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

[mitchell porter]

After staring at the http://math.ucr.edu/~huerta/guts/node11.html" assignments for a while, I have devised a new approach to this whole idea. I haven't even tried to get the right numbers of particles, I just want to mention it as a mutant form of the hypothesis which might assist its analysis.

Alejandro's idea involves pairing (anti)quarks, adding the electric charges, and then supposing that these pairings have superpartners, and is called the super-bootstrap. I do the same, except that I add the ordered pairs (weak hypercharge, weak isospin), so I call it the "hyper-bootstrap".

To add ordered pairs, the rule is (a0,b0)+(a1,b1)=(a0+a1,b0+b1). There is also a secondary "rule" that you can add two ordered pairs which both have nonzero weak isospin, only if one has isospin +1/2 and the other has isospin -1/2. Also, you only add quarks; leptons are an exit point. (This is "because" only quarks feel color, and the strong force is the rationale for all the pairings.) And finally, you only add two ordered pairs at a time.

To begin with, we suppose we only have left-handed quarks and right-handed antiquarks to work with; so we have ordered pairs of the form (+/- 1/3, +/- 1/2). Because of the secondary rule about only adding nonzero isospins of opposite signs, the only ordered pairs we can make from these are (0,0) and (+/- 2/3, 0). That is, left-handed neutrino / right-handed antineutrino, and left-handed down-type antiquark / right-handed down-type quark.

Next, suppose we are adding ordered pairs of the form (+/- 2/3, 0). From this we can again get (0,0), and we can also now get (+/- 4/3, 0), i.e. right-handed up-type quark / left-handed up-type antiquark.

Next, suppose we are adding ordered pairs (+/- 2/3, 0) and (+/- 4/3, 0). This allows us to get (+/- 2/3, 0) and (+/- 2, 0). So here the hyper-bootstrap offers an additional way to obtain (+/- 2/3, 0), as well as putting right-handed electrons / left-handed positrons (and their muon and tauon counterparts) within reach.

Finally, suppose we add (+/- 1/3, +/- 1/2) and (+/- 2/3, 0). This allows us to obtain (+/- 1, +/- 1/2) ... left-handed leptons and right-handed antileptons ... and (+/- 1/3, +/- 1/2) ... left-handed quarks and right-handed antiquarks again, the hyper-bootstrap feeding into itself again.

As happens for Alejandro, I don't have a rule that prevents me from combining (+/- 4/3, 0) with itself, so I also get the annoying extra combination (+/- 8/3, 0). edit: Nor do I have a rule against adding (+/- 4/3, 0) with (+/- 1/3, +/- 1/2), which produces (+/- 1, +/- 1/2) as above, and another nonexistent assignment (+/- 5/3, +/- 1/2).

Obviously the hyper-bootstrap and the super-bootstrap have considerable similarities - including the leftover at the end! And we need to examine whether the actual multiplicities, of quark fields and their combinations, work at all. But it's interesting that even at the slightly finer-grained level which considers isospin and hypercharge quantum numbers separately, you can still define a similar scheme.

 

[mitchell porter]

A sketch is attached.

 

[arivero]

There is also a secondary "rule" that you can add two ordered pairs which both have nonzero weak isospin, only if one has isospin +1/2 and the other has isospin -1/2.

It seems reasonable, as then we can look for some symmetrization argument to justify the idea. But is is also peculiar. It means that the uu and dd combinations only happen for R type quarks.

Looking at the reference of Huerta, I note that in http://math.ucr.edu/~huerta/guts/node10.html the previous section he takes some pains to discuss the adjoint representation of U(1) and its role in the hypercharge. A subltle point here is that U(1)-hypercharge is still chiral (as Distler likes to stress) and then it needs complex representations, while U(1) electromagnetism is not.

 

[mitchell porter]

I've counted up the combinations, see attachment.

As input, I've taken every ordered pair (weak hypercharge, weak isospin) that is actually realized by a quark in the standard model. In the table I list every possible summation of two such ordered pairs (I have dropped the "secondary rule" which excluded outcomes with a "weak isospin of +/- 1"). Finally, I calculate multiplicities (represented in the table by subscripts) by assuming that I'm just working with udscb.

For example, in adding (-1/3,1/2) and (1/3,-1/2) to get (0,0), there are nine combinations, because the inputs correspond to an electric charge of magnitude 1/3, so there are three flavor options for each. Whereas, in adding (1/3,1/2) and (2/3,0) to get (1,1/2), we are adding an electric charge of magnitude 2/3 to an electric charge of magnitude 1/3, so (by the rules of the game) we have two flavor options for the first (no top) and three flavor options for the second. Everywhere in the table, to get the multiplicity, I just multiply two numbers in this fashion, except along the diagonal, where we are pairing elements of the same set. So three flavors gives six possibilities (dd ss bb ds sb bd), two flavors gives three possibilities (uu uc cc).

Each ingredient of each combination is specified by a handedness, a flavor, and whether it's a quark or an antiquark. So we are talking about pairings of the form "left-handed bottom antiquark + right-handed charm quark".

In making sense of the resulting table, I have excluded from consideration (for now) any combination of isospin/hypercharge quantum numbers which does not correspond to a standard model particle. These are labeled "exotics" and crossed out. We are therefore left with an enumeration of "how many ways to reproduce the weak quantum numbers of any standard model fermion, by pairing quarks other than the top".

For the quarks, for all but two outcomes, there are six ways to do it. What we really want is three (the number of generations), but perhaps we can think of pairing the six off in superposition. For (1/3,1/2) and (-1/3,-1/2), there are nine options, as if we want three elements in superposition per flavor, rather than two. Curiously, these are states with electric charge of magnitude 2/3, so maybe we should group them into superpositions with two, two, and five elements, with the five-part superposition being the top.

For the leptons, characteristically there are 12 (6+6) or 13 (4+9) ways to obtain any given outcome. The exceptions are (+/-2,0), but these can be paired up with half the (0,0)s - we have 26 of those. Anyway, here it seems we want four elements in a superposition corresponding to a single standard model species of fermion (specified at the flavor, handedness, (anti)particle level), rather than two.

And then there are all the exotics, the pairings that don't obviously correspond to anything. Some of these have the electric charge of a quark, but the hypercharge and isospin are wrong.

 

[mitchell porter]

You could say that this "hyper-bootstrap" is the super-bootstrap at four times the resolution. Where previously we just combined quarks and antiquarks (e.g. as described https://www.physicsforums.com/showthread.php?t=457825&page=8#127".

As a statement about actual physics, my tabulation of combinations is about as naive as it could get without being completely irrelevant to the real world. All the inputs, at least, are real. Unrestricted combination of left quarks and right quarks is probably wrong, but we do have to take chirality into account eventually, since left and right have different electroweak quantum numbers. I also haven't taken any representation theory into account. If someone just told you that gluons have the form "color-anticolor", where color is RGB, you would assume that there were 9 gluons, but in fact there's only 8. The multiplicities in my table may be reduced or altered by similar considerations. Also, we know that the actual QCD spectrum is http://physics.stackexchange.com/questions/13458/what-the-heck-is-the-sigma-f0-600" . At this point, in the quest for a hidden supersymmetry in the standard model, we still don't know whether it's better to look at the physical hadron spectrum or at the algebra of composite operators.

So this table at least illustrates the idea - that by pairing up quarks, you get combinations with the quantum numbers of all the standard model elementary fermions. But the exact principles on which the table was assembled are very naive, and its properties may change considerably as it become more physical. That is, we could construct an extension of Miyazawa's original hadronic supersymmetry scheme, or an electroweak extension of a dual resonance model, and then see what the tabulation of composite states/operators looks like.

 

[arivero]

I will crosscheck the hyper-bootstrap pairings during the week end, at a first glance they seem to be working well? Have you taken care of separating the I=1 and I=0 weak isospin combinations, for the L-L sector?

The reading of Huerta is interesting. It is clear that there are some differences between u-type and d-type, so we can expect uu to have different role than, say, dd. I am thinking that some detail about being in the fundamental or the adjoint representatios should emerge somewhere, after all we are expecting dd and ud to partner with particles in the fundamental representation of the gauge group, while uu should parnert with particles in the adjoint of the unbroken gauge group (and on the other hand, charged under electromagnetism, so somehow in a fundamental repr of U(1))

Also, which is the difference, Huerta-wise, between electromagnetism and hypercharge? Does the former use real representations, while the later uses real ones? Could it be relevant?

 

[arivero]

Working a little bit with the table, it seems that substituting the naive symmetrisation by a better one will save the day. For quarks, the d comes in packages of 6 and 6, and then u comes in 9 plus 6. But the later 6 is in the diagonal, so the full, unsymmetrised, box actually "12 and 12" for the d and "18 and 6" for the u, which restores the counting and your previous statement where the hyperbootstrap is four times the superbootstrap.

I guess that what we want to go down fro 24 to six is to use the traditional spin sum for 1/2 particles 2x2=3+1 and reject the triplet, isolating the scalar singlet. Some similar trick could be worked out for isospin, but here the it makes sense to use the real thing. Still, it will be amusing in the up sector.

For the charged leptons, some extra work seems to be required: we have (6+6)+6, or if we consider the full box, (12+12)+12. Perhaps the first sum must be symmetrised on its own, reducing to one half. This extra work is strange, because in the superbootstrap the charged lepton sector is similar to the d sector. It could be related to the point of having particle-antiparticle here, and then it is always possible to distinguish each particle, while in the quark sector we can have undistinguible particles.

For the quarks, for all but two outcomes, there are six ways to do it. What we really want is three (the number of generations), but perhaps we can think of pairing the six off in superposition. For (1/3,1/2) and (-1/3,-1/2), there are nine options, as if we want three elements in superposition per flavor, rather than two. Curiously, these are states with electric charge of magnitude 2/3, so maybe we should group them into superpositions with two, two, and five elements, with the five-part superposition being the top.

For the leptons, characteristically there are 12 (6+6) or 13 (4+9) ways to obtain any given outcome. The exceptions are (+/-2,0), but these can be paired up with half the (0,0)s - we have 26 of those. Anyway, here it seems we want four elements in a superposition corresponding to a single standard model species of fermion (specified at the flavor, handedness, (anti)particle level), rather than two.

 

[mitchell porter]

Some more attachments which should make it easier to compare super and hyper...

I have some new thoughts about how to make this work in field theory. The important point is that, along with the option of simply identifying leptons as mesinos and quarks as diquarkinos, one may also regard mesinos and diquarkinos as extra states which mix with fundamental quarks and/or leptons, with which they share electroweak quantum numbers. This appears to require terms in the Lagrangian that combine a chiral fundamental field with a composite of the opposite chirality. That is, together with, or instead of, ordinary mass terms like "qbar_L q_R", one also has "qbar_L D_R", where "D" is the composite which mimics the quark "q". This is a way for the diquarkinos corresponding to udscb to mix with them, contributing some or all of their mass. (In the simplest scenario, the top and all the leptons are wholly composite.)

 

[arivero]

Going to mesinos and diquarkinos has the advantage that we don't worry anymore that the supersymmetry generator violates the barion number (actually, B-L). On the other hand, the fundamental view induces to go even beyond the hyper-bootstrap to the, er, LR-bootstrap?, using B-L, I3R and I3L as the quantum numbers. In this case the electric charge formula is, if I recall correctly

Q= 1/2 (B-L) + I3R + I3L.

Where for instance a uR quark has B=1/3, I3R=+1/2, I3L=0. While a, say, eL lepton has L=1, I3R=0 and I3L=+1/2.

Some more attachments which should make it easier to compare super and hyper...

Yup, it is clear now. As expected, the down squark and charged slepton sectors are way less problematic, sneutrinos are midly problematic (they are off diagonal, so it only happens that you get some extras if you do not use the decomposition 24+1 of SU(5) irreps) and the diagonal sector, the really intriguing one, is the up squark and the extra, "H" sector.

 

[arivero]

Current thoughts: Mass is generated by anomalous breaking of superconformal symmetry in the strong interactions, which is then transmitted to the charged leptons (origin of the shared 313 MeV scale) and also to the electroweak gauge bosons. The whole standard model may have a "Seiberg-dual" description in terms of an SQCD-like theory with a single strongly coupled sector, with the electroweak bosons being the dual "magnetic gauge fields", and lepton mass coming from "technicolor instantons" in the electric gauge fields (analogous to the origin of nucleon mass in QCD).

This is a transposition of recent ideas, due to http://arxiv.org/abs/1106.4815" and collaborators, to the present context.

I have looked again the article of Csaki, Shirman, Terning, as well as Terning textbook --which I happened to buy randomly in January, in a generic library (!) in Paris-- chapters about duality. I am very surprised that they have not found the sBootstrap effect; even in some cases it is reasonable, in their context, to separate a particular quark from the rest, as we do. Same worry with Luty, and with other people who were taking some advanced look to composites: Alex Pomarol, Flip Tanedo,...

 

[arivero]

Some more attachments which should make it easier to compare super and hyper...

It seems that the reduction from hyper down to super works in a sequential way:

first, we reduce the four copies down to one. This should be to take the singlet LR-RL of each of the boxes.

Then, we get the symmetrical combination, say ab+ba, of the pairs. This is the "15 out of 5x5=15+10" in my language, or just the upper triangular matrix including the diagonal, in your drawing.

I still don't get why the procedure does not commute, if you first do the triangular matrix, then it becomes obscure how to do the RL-LR selection. I hate tensor products.

 

[arivero]

Interestingly, if one goes finer than hyper-, down to Mohapatra-Pati-Salam, the added charges do not bootstrap explicitly: the single quarks have "hypercharges" (actually, L and R isospins) either (1/2,0) or (0,1/2). The charges of L and R will add, so the composites can have only an integer sum, one or zero --via (-1/2,1/2)--. What is happening, then? That the susy operator, seen from the M-P-S point of view, violates barion-lepton number, but as it preserves electric charge, it must also violate I3 isospin proyection.

In the hBootstrap, all of the barion-lepton number is hidden as a piece of the hypercharge, so this violation is not always seen, because it is internally compensated inside I.

(Mitchell, should we write some note about all of this, more systematic that the forum thread?)

As a lateral note, while reading on GUT models, I have been amused by the way that SU(5) GUT makes its "composites" for the 10 representation, building from two 5s.

 

[mitchell porter]

I think a proof of concept (in field theory or string theory) would be desirable first: if not a realization of the full sbootstrap, then at least a demonstration of a mechanism that could plausibly make it work.

 

[arivero]

I think a proof of concept (in field theory or string theory) would be desirable first: if not a realization of the full sbootstrap, then at least a demonstration of a mechanism that could plausibly make it work.

I see your point. We have an algebra, but we don't have a mechanism, so it is still only math -and a naive one, for math-, not physics.

 

[mitchell porter]

Another approach doesn't involve supersymmetry at all, but instead a new ultrastrong confining force. You would start with udscb quarks, which also have "ultracolor" charges, and one or more further fundamental fermions - I'll call them n, n', n"... - which have ultracolor charge but not color charge, i.e. they feel the ultrastrong force but not the strong force. Under this interpretation, the mesinos and diquarkinos are not superpartners of mesons and diquarks, they are "ultrabaryons", baryons of the ultrastrong force, with one or more of the n fermions present along with the two quarks (i.e., if N is the rank of the ultrastrong gauge group, then there would need to be N-2 of the n particles in the ultrabaryons relevant for the sbootstrap). Leptons would still be mesinos, and quarks could mix with diquarkinos, but all the other apparatus of supersymmetric theories (gauginos, higgsinos) wouldn't be relevant.

 

[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.