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

arivero
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In post #549 here I answered:

arivero said:
This is the blindness -the wrong turn- I try to fight in the last years: our world IS susy at low energies, and because of it we confused the pion with the muon in the fifties.

It was a very prepostereous thing to say, so five minutes after proposing it (basically a couple of publications by John H. Schwarz in 1971, following the discovery of the Ramond string), everyone, including Schwarz, forgot about it. But with three generations, the degrees of freedom match. It is susy, it is the qcd string, they were right from the start, and the only point today is why the non-chiral interactions get their gauge bosons massless, but not the partners. If we find the gauginos -and only them- the question will be settled.

And then I was surprised by the comment of Tom, asking how the pairing was done. Well, I thought that I had discussed it in some thread in BSM, but after looking at it, it seems that I did only a few sparse remarks here and there. On other hand, people was not liking to interrupt the flow of the thread and I have been either contacted privately or suggested to open a new thread. So here it is. The development can be traced in some draft papers:

http://arxiv.org/abs/hep-ph/0512065 http://arxiv.org/abs/0710.1526 http://arxiv.org/abs/0910.4793 http://www.vixra.org/abs/1102.0034

Next post is my answer to Tom question. Keep in mind that we produce squarks, while the quarks are just the ingredient to terminate the extremes of the string.
 
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look at the data.

It is about taking seriously the ideas of http://dx.doi.org/10.1016/0370-2693(71)90028-1" ): the fermion in the dual model is susy to gluonic strings. So now all you need is to terminate the gluonic string. Regretly in 1971 there were only three states available to terminate the string: u, d, and s. Now we have the full history, and the experimental data tell us that we can terminate the gluonic string with five and only five different states: u, d, s, c, b.

So just count, please, just do the SU(5) global flavour game, and count. How many states do you get of charge +1? six, by terminating with particle and antiparticle. How many of charge +2/3? six of each colour, by terminating with an antiparticle at each end of the string. How many of -1/3? six. How many +1/3, -1, -2/3? Same: six, six, six. And how many neutrals? of course, twelve: the other half of the 24 of SU(5).

BONUS: Does it means that string theory, given as input the 3-2-1 gauge theory of the SM, predicts three generations? No exactly; only if we require that the neutral leptons must be produced too. If we only look at the quark sector, then any pairing of (2^{p}) "up quarks" with (2^{p+1} -1) "down quarks" will produce equal number, 2^p (2^{p+1} -1) of up and down combinations, and p=1 is just the simplest case. Numerically minded people will notice that p=4 amounts to 496, but a theory with 16 light "down" quarks, 31 light "up" quarks and a total of 248 generations seems not to be the object that Nature has offered us.

EDIT: Allow me a correction to this remark: Of course, the quark sector condition works for any integers q and 2 q -1, with q an even number, not necessarily a power of two. But that the powers of two are an interesing subset was noted by Peter Crawley in other thread time ago and I am kind of obsessed with this, because it could constitute the way to reconnect with usual string models, via the above p=4 case.

EDIT: other references using "fermion-meson": L. Brink and D. B. Fairlie http://dx.doi.org/10.1016/0550-3213(74)90529-X Nuclear Physics B Volume 74, Issue 2, 25 May 1974, Pages 321-342 ; Edward Corrigan and David I. Olive http://www.slac.stanford.edu/spires/find/hep/www?j=NUCIA,A11,749 Nuovo Cim.A11:749-773, 1972. Modernly, there are some papers, in the framework of SQCD and also in Holography, that work with "mesinos", generic susy partners of mesons. But note that phenomenologists restrict the name "mesino" to the composite combination of squark and quark
 
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Can you present a table (or a ereference) where the pairing is shown explicitly?
Why do you use SU(5) instead of SU(6)?
How do you count different charges like color, flavor, weak isospin and hypercharge and all that?
 
tom.stoer said:
Why do you use SU(5) instead of SU(6)?

Because the top quark doesn't bind into mesons (nor diquarks, for the same token).

This is, I am promoting an experimental peculiarity (that the mass of the top is higher than both the QCD scale and the W mass) to a main role.

But you can look also at it from a pure theoretical side. Take SU(3)xSU(2)xU(1) as given, and assume that SU(3) is the force that, at some scale, has this role of building the open string, this is, of binding pairs of particles. Then:

- First, you ask if there is some number of generations such that the possible pairs of terminations are in the same number that the squarks for these generations. The answer is none, so:

- Second, you go for the lesser goal: ask if there is some number of generations so that a subset of the quarks are the same number that the squarks you should have. The answer is yes, that q quarks of type down and 2 q - 1 quarks of type up, when q>1, combine to from the squarks needed for q (2q-1)/2 generations of particles.

- Third, make features out of bugs: postulate that the quarks that do not participate in the binding must have a high mass. On first approach, you can think that the subset of binding quarks should be massless, and the other of infinite mass. And we know from Nature that it is enough for them to have a mass equal or higher than the electroweak scale.

- Fourth, if you wish, add leptons to the mix. Of course leptons doesn't bind, they are SU(3) neutrals. But you want to produce sleptons. It happens that any solution of the second step also produces the needed number of charged sleptons (check combinations, now with quark/antiquark). And only for the simplest case, q=2, we get the expected number of neutral sleptons.

So, the full answer is, we do not use SU(6), because Nature hints us that we can relax to use another smaller number of flavours. Inspection of the quark sector tell us that we can use SU(q+2q-1) with q>1, and of all of these SU(3q-1), only SU(5) produces also the neutral sleptons.

s in squark and slepton stands, as usual, for "scalar". It refers to the spin zero partners of the elementary fermions, so that the electron has two slepton partners of charge -1, the positron has two slepton partners of charge +1 and so on.
 
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arivero said:
It is about taking seriously the ideas of J.H. Schwarz... the fermion in the dual model is susy to gluonic strings.
I think you are misinterpreting the paper. The "duality" in dual models (Dolen-Horn-Schmid duality) is that you get the amplitude by summing over s-channel diagrams or by summing over t-channel diagrams, not by summing over both at the same time as in ordinary field theory. The string theory explanation is that the dual-model s-channel sum and the dual-model t-channel sum are just different representations of the same sum over string histories, but with the world-sheet cut in different ways (in order to define a path integral). This is mentioned very briefly in Appendix A of Polchinski (page 332, "Relation to the Hilbert space formalism"), where he calls it "world-sheet duality". But this is not supersymmetry.
 
mitchell porter said:
I think you are misinterpreting the paper. The "duality" in dual models (Dolen-Horn-Schmid duality) is ... But this is not supersymmetry.

Hey, no, I never told that the duality of dual models is a supersymmetry; what we know is that the fermions in the dual model are known to be supersymmetric to the bosons in the dual model. Of course this discovery is going to happen after 1971. First they are going to discover wordsheet susy, then years later they are going to discover that it also implies Space Time susy. But never, neither by them -at least in the mainstream- nor by me, a dual model setup between fermions and bosons has been claimed. I am sorry that my wording could be misconstrued in this sense.

The reason to quote this paper is to show that, in the years after the discovery of the fermionic states of the string, by Ramond and then by Neveau-Schwarz, there was no problem to see the string as a holder both for quark and gluonic states, which is the thing I am using: elementary fermions (quarks and leptons) in the fundamental level of one side, gluons (mesons, diquarks) in the fundamental level of the other.

Some years later, with the standard model already established, it could seem strange to have elementary entities on one side and composites in the other, so Schwarz took the bold step of promoting the bosonic sector also to the status of elementary, moving all the game to Planck scale. My claim is that this was the wrong turn, and that the initial view of fermions plus gluons was the right one, when gluons are terminated with light quark states.
 
arivero said:
... the bold step of promoting the bosonic sector also to the status of elementary, moving all the game to Planck scale. My claim is that this was the wrong turn, and that the initial view of fermions plus gluons was the right one, when gluons are terminated with light quark states.

Still, it is amusing that if I forget about the neutral sector, then there is also a solution with a total of 248 generations. This joins to other "2-sigma signals" of a link between the solution with five flavours and the solutions that appear in critical superstring theory. Marcus and Sagnotti found an interpretation of SO(32) as an open string with five different terminations. Usually this is guessed to be related to the tadpole count, related to the space time dimension. And if we had some reason to look only for the particular "Mersenne" solutions (with the number of up quarks being a Mersenne prime instead of a generic 2 q -1), we could invoke hep-th/9904212 to claim that our solution is the result of going from D=10 to D=4
 
arivero said:
Some years later, with the standard model already established, it could seem strange to have elementary entities on one side and composites in the other, so Schwarz took the bold step of promoting the bosonic sector also to the status of elementary, moving all the game to Planck scale. My claim is that this was the wrong turn, and that the initial view of fermions plus gluons was the right one, when gluons are terminated with light quark states.
I can find at least one example of supersymmetry between elementary excitations and composite excitations [edit: http://arxiv.org/abs/hep-th/0207232" but maybe I got it wrong, will need to read later], so that approach to "hadron supersymmetry" really might work. But in Schwarz 1971, the mesons aren't superpartners of the fermions, the mesons are "DHS-dual" to the fermions.
 
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mitchell porter said:
But in Schwarz 1971, the mesons aren't superpartners of the fermions, the mesons are "DHS-dual" to the fermions.

More precisely, you mean that in a dual theory with fermions and bosons it is possible to build diagrams (the most typical, fermion-boson scattering) where the s channel particle is a fermion and the t channel particle is a boson, or reciprocally. I do not deny this. Both of them are elementary states of the string, are not they?

What I was pointing out, by referring to these old papers, was that in a first impression people has not problem to consider the Ramond fermion as a quark and the bosonic states as mesons or gluons. Then people puzzled about it and preferred to consider that speaking of fermions as quarks was just "customary speak" (example, in Scherk 1975 review) and then finally the whole theory was promoted to the status of GUT-Planck scale entities, so that nobody had to worry about the material interpretation of a open bosonic string as a terminated string. And yes, 20 years later we see D-branes coming as a revenge :-D but we are too far away from the original situation.

But a thing that we have learned along the way (one learns things, even during a long wrong turn) is that we need to produce the same number of bosonic and fermionic states. And that it must be so for each charge, because strings have susy, and susy commutes with the charge generators.

And amazingly, if one checks the original situation, the standard model with the gluonic string, one finds that it agrees with this requirement: their strings can be terminated, charge by charge, in a way that the number of boson and fermion states matches.
 
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  • #10
So the "wrong turn" was to consider the bosons in the dual model as fundamental rather than as composite, because what we need is a model exhibiting supersymmetry between fundamental fermions and composite bosons?
 
  • #11
arivero said:
But a thing that we have learned along the way (one learns things, even during a long wrong turn) is that we need to produce the same number of bosonic and fermionic states. And that it must be so for each charge, because strings have susy, and susy commutes with the charge generators.

For a SUSY theory, not just the spectrum must be supersymmetric, but also the interactions between the particles. Otherwise the supercharges are not conserved. How would that come about here?
 
  • #12
suprised said:
For a SUSY theory, not just the spectrum must be supersymmetric, but also the interactions between the particles. Otherwise the supercharges are not conserved. How would that come about here?

So far, I have not found a way to produce the gauginos with the same mechanism, the termination of open strings produces exactly all the needed scalars, but only them.

My personal expectation is that the LHC could find the gauginos but not the scalars, because the scalars are already there as QCD strings. It could be different if we were able to build the gauge sector as a kind of closed strings.

There are two puzzling lateral issues, related to the W and Z. On one side, a sort of "duality": that the sum of all the decays of Z seems to have the same rate that the decay of a pion having the same mass. On other, that the scalars that give mass to the Z and W are, in susy, partners of a chiral fermion, and that then we need six extra scalars (for Z, W, and Z0) for any mass mechanism, and three of them are eaten into the 0 helicities of Z and W. My guess is that these scalars are the ones we produce from uu terminations, which have no role in the reproduction of squarks and sleptons.
 
  • #13
This is all quite interesting, but also rather hard to grasp at first glance. So for my own reference, and perhaps the edification of confused onlookers, let me present a two-paragraph idiot's guide to what's going on here.

1. There is an obscure research program or line of thought called hadronic supersymmetry. It proposes that quarks and http://en.wikipedia.org/wiki/Diquark" . The second paper, in particular, starts with a nice review of history and motivations, and also contains the most mathematically sophisticated approach that I've seen. I'm not saying it's correct, just that it gives a theorist more to work with.

2. Alejandro Rivero, in his papers listed in #1, proposes to extend hadronic supersymmetry to the leptons.

If anyone wants to understand what this discussion is about, I suggest that those are the two ideas to cling to. Alejandro is trying to motivate or implement his idea by digging up these "dual models" from the dawn of string theory, but it's very unclear to me whether his "path not taken" actually exists. Would different dual models or different string theories have been discovered, ones that we don't know about today? Or would the formal theory have developed in the same way, but with different ideas about phenomenology? For my part, I intend to read Catto 2003 next, understand his model of hadronic supersymmetry, and then see what Alejandro's proposed extension looks like when Catto's approach is used as a base.
 
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  • #14
Indeed Lichtenberg and Catto are relevant references, but I was disappointed that they were only using it as a way to calculate baryon masses. As they are not interested on the fundamental level, they fail to appreciate the miracle that happens when three generations and five light quarks are considered. On the contrary I think that this miracle, and its uniqueness, is important and tell us something about our expectations to find the partners of the standard model particles.

(still, I am going to re-read them... Thanks for the reminder!)

mitchell porter said:
So the "wrong turn" was to consider the bosons in the dual model as fundamental rather than as composite, because what we need is a model exhibiting supersymmetry between fundamental fermions and composite bosons?

At least, the scalars. I can not tell anything yet about the other bosons, nor the gauginos. As for the "because", I would not say that "we need". It is just that susy happened as a prediction of the evolved R-NS dual model, and that string theory (and dual models) does not need to take strong positions on the issue of compositeness vs fundamental. Of course, the "right turn" had been to postulate that the endings of a bosonic open string were forcefully light fermions of the same theory, and then in 1975 they had predicted three generations and a non-light top quark.
 
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  • #15
mitchell porter said:
but it's very unclear to me whether his "path not taken" actually exists. Would different dual models or different string theories have been discovered, ones that we don't know about today? Or would the formal theory have developed in the same way, but with different ideas about phenomenology?

Currently I am fantasising that at the end of the path we had investigated the case with 16 up quarks and 31 down quarks, producing 16*31 = 496 ud combinations and (31*32)/2 = 496 dd combinations and so 248 generations (each generation, of course, needs two scalars to pair each fermion of a given charge), and then the scalars from the extant (16*17)/2= 136 uu combinations had been used to give mass to some objects, breaking some underlying symmetry group from 248 elements to something with 248 - 136 = 112 elements. Or something so :biggrin:

the joke was about the decomposition of E8 as a sum of representations of SU(2)xE7, this is (3,1)+(1,133)+(2,56): the whole representation is a 248, while the last subrrep is a 112. If you were guessing other family of objects, please tell me!
 
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  • #16
Sorry to say that, but I think this simply does not sound right. It's a gut feeling ...
 
  • #17
tom.stoer said:
Sorry to say that, but I think this simply does not sound right. It's a gut feeling ...

If you refer to #15, it is only a (half-)joke. Mitchell wondered if the formal theory had developed in the same way, and I answered by pointing out that it was possible to arrive to write SO(32) or E8-like scheme even when starting from this empirical approach.

Or do you refer to the whole idea? I am very surprised that you all are not impressed. OK, I could understand that people only worried by gravity can fail to be impresed by any particle-related juggling. But if someone is into particles, to notice that the exact number of scalars of the SSM can be produced from this simple combination game -and with the right charges for almost all: charge only fails for the six scalar partners of the non-Dirac fermions who marry the W an Z-, well, it should deserve at least some weeks of attention. My opinion, of course.
 
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  • #18
Summary and prognosis:

Hadrons for the first n flavors have an approximate SU(2n) symmetry called "spin-flavor symmetry". http://prd.aps.org/abstract/PRD/v12/i1/p147_1" you may see De Rújula, Georgi, and Glashow employing first SU(6) spin-flavor symmetry (u,d,s) and later SU(8) (u,d,s,c) to explain hadronic properties.

As mentioned in http://arxiv.org/abs/hep-th/0302101" proposed that they might be placed into a single symmetry multiplet, but to do this he had to anticipate supersymmetry, since mesons are bosons and baryons are fermions. He extended SU(6) to SU(6|21); this was the real beginning of "hadronic supersymmetry".

The most commonly believed explanation of this, within QCD, appears to be that a meson is a gluonic string connecting a quark and an antiquark; and that inside a baryon, you end up with two quarks on top of each other at one end of a gluonic string, and with the third remaining quark at the other end; and that this structural similarity accounts for the shared Regge slope. This is the picture that Lichtenberg and Catto employ; and Nobel laureate Frank Wilczek is http://arxiv.org/abs/hep-ph/0409168" .

However, there is an alternative way to get http://arxiv.org/abs/0901.4508" , and it rests on a different, equally simple picture. Instead of a baryon being a string connecting a quark and a diquark, it's a string with a quark at either end and a third quark smeared along the string. In other words, the string itself is a fermionic string.

I think this, and the holographic approach to QCD, and Type II string models where all the standard model particles are open strings stretched between branes, together provide a context where the viability of Alejandro's idea can be explored. http://arxiv.org/abs/0910.5955" , so it may not even be necessary to regard the two approaches to hadronic supersymmetry as mutually exclusive. The extension to leptons is a lot more problematic, but I think we have here a set of tools flexible enough to explore many variations on the idea, but rigorous enough to ensure that questions do have unequivocal answers.
 
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  • #19
arivero said:
Or do you refer to the whole idea? I am very surprised that you all are not impressed. ... But if someone is into particles, to notice that the exact number of scalars of the SSM can be produced from this simple combination game -and with the right charges for almost all
The problem is that up now it's only algebra w/o any fundamental dynamics. It looks like a bottom-up approach, but I can't see if this will produce something like a dynamical theory - or perhaps it may - but this will then be some sort of string theory again.

Regarding gravity: w/o gravity there is no need for string theory as far as I can see; string theory requires SUSY + additional dimensions - which we do not see in nature. String theory seems to be kind of framework to "produce theories as something sitting on top of vacuum states". OK, this is nice but afaik there's no additional benefit. w/o gravity it seems that string theory is nothing else but a very complicated "dual reformulation" of a huge class of (SUSY) gauge theories.

That's the reason why I am not very much impressed.
 
  • #20
Also, leaving the top out is like letting the fat kid not play ball, which conjures up unpleasant childhood memories for me. :-p

(More seriously, though, this is interesting speculation that I unfortunately probably won't have the time to fully familiarize myself with. There seems to be just enough fuzziness such that things might end up being merely a coincidence after all, if a suggestive one. Also, I'm unclear about the mass scales -- do the proposed superpartners have the same masses?)
 
  • #21
mitchell porter said:
, so it may not even be necessary to regard the two approaches to hadronic supersymmetry as mutually exclusive.

And in fact one can go directly with susy without arguing about string theory, but still my feeling is that the algebra will have its origins from strings, at the end.

mitchell porter said:
The extension to leptons is a lot more problematic,

One could say that the coincidence for charged leptons is trivial, as it follows from the coincidence for quarks: given p,r quarks, the number of charged mesons of a kind is also p*r.

My hopes for leptons are based in some hints: One, that for neutral mesons it works only for the p=2 r=3 solution, ie the total of neutrals in SU(p+r) is (p+r)^2 - 2p*r -1, and it is a very happy think that oscillations have doubled the number of neutrinos from Weyl to Dirac. Two, that we have the muon at the same scale that QCD and particularly very near of the pion. And three, that the theory of Koide predicts the charged leptons from a quantity amazingly close to QCD "current quark mass". Of course there is some tension between this and the second point.
 
  • #22
S.Daedalus said:
Also, leaving the top out is like letting the fat kid not play ball, which conjures up unpleasant childhood memories for me. :-p

It is more as, the fat kid will be the goal keeper. And indeed unpleasant.

Hey, I think you have explained why topcolor and ETC (extended technicolor) theories are dismissed in favour of Higgs mechanism... the Higgs mechanism does not have any particular role for the top. But then it fail to explain why y_t=1

S.Daedalus said:
Also, I'm unclear about the mass scales -- do the proposed superpartners have the same masses?)

What happens is that it is broken, but only mildly broken. And then all of the phenomenological work we have is not useful to us, because it is done on the assumption that the break is huge enough to hide the scalars up in the TeV scale.
 
  • #23
tom.stoer said:
The problem is that up now it's only algebra w/o any fundamental dynamics. It looks like a bottom-up approach, but I can't see if this will produce something like a dynamical theory - or perhaps it may - but this will then be some sort of string theory again

No problem about it been a string theory, we were not telling that the wrong turn was to do strings, the wrong turn was to do "elementary Planck scale strings". And yes it is only algebra and we could do it without referring to strings nor dual models. But it does not seem to me an fuzzy or ad-hoc algebra. Let me review all the steps and what do we get in each.

  1. We postulate that some number r and p of two kinds of particles, call them A and B, must form equal number of combinations of kind AA and kind AB.

    There is no loss of generality. The number of combinations AA is r (r+1) / 2 and the number of AB is r p, so equality implies that
    r= 2 p -1
    ​
  2. For the abelian U(1) charge, there are two posibilities: either A=0 and then AB has equal charge than B; or A not zero and then AA must be -B and AB=-A. In the first case the charged leptons have charge B, in the second case they have charge 3A. Note that the first solution is not really valid because AB should be an antiparticle, but I mention it because it is very similar to the exotic quark assignment found by anomaly arguments. With the second solution, we conclude that the A quarks are down quarks, and the B quarks are up quarks. We conclude that there are p quarks of type "up" and r= 2 p -1 quarks of type "down".
  3. Note that for the total of combinations to be an even number -to do pairs of scalars- then p itself must be even (because r is always odd). So the minimal solution is p=2 r=3 and they produce six equal scalars and thus three generations of them.
  4. The number of charged "sleptons" of a given charge is p r too, so always equal to the number of "down" type "squarks". No surprises here
  5. The number of neutral "scalarleptons" is, from SU(p+r) and substracting the charged ones, (p+r)^2-1-2pr. Asking it to be not two but four times the number of generations, we have
    (p+r)^2-1-2pr = 2pr​
    so that (p-r)^2 = 1 and the only solution compatible with the quark sector is the minimal solution.

What about the combination BB? Where, there are p (p+1) /2 of them. For the above solution, it means three of each BB type. On other hand, the gauge part of the Supersymmetric Standard Model has six scalars in the W and Z supermultiplets. My guess is that the combination BB can not partner to three generations of Dirac particles and because of this it is somehow blind to vector-like charges, ie blind both to colour and electromagnetism, while it can see the chiral charges (hypercharge and perhaps SU(2)). Not seeing color, there is only three BB (uu, uc, and cc) and three antiBB, and then they would match with the above six scalars. This impression of mine comes with some extra support from the p=16 example I spoiled in #15 before, where the "BB" combination also had a role related to symmetry breaking (between SO(32) and SO(16) or between E8 and E7).
 
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  • #24
Let's look at this from another angle. Is the essential idea that all the sfermions (squarks and sleptons) are actually diquarks and mesons? Please correct me if that overlooks something - I have really struggled to get the idea straight in my head - but I think that is the qualitative essence of the proposal.
 
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  • #25
mitchell porter said:
Let's look at this from another angle. Is the essential idea that all the sfermions (squarks and sleptons) are actually diquarks and mesons? Please correct me if that overlooks something - I have really struggled to get the idea straight in my head - but I think that is the qualitative essence of the proposal.

The strong version of the idea is as you describe. There is also a weak version, that the Supersymmetric Standard Model has a hidden global SU(5) symmetry, but this weak version is irrelevant here.

And there is a stronger version: that all the scalars of the Supersymmetric Standard Model are actually diquarks and mesons. This version needs more handwaving, because it involves some play with chirality, Dirac vs Weyl, etc. But in this version, also the scalars that give mass to the W and Z should be a peculiar kind of diquarks, build from the uu uc cc combinations.
 
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  • #26
So far I have three ideas for how to realize this:

1. Look for a http://arxiv.org/abs/hep-ph/9712389" in which this is a residual trace of supersymmetry among composite particles.

2. Look for a version of the supersymmetric standard model in which there is an http://arxiv.org/abs/hep-th/0207232" . It has to be an extra supersymmetry because in the SSM, by definition, the superpartners of the fundamental fermions are fundamental sfermions, not QCD composites, so if certain QCD composites are also superpartners of the fundamental fermions, it has to be a different supersymmetry.

3. Look for a "less than minimal" supersymmetric standard model, in which the only supersymmetry is the postulated relation between fundamental fermions and QCD composites. This is the fuzziest idea. It could involve looking for a hidden supersymmetry in the standard model itself, or for a hidden trace of supersymmetry in a supersymmetric theory broken to the standard model.
 
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  • #27
I have identified a class of models which seem ripe for the inclusion of "lepto-hadronic supersymmetry" (LHS): single-sector gauge-mediated supersymmetry breaking models, especially when approached holographically. There's too much to sum up now, but see http://www.claymath.org/workshops/lhc/kachru.pdf" (especially part 7).

These papers are all written under the usual assumption that the superpartners of the known particles exist at high energies, and the model-building choices reflect the interaction of that assumption with various other conventional assumptions about how the world works. So implementing LHS in this framework will necessarily subvert some of the model-building choices which are standard in this literature. But it really looks like it could be done!
 
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  • #28
mitchell porter said:
http://www.claymath.org/workshops/lhc/kachru.pdf"

Hey, really I am enyoing these talks. With things as gauge bosons involved in susy breaking, and compositeness for al the quarks except the top, it sounds very much as if they were following research lines near to the conjecture here, even to the "strongest version".

Also, it seems it is a hard job. Damn, give me another five years.
 
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  • #29
Let's look at this from a simple angle again. One version of what we're looking for would be a theory where hadrons are quarks bound by gluons, and where leptons are gluinos bound by squarks. Two immediate problems: there ought to be quark-gluino bound states too, and there ought to be leptonic resonances. How hard are those problems to fix, and are there other obvious problems?
 
  • #30
mitchell porter said:
Let's look at this from a simple angle again. One version of what we're looking for would be a theory where hadrons are quarks bound by gluons, and where leptons are gluinos bound by squarks. Two immediate problems: there ought to be quark-gluino bound states too, and there ought to be leptonic resonances. How hard are those problems to fix, and are there other obvious problems?

I am not sure if it is the same theory, because I am not sure about how to describe leptons and quarks. I am intrigued that the QCD strings is inherently a bosonic string; can we build an extended string out of a fermionic field? I'd say no. Can we find a superpartner to the QCD string?
 
  • #31
Sorry to say that, but I still don't understand why the SUSY explanation shall provide any benefit. It adds new and un-observed particles (and perhaps resonances / bound states). It adds new questions and nearly no answers. It seems to be a solution hunting for a problem b/c there is no problem in QCD, we perfectly understand its structure.
 
  • #32
tom.stoer said:
Sorry to say that, but I still don't understand why the SUSY explanation shall provide any benefit.
As far as I'm concerned, the question is: Is there a supersymmetric theory which gives us the standard model, and in which the numerical coincidences which Alejandro has noted, actually arise from supersymmetry? Alternatively, can we prove that no such theory exists? If it can't be done, it would be good to understand why.
arivero said:
Can we find a superpartner to the QCD string?
This is a basic question about how supersymmetry works in theories like super-QCD, to which I do not know the answer. Supersymmetric theories are diverse and very complex. For example, my earlier remark about "gluinos bound by squarks" was rather naive; it looks like the most important interactions of gluinos are with gluons. In discussions of MSSM, you will find people saying that the superparticles will in any case decay to ordinary particles, so composites would not be stable, but that is under the usual assumption that they must be too heavy to have been seen already. So among other things, one should probably look at the behavior of massless super-QCD first - a theory which already comes in many forms: "pure SQCD" with no quarks; SQCD with adjoint quarks, SQCD with quarks in the fundamental representation; SQCD with various numbers of flavors and colors. The 1990s results of Seiberg on electric-magnetic duality look to be of basic importance in understanding these theories.

In all these theories, massless and massive, the elementary fields can be arranged into superfields. But what about composite objects like mesons and baryons - are they generically part of supermultiplets as well? This is what I don't understand. By the way, http://en.wikipedia.org/wiki/Seiberg_duality" involves the appearance of an extra meson superfield on one side.

Back in comment #18, I mentioned a minor research program from string theory - "orientifold planar equivalence" - in which meson strings have baryon strings as superpartners. In the baryon string, the third quark is smeared along the length of the string. See these http://physik.uni-graz.at/itp/iutp/iutp_09/welcome.php?sf=13", but not on the arxiv). In the third lecture, pages 12-13, Armoni actually mentions quark-diquark supersymmetry (Lichtenberg's hadronic supersymmetry), and says this is an alternative explanation (he explicitly says that a certain fermion in N=1 SYM becomes superpartner of the meson). Though I wonder if this picture, with the third quark smeared along the string, might arise from a symmetrized version of the quark-diquark string.

Anyway, obviously we need to look at this and see if it can be extended to include your extension of hadronic supersymmetry to leptons. The framework is unfamiliar to me ("type 0' string theory") so I don't know what pitfalls lie ahead.
 
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  • #33
tom.stoer said:
Sorry to say that, but I still don't understand why the SUSY explanation shall provide any benefit. It adds new and un-observed particles (and perhaps resonances / bound states). It adds new questions and nearly no answers. It seems to be a solution hunting for a problem b/c there is no problem in QCD, we perfectly understand its structure.

The whole "program" is to have less un-observed particles that in standard susy (as in the MSSM). On one side, you know that the the minimal SSM is smaller that the MSSM by two scalars, at the cost of not having a higgs mechanism. On other side, you can arrange all the scalars of this SSM using a SU(5) based flavour symmetry with seems very much as QCD with five flavours. The goal is not to understand QCD, the goal is to understand this flavour and see if it allows a formulation in terms of gluon-like composites, so that the total of particles in the "sBootstrapped SM" is still less than in the SSM.

Even if we understand QCD, we don't understand yet ETC, ie the multiple reincarnations of topcolor and extendedtechnicolor that could be still around the corner in CERN (and Fermilab!). So there is a benefit even if you don't buy the whole program.
 
  • #34
OK, I'll try to get that
 
  • #35
A problem I still don't get about relating gluons to strings is that the QCD string is not a single gluon state... the QCD string appears at long distances and intuitively it seems as a "classic field". But a classic field is a collective of elementary excitations; it is because of it that force fields are always bosons, is it not? It is not easy to build a collective field out of fermions (note that a fermionic field, at least in 3d, is proportional to hbar: it dissapears in the classical limit).

mitchell porter said:
So among other things, one should probably look at the behavior of massless super-QCD first - a theory which already comes in many forms: "pure SQCD" with no quarks; SQCD with adjoint quarks, SQCD with quarks in the fundamental representation; SQCD with various numbers of flavors and colors. The 1990s results of Seiberg on electric-magnetic duality look to be of basic importance in understanding these theories.

(...) By the way, http://en.wikipedia.org/wiki/Seiberg_duality" involves the appearance of an extra meson superfield on one side.

Back in comment #18, I mentioned a minor research program from string theory - "orientifold planar equivalence" - in which meson strings have baryon strings as superpartners. In the baryon string, the third quark is smeared along the length of the string. See these http://physik.uni-graz.at/itp/iutp/iutp_09/welcome.php?sf=13", but not on the arxiv). In the third lecture, pages 12-13, Armoni actually mentions quark-diquark supersymmetry (Lichtenberg's hadronic supersymmetry), and says this is an alternative explanation (he explicitly says that a certain fermion in N=1 SYM becomes superpartner of the meson). Though I wonder if this picture, with the third quark smeared along the string, might arise from a symmetrized version of the quark-diquark string.

I am downloading them for the weekend!
 
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  • #36
I want to tackle https://www.physicsforums.com/showthread.php?t=180275" exists, I think this is the least likely avenue (mentioned so far) towards a realization of very-low-energy supersymmetry. But it might be instructive to walk a short distance down this road, and see what there is to discover.

So, to begin, here's http://physics.stackexchange.com/questions/3342/space-time-filling-d-branes-in-type-i-superstring-theory" ). I say "almost" because I'm used to a stack of n D-branes giving rise to a SU(n) theory, not a SO(n) theory; I suppose the O-plane has something to do with the latter.

So what's going on in Marcus and Sagnotti's paper? I have put together an explanation, a crucial part of which came from section 3.3 of http://gradworks.umi.com/32/71/3271005.html" ). The fundamental issue is how to obtain the "Chan-Paton factors" which contribute to the amplitude when you have strings ending on branes. When M&S wrote their paper, it wasn't even understood that there are branes in the Type I theory, so they came by their construction another way. But in Rinke I read that, normally, the Chan-Paton factor is obtained from a Wilson line in the worldsheet theory of the brane(s) to which the string is attached, a Wilson line which follows the path of the string endpoint. The method of M&S is an alternative, in which you have fields living on the endpoints and the Chan-Paton factor comes from including them in the path integral. They are called boundary fermions and they have had a revival in recent years, including an application in Berkovits's pure spinor formalism.

Along with the space-filling D9-branes, the only stable branes in Type I string theory are D1-branes and D5-branes. I had thought that maybe I could find a braney explanation of why M&S needed five pairs of boundary fermions (quark, antiquark being one pair) in the D5-branes: open strings in Type I can end on the D1s and D5s as well as on the D9s, so there's a calculus of Chan-Paton bookkeeping which extends to those lower branes as well. But I haven't done the work to understand it yet. You can read about some of it in section 14.3 of Polchinski volume 2.
 
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  • #37
Alejandro, what's your philosophy regarding the Higgs?
 
  • #38
mitchell porter said:
Alejandro, what's your philosophy regarding the Higgs?

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

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

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

As for the "disguise" of the higgses in my own construct, we can discuss it, if you want. But note that the above applies to any SUSY model, not just mine.
 
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  • #39
arivero said:
(I guess you could also try to go up to spin 3/2, in any case the counting is the same)

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

me again said:
As for the "disguise" of the higgses in my own construct, we can discuss it, if you want.

Really, the only idea is that you could have noticed that after the full (and exact) pairing for \pm 1,0, \pm 2/3 and \pm 1/3, there are still six combinations left, uu, uc, cc and their antiparticle versions. I can not use them to make Dirac fermions, and then I suspect that these combinations are chiral in a way that they can only couple in an axial way: they can not see QCD, and they can only see EM in the way it comes from SU(2) and hypercharge.
 
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  • #40
With respect to my comments #29 and #32, http://arxiv.org/abs/hep-th/9708113" looks exciting (I haven't read it yet, and I'm posting about it, that's how exciting): It's about how to obtain QCD as a limit of super-QCD, and it actually talks about the meson states of QCD. This is what's missing in all the literature on supersymmetric preon models. Over 100 papers talk about "composite superfield" or "composite supermultiplet", but they never bring standard model mesons into these supermultiplets, they only talk about quarks and leptons.

Here's what they (Sannino and Schechter) say:
At the fundamental gauge theory level the supersymmetric theories contain gluinos and squarks in addition to the ordinary gluons and quarks. At the effective supersymmetric Lagrangian level, all of the physical fields are composites involving at least one gluino and one squark. This means that none of them should appear in an effective Lagrangian for ordinary QCD. Where the mesons and glueballs, which are the appropriate fields for an effective QCD Lagrangian, actually do appear are in the auxiliary fields of the supermultiplets, which get eliminated from the theory...

The simplest approach to relate the supersymmetric (SUSY) effective theories to the ordinary ones is to add suitable supersymmetry breaking terms... The standard procedure assumes the breaking terms to be ‘‘soft’’ in order to keep the theory close to the supersymmetric one. Indications were that the soft symmetry breaking was beginning to push the models in the direction of the ordinary gauge field cases. However the resulting effective Lagrangians were not written in terms of QCD fields.

In this paper we will provide a toy model for expressing the ‘‘completely broken’’ Lagrangian in terms of the desired ordinary QCD fields. Since we will no longer be working close to the supersymmetric theory we will not have the protection of supersymmetry for deriving ‘‘exact results.’’ In practice this means a greater arbitrariness in the choice of the supersymmetry breaking terms. The advantage of our approach is that we end up with an actual QCD effective Lagrangian.
"Mesonic superfields" show up in Part III. This seems really promising, because it's an analysis at the level of a Lagrangian, and not just talking about quantum numbers.
 
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  • #41
Equations 3.2-3.4 in that paper are something to stare at, especially if you're a supersymmetry novice. But let's try to interpret them with http://www.phys.columbia.edu/~kabat/susy/3plus1susy.pdf" ). One normally considers only "phi" to be the scalar superpartner of the fermionic "psi", with "F" left out in the cold, but here the physical meson fields are being found inside an "F". Also, the plan in the paper is to completely decouple the superpartners of the known particles, leaving just QCD, so they want everything except the third term of equation 3.4 to drop out. But our objective is to identify some of the leptons with superpartners of those mesons, so presumably we want to keep some or all of "psiT". What if we get "FQ" to drop out? "psiT" is "quark times antisquark plus antiquark times squark", and we also still have scalar squark-antisquark composites in the picture, alongside the mesons. It seems a little messy. But if we boldly ignore all the details, the message seems to be that a lepton, in this scheme of things, will be "quark times squark".

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

Meanwhile, let me also note the existence of some papers by Kyianov-Charsky (also spelt Kiyanov-Charsky and Kiyanov-Charskii), in which QCD mesons and baryons are similarly derived from super-QCD, with the explicit intention of realizing hadronic supersymmetry: http://arxiv.org/abs/hep-ph/9501412" .
 
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  • #42
A differente venue: http://arxiv.org/abs/0909.5430 "SUSY Splits, But Then Returns", by Sundrum, refers to some previous works (ref 12, 13) on emergent supersymmetry. It would be very surprising if some of these models, which are proposed at the level of toy models, at the end happen to be so accuratelly reflected in Nature.
 
  • #43
Two more ideas on how to construct a theory realizing "hadronic supersymmetry extended to leptons":

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

2) Look for a realization of hadronic supersymmetry in a string phenomenological model, and then see if it can be extended to the leptons. The papers on "orientifold planar equivalence" that I cited earlier (comments #18, #32)) don't quite work here, because as I understand it they are just illustrative toy models, not real-world models. What I'm thinking here is that string phenomenology (so far as I can see) mostly contents itself with obtaining states which can correspond to free quarks and gluons at high energies. Mesons and baryons are a low-energy phenomenon and are left for field theorists to derive from QCD. But what do the existing accounts of hadronic supersymmetry look like if we restate them within the framework of a beyond-SM theory? We might get some clues for the extension to the leptons. (I suppose one could do this, not just for string models, but also for MSSM and SUSY-GUT.)
 
  • #44
Update on the bottom-up and top-down strategies:

1) There are a number of papers on expressing the Nambu-Jona-Lasinio model (http://en.wikipedia.org/wiki/Nambu%E2%80%93Jona-Lasinio_model" try to apply NJL to SQCD.

2) "E6 diquarks" are one of the exotic particles that have failed to turn up at the LHC - but I think these are vector diquarks. Nonetheless, if you visit the 1989 http://www.sciencedirect.com/science/article/pii/0370157389900719" (still frequently cited), and view the discussion on pages 199-200, about leptoquark, diquark, and quark couplings in the superpotential... there might be some guidance there, for how, say, a super-NJL model might embed into a theory with leptons.

(Also see http://arxiv.org/abs/hep-th/0604017" ?)
 
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  • #45
I got an email from Bernard Riley telling that also him, back in http://vixra.org/pdf/1004.0101v1.pdf, got worried about the point of having spin 1/2 and spin 0 particles with very near masses, say muon and pion etc.

Again, it is beyond all belief that two different mechanism of mass generation (SU(3) colour versus Yukawian Higgs) without any relationship between them, and coming down from mass Planck scale, at the end produce a value with a difference not beyond a 10%. The problem is that there is no dynamics unifying both mechanism... So the reports of Mitchell are interesting, they indicate that is could be possible to build some mechanism, after all.
 
  • #46
arivero said:
I got an email from Bernard Riley telling that also him, back in http://vixra.org/pdf/1004.0101v1.pdf, got worried about the point of having spin 1/2 and spin 0 particles with very near masses, say muon and pion etc.

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

Hi Arivero,

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

https://www.physicsforums.com/showthread.php?t=46055
 
  • #47
The paper where I first came across "diquark coupling" vs "leptoquark coupling" as a model-building choice was http://prd.aps.org/abstract/PRD/v41/i5/p1630_1" (1990). "We envisage a cascade mechanism, whereby quarks and leptons gain mass at various orders of perturbation theory from masses induced at the preceding order of approximation. In this way we hope to explain at least some of the qualitative features of the observed mass spectrum."

It has very few citations, especially in the past decade, but there is a recent one, http://arxiv.org/abs/0906.4657" ). "Radiative models of flavor have a long history...", and to prove their point, they list 17 papers (refs 19-35), starting with Weinberg in 1972.

At this stage, I have no idea whether such models provide guidance in the search for a theory realizing Rivero supersymmetry ;-) or whether the details of the masses is just a distracting complication. My basic notion of how to make it work is still SQCD with preons, so that e.g. the lepton-meson multiplet involves composite particles on both sides. But maybe it requires something more subtle, like Seiberg duality or holographic cascades.
 
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  • #48
OK, I'm sold, it would be extremely stupid to be thinking about how to realize supersymmetry in this way, and to ignore the similarity of the pion mass and the muon mass. Instead, it's absolutely the best clue about how to do it, for the very reason you (Alejandro) state: the method of mass generation is supposed to be completely different.

Electron, muon, and tauon masses satisfy Koide's formula to high precision. Pion, kaon, and eta-meson masses satisfy a Gell-Mann–Okubo mass formula, but only approximately. I don't understand the https://www.physicsforums.com/showthread.php?p=1451883#post1451883" tries to do so.

Also, today's http://arxiv.org/abs/1106.3074" looks important. There is a good chance that we should be trying to take advantage of such relationships (e.g. as in the paper by Sundrum). But in all cases, the authors think of the superpartners as something additional to all the known particles. We need to somehow retrace their steps, but with the role played by supersymmetry entirely folded into the known, Standard Model particles.

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

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

http://arxiv.org/abs/hep-ph/0501200" :

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

So here we have a symmetry connecting diquarks to mesons. Earlier, we had an interpretation of QCD mesons in terms of a supersymmetric duality. We also have a realization of this supersymmetric duality for the MSSM, in a way which extends to the W and Z. It remains only to decisively fold the leptons themselves into this circle of relationships.
 
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  • #49
Now getting very close to a coherent field-theoretic thesis: We should be trying to generate the masses through a superconformal anomaly. The idea is that the pion mass is generated by a conformal anomaly (or at least breaks conformal symmetry in the chiral effective theory); and in "anomaly mediated supersymmetry breaking", squarks and sleptons acquire their masses from a superconformal anomaly; but in the scenario here, squarks are diquarks and sleptons are mesons. Maybe the answer is just SQCD + AMSB!
 
  • #50
Mitchell, did you got your preprint online? If you wish, I can upload it somewhere, if only for google to find it...
 

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