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

[mitchell porter]

"Two-index SU(N) theories" by Francesco Sannino has some diquark-looking diagrams from a 't Hooft large-N expansion (pages 13-15). These theories also have a relationship to super-Yang-Mills, since the antisymmetric two-index quarks can model gluinos as well as diquarks.

The paper also mentions a kind of large-N expansion I hadn't heard before. Along with the usual large-N expansion and the two-index large-N expansion, there is now a chiral large-N expansion which seems to treat some Weyl fermions as quarks, and others as diquarks.

 

[arivero]

Finally took some time to upload to arxiv the collection of group theoretical comments about SO(32) SU(15) etc ... Not included the present discussion in thread 1063905

An interpretation of scalars in SO(32) https://arxiv.org/abs/2407.05397​

We propose an interpretation for the adjoint representation of the SO(32) group to classify the scalars of a generic Supersymmetric Standard Model having just three generations of particles, via a flavour group SU(5). We show that this same interpretation arises from a simple postulate of self-consistence of composites for these scalars. The model looks only for colour and electric charge, and it pays the cost of an additional chiral +4/3 quark per generation.

 

[arivero]

Hmm and now I notice that the argument in https://www.physicsforums.com/threads/asking-for-a-six-preon-theory.1063905/post-7102865 is a sort of counterexample to my "uniqueness theorem". It shows that if we give more freedom about the particle set, allowing for leptons, then the classic Georgi-Glashow model is able to generate all their superpartners, with one generation.

And now I wonder if all the unification groups have this property, of having a subset n such that their composites contain exactly the superpartners

 

[arivero]

I asked AdR for permision to use his old drawing; he had a colour scan somewhere in his archive

 

[arivero]

A referee did an interesting objection to the sBootstrap idea: there is no explanation of why the spectator quark is the top quark. It could similarly be the up or the charm. Honestly I do not see how to find out which one is, because we newer got a model of masses.

We speculated time ago to get the masses out of 84-dimensional representations, so with groups similar to SO(9), SU(9) or SU(12); or lacking that, some 21 or 42 dim representation. We could also try to change our 15s of SU(5) for some 10, but very peculiar. Instead of 6 (-1/3), 6 (+2/3) and 3 (+4/3),
it should have 6 (-1/3), 3 (+2/3) and 1 (+2/3).

Another approach could be to consider the sBootstrap a theory of preons and see if the ideas of Terazawa and Koide can be useful.

A third way, not considered, could be to find goldstone bosons, under the principle that they are massless. In this case I am not sure how group theory helps; I guess one must substract dimensions of the adjoint for the original and the broken group.

 

[arivero]

Thinking if it is possible to alter the masses of the scalars somehow breaking the flavour symmetries or mixing the 15 irrep with the 10, in the same way that the octect mixes with the singlet. I do not see how. But you could enjoy the drawing of this SU(3)xSU(2)

Note, if you are new to the thread, that the number of particles is equal to the number of scalars of the supersymmetric standard model, with three generations, except that we get those awful +4/3 things

It is funny to consider the transformation from particle to antiparticle at the preon level. Look at the Q=+1/3, it is a triangle (ud,us,ub) and another (cd,cs,cb). If you change c to c, the point is mapped to the Q=-1 triangle, if you change d to d, it is mapped to the Q=+1.

And now look Q=-2/3. The internal points are mapped to three external points of the octet Q=0. The vertexes (dd,ss,bb) are mapped to the combinations of singlet and octet "neutrals", the typical mix pi eta eta' in meson theory.

Can we get from here a specific characterisation of the "stop" pair of scalars? Not sure.

 

[arivero]

Updated v3 with a discussion of masses, https://arxiv.org/abs/2407.05397. Most koide related, but here the interesting thing is not the realistic but the "alpha=0" that provides pairs for everyone.

each particle in the (3,2) has one of the same mass when exchanging c<--->u
each particle in the (8,1) has an antiparticle in the (8,1) too.
The particles in the (6,1) come in pairs.

The selfenergies (or "masses") of the "preons" u,c,d,s,b are in this example 313,313,470,0,470. I think the model could be improved by including weak isospin.

 

[mitchell porter]

A natural counterpoint to these investigations can be found in the study of Seiberg dualities, which are really the modern version of preon theories. Recall that a Seiberg duality consists of a strongly coupled "electric" theory in the UV, and a "magnetic" theory in the IR containing weakly coupled states, which are actually bound states of the UV theory. The preons here are the fields in the UV.

Seiberg's original examples have N=1 supersymmetry in both the UV and the IR, but Sannino et al have written a number of papers in which the IR theory has supersymmetry, but the UV theory does not, though it may have a "gaugino" and/or "mesino" field. This may seem artificial, but I think this kind of non-susy theory can appear in string theory (see Armoni et al).

Sannino et al's latest, "Charting Standard Model Duality and its Signatures", came out this week. It shows the pros and the cons of such an approach. From our perspective, one downside is the multitude of extra fields. They are listed in table II. In the "magnetic" section, you can see that in addition to the SM fields (q, L, phi), there are "gaugino", "mesino", and "mes-Higgs" fields (lambda, M, phi_H).

Page 3 describes the series of effective theories interpolating between IR and UV:

Standard Model -> MSSM + extra superfields -> nonsusy dual + gaugino + mesino -> dual GUT

There are six flavors of dual quark in the UV, just as there are six flavors of quark in the IR standard model. One feature of this model, which could be an upside from our perspective, is that the UV chiral flavor symmetry SU(6)_L x SU(6)_R, gives rise to an IR flavor symmetry SU(3)_g x SU(2)_L x SU(2)_R, i.e. it includes a generation flavor symmetry *and* the chiral electroweak symmetry! (One of the missing pieces of the sbootstrap is how to obtain the latter.)

What about IR yukawas? Basically, in the second EFT above (the extended MSSM), there is a single yukawa, and a multitude of scalars in the "mes-Higgs" which have different VEVs, and the SM yukawas arise from the combination of these. The mes-Higgs is a UV meson composite of the UV gaugino and dual quarks (see equation 3), and the VEVs come from unknown operators in the far UV. After equation 10, they describe the couplings as "democratic", which should ring a bell for anyone who has studied the literature around Koide, but they don't actually explore that connection.

The reason I regard this as complementary to what @arivero is doing, is that it is an actual quantum field theory whose premises have some overlap with his. Sannino et al have an actual QFT but no hard numbers, just orders of magnitude. @arivero doesn't have a QFT, but a kind of susy preon idea, along with some simple mass formulas. The logical first step in bringing them even closer, would be to incorporate the "hadronic supersymmetry" and the "lepton-meson supersymmetry" of the standard model, into a Seiberg duality, rather than waiting for an entirely new supersymmetry to show up at the TeV scale.

 

[arivero]

The preprint about the sBoostrap from the point of view of SO(32) is now published as Eur. Phys. J. C 84, 1058 (2024). https://doi.org/10.1140/epjc/s10052-024-13368-3 if someone happens to need a reference some day.

It includes also some review of Koide, as I said before, but I will discuss it in the other thread.

My feeling is that it is equivalent to a classical Letter of Nuovo Cimento; the editorial process has been accelerated, they have labeled it as Letter and not Article, and surely the editor criteria has been the main weight for approval. In some sense it is correct because the EPJC was created as a fusion of multiple European journals including the particles section of Nuovo Cimento.

 

[mitchell porter]

Besides being a physical hypothesis, supersymmetry is also a formal tool that can be used in the study of non-supersymmetric theories. For example, there has been recent work by Murayama on using broken super-QCD to prove confinement and chiral symmetry breaking in various QCD-like theories. (I thought I posted about it here, but can't find it.) Basically, you describe the QCD-like theory as an SQCD in the limit where the superpartners become very heavy and drop out of the physics, but you make sure that the properties of interest, that can be proven for the SQCD, continue to hold in that limit.

Now there is another formal use of supersymmetry: "Field Space Geometry and Nonlinear Supersymmetry" by Yu-Tse Lee. The relevant concept here is that of "field redefinitions". I suppose an example of this from the standard model, can be seen in the shift between mass eigenstates and flavor eigenstates, in quarks and neutrinos. All the predictions (like scattering amplitudes) must be the same, however the fields are defined, and so field redefinitions reveal yet another aspect of physics in which there's a flexibility of description, independent of underlying physical realities.

There is a "field space geometry" for redefinitions of scalar fields and another for redefinitions of fermion fields, and the author is now combining these by embedding every scalar and fermion in a superfield. The price of this is to introduce fictitious superpartners, but these once again are formally treated as so massive that they can be neglected, Meanwhile, the author says,

"The supersymmetric extension of an effective field theory we constructed standardizes particles as superfields and packages Wilson coefficients as two potentials on the superfield space M"

From a sBootstrap perspective, what interests me is whether there is anything here that can fulfil the agenda in e.g. the last paragraph of #338. One motivation of the sBootstrap is these quasi-supersymmetries already implicit in the standard model and its effective theories; Lee's superfield space can take any theory made of scalars and fermions (equation 14) and extend it to an effective theory descended from something supersymmetric. What happens if we apply his method to the standard model and/or its effective theories, but we actually embed hadronic supersymmetry and lepton-meson supersymmetry?

Well, we can't really do it yet, since he hasn't incorporated gauge fields into his superspace method. But, gauge fields are being incorporated into the "field space geometry" approach (see references in Lee's section IV, on "the incorporation of gauge fields [into field space geometry] using vector multiplets". Presumably he sees, or hopes for, the extension of his own method via the inclusion of vector superfields.

 

[mitchell porter]

Mikhail Shifman, one of those great Russian physicists who moved to the west in the 1990s, has been an inspiration to me since the early days of this thread (see the final paper mentioned in #48). But today he's posted a paper

"QCD Chemistry: Remarks on Diquarks"

in which he says that heavy-light diquarks (containing one heavy and one light diquarks) "don't exist". That sounds bad for the sbootstrap! But what exactly does he mean? I think his proposition is, that at a certain energy scale, light diquarks become pointlike objects (page 7), whereas for example a "compact $bu$ diquark" never does (page 9). (And he says $cq$ diquarks lie on the borderline, page 10-11.)

In slightly more detail, his proposition is that light diquarks act pointlike at a scale which is about 9 times the QCD scale, with a mass similar to the mass of a single constituent quark, whereas the much greater current mass of the bottom quark dominates $bq$ dynamics, and drowns out whatever it is that happens with the ud diquark.

I think this is not a problem, if we suppose (as is repeatedly proposed in this thread) that diquarks are fundamentally open strings. It would just mean that the light diquark strings sometimes get into a zero-length regime, but the heavy diquark strings never do.

Just as a reality check, let me emphasize that there is no reference to supersymmetry in this paper (although Shifman has written plenty on that topic). This is purely an exercise in trying to develop heuristic nonperturbative models of quark behavior in the messy real world of heavy baryons.

What this suggests to me, is that there is an effective field theory for QCD, in which light diquarks can be treated as fields, while heavy diquarks could be modelled within a true string dual that exists at higher energies. From a sbootstrap perspective, perhaps the EFT can be approached via formal supersymmetric methods like those I mention in #340.

But what about hadronic supersymmetry for the heavy diquarks? As it turns out, there is a specific model for that, known as "superflavor" (e.g. Georgi & Wise 1990). This was originally devised for hadronic supersymmetries of the form baryon $Qqq$, meson $Q\bar{q}$, where $Q$ is a heavy quark and $q$ is always a light quark.

I did find superflavor being used in a Chinese paper (Jia et al 2014) about genuine supersymmetric phenomenology - instead of the meson $Q\bar{q}$, they have the supersymmetric baryon $\tilde{Q}\bar{q}$, where $\tilde{Q}$ is a heavy squark! It raises the question of how superflavor relates to the genuine, fundamental supersymmetry of their model; a question relevant to the sbootstrap if we do think that it is based on a fundamental supersymmetry and not just an emergent one. It wouldn't surprise me if there is some kind of duality here (as always, Seiberg duality comes to mind), with a light formal field-theoretic supersymmetry and a heavy emergent hadronic supersymmetry being two faces of some underlying super geometry.

 

[mitchell porter]

There is a preon model due to Bogdan Dobrescu

"A model of quark and lepton compositeness"

which has some similarity to the sBootstrap.

In the sBootstrap, we start with the five light quark flavors, we consider meson- and diquark-like pairings, and then superpartners of those, and (in theory) we get back all three generations, plus a handful of excess particles. And we often think of all this in terms of quarks on the opposite ends of a string.

In Dobrescu's preon model, he starts with fermionic preons that have standard model charges, and which also couple to a new strongly coupled preonic gauge group. Then, instead of binding them with string and looking at superpartners, he also adds another fermion in a "symmetric 2-tensor conjugate" representation of the preonic gauge groups.

The point of the analogy is that one model of a "fermionic string" is that it is a bound state of a quark, antiquark, and gluino. In Dobrescu, the 2-tensor fermion plays the role of the gluino. He ends up with "prebaryons" of the form

(preon with standard model charges + 2-tensor preon + preon with standard model charges)

with overall standard model charges that are just the sum of the standard model charges of the preons. And of course, that's how the combinatorics of the sBootstrap works!

First and perhaps most important, this gives us a new way to implement the combinatorics of the sBootstrap. Instead of a string with preon-quarks on the ends, we have a standard-model-singlet 2-tensor fermion which combines (thanks to the preonic gauge interaction) with two preon-quarks to form massless "prebaryons", among which are to be found the standard model fermions.

(Incidentally, this is not necessarily completely different from a string-based approach. See earlier comments about the work of Armoni, Shifman, and others.)

Second, it is of interest to grasp the specific combinatorics employed by Dobrescu. The sBootstrap starts with two up-type quarks and three down-type quarks (and all their antiparticles). Dobrescu starts with 15 fermion preons corresponding to the states of a standard model generation (without a right-handed neutrino), which he labels Q U D L E, and four more preons that are standard-model singlets. He then considers all possible pairings of these, as components of three-preon "prebaryons" where the third preon is the 2-tensor.

The results can be seen in his Table 2 (page 4), and are discussed starting at the bottom of page 3. An important part of his combinatorics, is that excess particles arise (beyond those needed for three generations), but they form vector pairs and are therefore presumed to acquire a superheavy Dirac mass.

This highlights another difference between Dobrescu's combinatorics and that of the sBootstrap, which is that he is working with chiral (Weyl) fermions and their hypercharge, whereas the sBootstrap is expressed in terms of Dirac fermions and their electric charge. From a fundamental point of view this is unsatisfactory, but we never quite found a clear model for a hypercharge sBootstrap. Well, Dobrescu shows us how it could be done, and one can consider e.g. a truncation of Dobrescu's QUDLE combinatorics, to see how much of the standard model he can get from his QUD preons alone (with or without the singlet preons too).

On the other hand, one can't just truncate Dobrescu's model, because of anomalies, and this leads us to some other features. His preonic gauge group is SU(15). That's actually what first caught my attention, since @arivero uses that group in his SO(32) paper. But @arivero is getting SU(3)_color x U(1)_em from his SU(15), along with the flavor symmetries SU(2)_up x SU(3) _down, whereas Dobrescu's SU(15) is completely separate from the standard model gauge groups.

Then there's the odd total of 19 preons in Dobrescu (not counting the 2-tensor fermion) - 15 corresponding to a single standard-model generation, and then 4 singlets. Regarding the 4 singlets, in a few places they serve the role of creating three prebaryons that correspond e.g. to three standard-model copies of a particular quark type, and then the fourth one forms a vector pair with an excess particles from elsewhere in the model. Also, the anomaly cancellations work out this way.

But we don't need to be too concerned with these details, except that Dobrescu has thereby given us a proof by example that this kind of model can work. The main question for me is, what happens if you try to embed sBootstrap combinatorics into a Dobrescu preon model?

 

[mitchell porter]

Craig Roberts has coauthored a large number of papers (most recently cited in this thread at #281 and #288) about the origins of hadronic mass. The latest such paper is

"Hadron Structure: Perspective and Insights" (Binosi, Roberts, Yao)

and it's quite dense with concepts and lore.

The authors distinguish between three contributions to mass generation: that due specifically to the Higgs boson (for hadrons, that basically means quark current mass); "emergent hadronic mass" which is a purely QCD effect (e.g. glueball mass would presumably be an example of this); and "HB+EHM", which is some kind of synergy between the two. The pion mass is an example of the latter - if the quarks were massless, the pion would be too (since they are Goldstone bosons of QCD's chiral symmetry). In reality they have a mass, but it is far more than the sum of their quark current masses.

On the other hand, consider the rho meson. It's just the spin-1 counterpart of the pion, but it has a mass which is 2/3rds of the way to the nucleon mass. I don't think Roberts et al explicitly say this, but the rho mass is basically equal to the pion mass plus two constituent quark masses. What they do say is that the rho, like the nucleon but unlike the pion, is a particle whose mass is dominated by the purely-QCD mechanism, whatever it is. (On page 2 they seem to say that two classic hadron mass formulas, Goldberger-Treiman and Gell-Mann-Oakes-Renner, explain a lot of this.)

Interestingly, they also mention the similarity between the muon and pion masses. But they don't say anything as wild as suggesting that supersymmetry is somehow involved (the closest thing to a model for that might be the Polchinski-Strassler paper mentioned here in #265).

On page 8, they may be giving a theory of the origin of the constituent quark mass. They mention a momentum-dependent running mass for light quarks which becomes approximately 350 MeV at zero momentum. Diquarks are mentioned in the context of the quark+diquark approximation of the baryon, but one should see Roberts's earlier works for the details of diquark masses.

These papers are just studying mechanisms of hadronic mass. But for those of us interested in the sBootstrap and in Brannen-Koide mass formulas, we should be interested e.g. in stringy and supersymmetric generalizations. As far as the strings are concerned, I would like to see whether counterparts of EHM and HB+EHM can be found in stringy models of QCD like Sakai-Sugimoto.

As for trying to bring in the leptons... If you look at the mass scales, it's as if the electron mass is at the "purely HB" mass scale (in that its mass is comparable to the current masses of the light quarks), the muon mass is at the HB+EHM scale (since it's around the pion mass), and tau mass is closest to the "purely EHM" scale (being greater than the nucleon mass).

It's a weird comparison to make because the standard model tells us that the charged leptons all get their masses via the same mechanism, "HB" - it's just the yukawa couplings that differ in magnitude. In a beyond-standard-model theory, it's not necessarily so simple - e.g. there can be systematic differences in how the different generations get their masses.

But here, we're looking at the idea that the leptons are quasi-goldstone fermions. And not just that - there are a number of BSM models in which all the standard model fermions are quasi-goldstones, but I think it's normally supposed that they are all fundamentally massless (i.e. superpartners to exactly massless pion-like particles, see #327), and then get all their mass via a Higgs interaction. Here we are asking whether there are contributions to lepton mass, that are super-QCD counterparts of "EHM" and "HB+EHM".

Furthermore, if we also want Koide's formula to result from a mechanism rather than a coincidence, we really need the super-QCD explanation of charged lepton masses to be the same for all three (in some sense)... If the charged leptons were all fundamentally massless quasi-goldstones, and the Higgs a top-pion (as it is in topcolor theories), you could try to directly mimic the SM Higgs mechanism in your underlying super-QCD theory... On the other hand, Martin Schumacher had some papers arguing that a version of the Higgs mechanism is responsible for baryon mass, with the sigma meson as the counterpart of the Higgs, and (I think) the pion condensate as the counterpart of the Higgs VEV. It seemed a bit too glib to be true, but he is actually building on ideas from Schwinger which are also part of the ancestry of the actual Higgs mechanism... Maybe there could be a Seiberg-dual perspective on standard model Higgs couplings, in which they become Roberts-Schumacher interactions in an underlying super-QCD theory, with an "EHM" contribution as well as an "HB" contribution.

 

[mitchell porter]

A comment on something that may or may not be a digression: I have just had my mind blown by learning, twenty years late, the gist of the "Dijkgraaf-Vafa correspondence". To begin with, it helps if you are familiar with the idea of color branes and flavor branes, with a string between color branes being a gluon (or gauge bosons), and a string between a color brane and a flavor brane being a quark (or fermion charged under a gauge field). Since this is string theory, usually there is some supersymmetry, and so these strings actually represent gluon-gluino and quark-squark superfields, respectively.

Now consider a Calabi-Yau manifold (the extra compact dimensions) with color branes wrapped around a "cycle" (topologist's jargon for a "hole", like the hole in a donut). As mentioned, the open strings between the color branes correspond (at the level of field theory) to gluon-gluino superfields. The branes are also capable of oscillating in directions normal to the cycle; these displacements are scalar quantities, and correspond to "chiral superfields" at the level of field theory (with a scalar and a spin-1/2 component).

It turns out that in string theory, there is a dual perspective available (very similar to AdS/CFT) in which the picture of "branes wrapped on a cycle" is replaced by "flux passing through dual cycles". The strings in the brane picture were open strings ending on the branes. In the dual picture, there are no more branes, so only closed strings are possible and they make up the flux. The flux actually corresponds to certain generalized charges that the branes possessed; so even though the branes aren't present in the dual picture, all their physical effects are.

The amazing thing is that the flux encodes information about composite objects in the field theory! The main superfields arising from the color branes were gluon-gluino superfields, and the fluxes tell us about gluino-pair condensates and glueballs made of gluons. They are closed-string objects made of webs of open strings.

It was amazing enough to be grasping this vision, but even more so that I was instructed in it by an AI (OpenAI's 4o model, so not even their more advanced 4.5 model). You can see the conversation here. I had been studying the actual papers, but there were basic questions for which I wasn't finding the answers, and the AI was able to answer them, and other questions that arose, with what I think was amazing flair.

In any case, having grasped how the glueballs and gluino condensates were represented by fluxes dual to the branes, I wanted to know about mesons and baryons - do they have a place in Dijkgraaf and Vafa's correspondence? At this point we need to introduce some flavor branes. It turns out that the flavor branes are the same on both sides of the duality. It doesn't sound that different to the way that holographic QCD (Sakai-Sugimoto) usually works. Mesons are quark-antiquark strings, so they are open strings among the flavor branes only, and baryons are branes wrapped around the dual cycles that emerge on the flux side of the duality (and connected by quark-like strings to the flavor branes).

Perhaps the most interesting thing here, is that this is also a picture of confinement. Confinement means that colored degrees of freedom become invisible; in stringy terms, this means that there are no color branes in the flux picture, just flavor branes, condensates, and composite objects. It's a remarkably thorough mapping of the phenomena of strongly coupled gauge theory, into string theory... But, it's supersymmetric, so if you want to understand QCD this way, you'll still need something more (again, something like Sakai-Sugimoto, which breaks the final supersymmetry).

However, in the sBootstrap, we have a supersymmetry, so what I wanted to know is, is Dijkgraaf-Vafa useful here at all? So far, I haven't made a connection. In fact, even though so much N=1 supersymmetric phenomenology has been studied over the years, I haven't found applications of Dijkgraaf-Vafa to phenomenology in general. I tried looking for something involving yukawa couplings, and found this paper, but didn't get anything from it yet. The paper piqued my interest because it talked about theories with an adjoint (the gluino) and several quarks, and reminded me of Armoni's work on "orientifold planar equivalence", cited a few times in this thread. I keep wondering e.g. if the diquark could be represented as a "flavino" fermionic string between flavor branes; but then it seems we want that for mesinos, which in the sBootstrap is where the leptons come from. It could be that Dijkgraaf-Vafa is from the realm of color, and the sBootstrap is from the realm of flavor, so they just don't have much to do with each other.

edit: I completely forgot to mention another aspect of the Dijkgraaf-Vafa correspondence, which is the role of "matrix models". This is a kind of noncommutative geometry, I guess, in which you literally do integrals over possible values of matrices, in order to recover open strings in a space-time. The key is to interpret the row and column numbers of the matrix as identifying particular branes. Matrix element (i,j) then corresponds to a string between brane i and brane j. The equations for a matrix model involve matrix-valued quantities, and determine the interactions among strings in the same way that you get Feynman rules from an ordinary Lagrangian. The more algebraic part of the Dijkgraaf-Vafa correspondence involves showing how the matrix model algebra is still present, even when you only have closed strings...

Phenomenologically, the matrix model that interests me most is the "IKKT model", a Japanese matrix model which has intrigued a minority of researchers for many years, and which has just had a renaissance - I give my take on it here. I think that technically it has some differences with the matrix models studied in Dijkgraaf-Vafa (for example, time is supposed to be emergent in it, as well as space!), but having understood the Dijkgraaf-Vafa path from matrix model to open strings to gauge theory and closed strings, it wouldn't hurt to look at it from that perspective too.

 

[mitchell porter]

Via Tommaso Dorigo, I have just learned of a possible observation of toponium (top-antitop meson) at CERN's big muon detector (CMS experiment). This interests me because I've always been keen on the idea that the Higgs boson could be a kind of toponium (the Higgs mass is basically 1/sqrt(2) times the top mass). But it also matters for the sBootstrap, because one of the premises of the sBootstrap is that you only use the five light quarks (light relative to the top quark, that is - usually bottom and charm aren't counted as light) as ingredients in the mesons and diquarks whose superpartners are all the standard model fermions.

I shall see what @arivero himself thinks, but in my opinion the existence of a toponium resonance is not inherently a problem for the sBootstrap. For example, in an interpretation of the sBootstrap as a Seiberg duality, it's not that there aren't six fundamental flavors of quark (only having five leads to problems with anomalies), but rather e.g. that one is massive and five are massless in the UV, while their IR duals are the sBootstrap composites and exhibit the familiar spectrum of masses.

There would still be the question of whether toponium has a superpartner (remember, one of the sBootstrap ideas is that the leptons are superpartners of mesons) - if so, where is it, and if not, why not. One perspective on this, is that it is a form of the general question, what about all the superpartners that ought to exist, but for which the sBootstrap doesn't have a use. This applies to the charge +4/3 "diquarkino" arising as the superpartner of a diquark made of two up-type quarks - a fermion with such a charge may actually exist in certain SUSY GUTs, as the spin-1/2 partner of an X boson. But it also applies to the superpartners of all the elementary bosons - photino, gluino, Wino and Zino, and higgsino.

If you're not worried about being an old-fashioned SUSY phenomenologist, you can just approach this in the spirit of the usual MSSM - these particles are out there, they're just heavy. But this kind of SUSY is a little out of fashion these days, at least in some circles. Part of the charm of the sBootstrap is that it gives SUSY an unexpected phenomenological role within the standard model (similar in spirit to the early days of SUSY phenomenology, when it was wondered if the photino might just be the neutrino). So one has a choice of approaching the sBootstrap as a kind of extra emergent SUSY embedded in the MSSM, or as a kind of partial SUSY existing within the non-SUSY standard model.

Anyway returning to CMS's "pseudoscalar excess" that might be toponium, in their paper they do say that alternative explanations are presently possible, and cite this earlier CERN preprint, in which they cover the possibility of a two-Higgs model. I also just wonder how confident we are in the modeling of top-antitop interactions, since the top and the Higgs are strongly coupled (because the top yukawa is so big). I was curious about this back in the days of the "750 GeV diphoton excess", for those who remember that...

 

[arivero]

Indeed I am a bit worried, lets see if they find some discrepancy with models.

 

[mitchell porter]

Their most recent reference (December 2024) for the calculation says

"Green's functions ... are obtained from the solution of a Schrödinger equation accounting for the exchange of potential gluons among the top and anti-top quark ... the ttbar pair transition into a quasi-bound state is favored. This state is colloquially referred to as ‘toponium’, although it should be noted that the top quark decays much faster than it can hadronize, i.e. Γ_t ≫ Λ_QCD, and thus a proper bound state cannot form, unlike the more common charmonia and bottomonia."

So there appears to be an objective difference. How that difference manifests will depend on the formalism or approximation being used. It would be especially interesting to know what the difference amounts to, in nonperturbative QCD, and in a fully string-theoretic framework.

 

[mitchell porter]

I report two paper which provide examples of ingredients one might expect in a field-theoretic treatment of the sbootstrap.

"Color gauge invariant theory of diquark interactions" (Wang, Zhang, Sun)

"A - BCD dualities" (Amariti, Mantegazza, Rota, Zanetti)

In QCD, we could say that the basic fields are quark, antiquark, and gluon. The Chinese diquark paper is developing Lagrangians in which gluon fields interact directly with diquarks. There is a precedent for this in the An-Wise EFT discussed in this thread at #270. An and Wise seem to say more about the conditions under which it is valid to treat a diquark as a point source interacting directly with gluon fields. This Chinese paper focuses more on writing out full multi-flavor Lagrangians. It also cites earlier work on diquark-meson interactions. From a standard model perspective, one supposes that if these are valid constructions, they must emerge as EFTs from QCD under various regimes.

The Italian duality paper describes dualities for various quantum field theories with N=1 supersymmetry and some combination of "fundamentals and antisymmetric flavors". A fundamental corresponds to a quark field, an antisymmetric corresponds essentially to a diquark and sometimes to a gluino. In the course of this thread, we have linked to a large number of papers on supersymmetric dualities and self-dualities, e.g. N=1 and N=2 theories with five or six flavors, and several works by Armoni with antisymmetric flavors (e.g. the orientifold field theories) which often descend from the dualities of SQCD.

In the Italian paper on page 4, you will find references to "mesons" Q Q-tilde and "baryons" Q Q. (Diquarks are literally the baryons of two-color QCD, as discussed at #48 and #110 in this thread.) Q and Q-tilde are superfields for quark and antiquarks, so we are really talking about meson and diquark superfields. Evidently there is potential here, for a crossover between "diquark papers" and "duality papers".

One thing missing so far, is electric charge or hypercharge or weak isospin or the electroweak sector. I note that back in #269 in this thread, I cited some duality papers in which the quarks also have U(1) charges. As for chiral SU(2), I've always been intrigued by the way that chiral perturbation theory (yet another example of an EFT descended from QFT) often introduces a formal gauging of the chiral symmetries. An expert on Stack Exchange also informed me about "chiral color" (and its problems).