scale" has something to do with electric-magnetic duality. One of our repeatedly examined options here is to explain everything in terms of SQCD, and SQCD provided the original examples of Seiberg duality (a form of electric-magnetic duality), and the relation in the sbootstrap between electromagnetic U(1) charge and SU(3) color charge is certainly not nailed down... So it is not beyond imagining that some version of this is at work.

 

[mitchell porter]

I want to propose a further twist on the idea of the sbootstrap.

The idea is: all six flavors of quark are fundamental, but only the top has a mass coming from a Higgs yukawa-coupling (or something analogous). The other quarks are massless to first order, but the mass scales come from mixing with diquarkinos made of the five massless flavors.

Why do I propose to exclude the top from the sbootstrap? Because of hep-ph/0501200, mentioned in comment #48. Turn to page 6 and set the number of flavors to 5. Chiral symmetry breaking produces 44 Goldstone states, 24 of them pions and 20 of them diquarks. This "Pauli-Gursey symmetry" is exact for 2-color QCD but the authors (Shifman and Vainshtein) hypothesize that it can be lifted to 3-color QCD. So let us hypothesize that it can be lifted further, to N=1 SQCD. Then we would have a set of mesinos and diquarkinos, arising not just from a combinatorial pairing up of quark fields, but from an absolutely basic feature of QCD-like theories, chiral symmetry breaking. But now, the counting of states is such that it naturally corresponds to six flavors of lepton but only five flavors of quark.

I haven't yet thought about what charge or hypercharge looks like in this setup. Some further subtle twist may be needed. (http://inspirebeta.net/record/153619" is the obvious starting point here.) But the Pauli-Gursey or Shifman-Vainshtein symmetry for 5 flavors is so close to what the sbootstrap needs, and has such solid field-theoretic credentials, that I have to regard it as, almost certainly, part of the final answer.

Incidentally, QCD with 3 colors, 6 massless flavors, and N=2 supersymmetry has the nice properties of being UV-finite and having a "arxiv.org/abs/0708.1248"[/URL].

 

[mitchell porter]

A technical paper on QCD and SQCD that was released today, http://arxiv.org/abs/1109.6158" , appears to be of interest for the sbootstrap.

If I'm reading it correctly, the author has constructed a Seiberg duality in which N=1 SU(3) SQCD with 5 flavors is dual to an SU(2) gauge theory. That SU(2) is a gauging of flavor symmetry. There are two light quarks, q and qbar (see page 10), but there are four other heavy quarklike degrees of freedom, q', qbar', Z, and Zbar (see pages 15 and 16). However, these Zs are coming from the fermionic component of the meson superfield that usually shows up in Seiberg dualities; for the sbootstrap, one might have wanted these mesinos to be the leptons. On the other hand, when Kitano (the author) says they have the quantum numbers of quarks, that doesn't include electromagnetic charge. In fact, in section 5, he tries to get the electroweak group from the flavor symmetry (and the Higgs from yet another component of the meson superfield).

I'm not even sure that the author's construction works according to his own criteria. But it seems worthy of study, perhaps in conjunction with http://www.sciencedirect.com/science/article/pii/0370157388901184" , which adds two new scalars to the standard model in order to explain dark matter and baryogenesis.

 

[arivero]

Indeed, being on my blissful ignorance, I have always been excited about the phase diagrams of QCD and the dualities of SQCD, and particularly that when the number of colours is 3, the content with five or six flavours seems to have special significance. On other hand, in some of the papers I have read recently (surely mentioned along the thread?) there was some attempt to understand the SU(2) that comes from SU(Nf-Nc) as if it were related to the electroweak group. But it is wild guessing.

 

[mitchell porter]

I want to note a peculiar way in which the sbootstrap seems to be friendly to the idea of tachyonic neutrinos.

In string phenomenology that involves open strings stretched between brane stacks, branes have charges, standard model quantum numbers get realized as particular linear combinations of brane charges, and then the quantum numbers of a particular open string come from applying these formulae to the charges of the branes on which it terminates. For example, http://arxiv.org/abs/hep-th/0605226" is a discussion of how to obtain hypercharge. You can see a prototype formula on page 5 and the general example on page 10.

The http://arxiv.org/abs/hep-ph/0512065" involve taking the first five flavors of quark and antiquark, paying attention to their electric charge, and then considering all possible pairings (see page 3). So let's suppose that we are actually talking about five flavor branes and five flavor antibranes, and that electric charge is the brane charge.

The curious fact is that the neutrinos would then correspond specifically to strings connecting a brane to an antibrane of opposite charge. Branes and antibranes can fuse and this involves the condensation of open strings between them which are tachyonic scalars. So if only branes of exactly opposite charge can fuse, then (in this brane-based version of the sbootstrap), only open strings corresponding to neutrinos can become tachyonic.

edit: Flavor branes fill macroscopic space and time, so the brane-antibrane fusion that supposedly produces tachyons could be regarded as a localized phenomenon. The existence (or just the possibility) of tachyonic neutrinos in a particular space-time region would be equivalent to the localized fusion of a brane and antibrane of complementary charge, and vice versa.

 

[arivero]

Linking with current developments, and given that the sBootstrap only fails to justify the gauginos, the remarks from Lubos and Strassler are an encouragement:

http://profmattstrassler.com/2011/10/19/something-curious-at-the-large-hadron-collider/
http://motls.blogspot.com/2011/10/cms-sees-susy-like-trilepton-excesses.html

 

[mitchell porter]

Is https://www.physicsforums.com/showthread.php?p=1499886#24") why you are interested in trilepton decays?

I've had no time to think about it, but one of the dualities in the http://arxiv.org/abs/1110.2115" paper which I've been promoting, pertains to d=4 N=2 SU(2) gauge theory (see section 6). You have a domain wall in the d=4 theory, and get a d=3 theory on the domain wall, which includes trapped W-bosons from the d=4 theory... I guess I'm wondering if you could get your fifth-power decay rate on one side of the wall, and your third-power decay rate on the other side, for a similar theory.

 

[arivero]

Is https://www.physicsforums.com/showthread.php?p=1499886#24") why you are interested in trilepton decays?

Well, yes and no, it is just a holistic view The trilepton thing could be good if it signals the wino and zino, as they are the only particles we do not explain in the sBootstrap. The study of quintic and cubic scalings in decay rates, the Z0 coincidence, was found separately of theoretical input, but it could be a hint that the Z and W mass is condensation via a QCD coupling, or perhaps a string theory with the QCD scale.

Note that in electroweak theory the jump from quintic to cubic happens at high energy, this is, when you can approach that W and Z are massless but still you keep Fermi constant as a way to have a scale for the interaction. On the other side, for neutral pion-like decay, photon is the massless particle and the scale is provided by QCD alone.

 

[friend]

Susy particles are supposed to occur at high energies. But perhaps these energies only occur in highly curved space. Has anyone done a study to see if these particle even propagate in flat space? And if these s-particles were produced in the early universe, are there any consequences we'd be able to see in the CMBR? Perhaps the CMBR places limits on what energies the s-particles should exist.

 

[mitchell porter]

Susy particles are supposed to occur at high energies. But perhaps these energies only occur in highly curved space. Has anyone done a study to see if these particle even propagate in flat space? And if these s-particles were produced in the early universe, are there any consequences we'd be able to see in the CMBR? Perhaps the CMBR places limits on what energies the s-particles should exist.

Supersymmetry is very flexible. The super-particles can be light or they can be heavy, it depends on the details of your theory. Even in a specific supersymmetric model, like the Minimal Supersymmetric Standard Model discussed several times in this thread, there are dozens of parameters which the model itself doesn't predict. So if you just work within the framework of the MSSM, all you can say is that experimentally, certain parameter values (such as light masses for all the super-particles) don't match experiment. In principle the super-particles could all be very heavy (as in "supersplit supersymmetry", which started as a joke about supersymmetry being completely undetectable), but then this would indeed have implications for cosmology - not just CMB; super-particles are a popular explanation for dark matter.

With a deeper model, you might get a theoretical reason for the MSSM parameters only taking particular values. For example, the "G2 MSSM" tries to figure out what characteristics the MSSM would have if it came from M-theory on a G2 manifold.

Note that in electroweak theory the jump from quintic to cubic happens at high energy, this is, when you can approach that W and Z are massless but still you keep Fermi constant as a way to have a scale for the interaction. On the other side, for neutral pion-like decay, photon is the massless particle and the scale is provided by QCD alone.

Would technicolor theories permit an exact analogy? Since then the electroweak scale is the "technicolor scale".

 

[arivero]

Hmm, I was trying now to approach the composite symmetry from a more general point of view, and it seems it is really not so restrictive. Let's asume as initial hypothesis that we have leptons and quarks with some SU(2) isospin symmetry, so a generation of leptons has electron and neutrino, and a generation of quarks has up and down. This makes 8 sleptons and 8 squarks of each color in their respective generations.

Next we ask if we can build these sfermions with composites, asking the composites to have a SU(N) flavour symmetry.

The maximal NxN representation of SU(N) has always N²-1 components, then it can accommodate n_g={N²-1}/8 generations of sleptons. Given that N²-1 is a multiple of 8 when N is odd, let's stay for the moment with the this case.

On the squark side, the maximal NxN representation, antisymmetric, has dimension N (N+1)/2, thus the corresponding NxN+NxN has place for N(N+1) components and it seems that we are always going to have an extra number of particles N(N+1) - (N²-1) = N+1

If there is something peculiar to N=5, it is not obvious. If we want to be more predictive, we will need to impose some conditions to the flavours of the composites, such as having also the SU(2) isospin symmetry.

In a first step towards SU(2) isospin, we want to branch SU(N) as SU(p+q) in a way such that the subrrepresentations add to the same number of particles. We know that it works for SU(3+2), the question is how general it is. If we keep insisting that the slepton sector must fit exactly, this amounts to ask 2 (p q) = (p² -1) + (q²-1) + 1, and so |p-q| = 1. I am a bit puzzled here because in the down-towards-top approach the lepton sector also provided a second equation for the number of generation; in the top-down approach it does not seem so. It seems that we need to look also the subrrepresentations of the squark sector.

 

[arivero]

Would technicolor theories permit an exact analogy? Since then the electroweak scale is the "technicolor scale".

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]

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.