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

[mitchell porter]

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

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

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

 

[arivero]

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

 

[mitchell porter]

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

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

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

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

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

 

[mitchell porter]

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

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

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

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

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

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

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

 

[mitchell porter]

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

 

[arivero]

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

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

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

 

[arivero]

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

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

 

[mitchell porter]

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

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

 

[mitchell porter]

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

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

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

 

[lpetrich]

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

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

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

 

[mitchell porter]

Massless QCD spontaneously breaks part of chiral symmetry (http://www.nikhef.nl/pub/theory/academiclectures/sm06_three.pdf). And in a standard model with no Higgs and massless fermions, the quark condensates do have the right quantum numbers to break electroweak symmetry a little - see Quigg and Shrock, II.A.1 and II.B.1. Here's an informal description of the resulting physics (also see this talk by Quigg).

 

[lpetrich]

From PDF page 20, the nonperturbative-QCD ground state has

$<\bar Q_L \cdot Q_R> = <\bar u_L u_R + \bar d_L d_R + \cdots>$

How would the quark fields "know" which ones to pair up with in the massless case? In the massive case, it's easy: the mass eigenstates.

 

[mitchell porter]

It seems (see page 20 of Wilczek's latest) that the degenerate ground states of massless QCD are indexed by unitary matrices (the matrix elements being VEVs like $<\bar q_{jL} q_{kR}>$, j and k flavor indices), and that the quark fields would be defined as the operator basis which diagonalizes the matrix.

 

[mitchell porter]

Alejandro's revisit to Koide 1981 (publication, preprint) in the other thread prompts me to outline yet another what-if scenario.

In Koide 1981 there are three generations of preons. In each generation, there is a subquark doublet with color charge, a subquark doublet with subcolor charge (subcolor is an extra SU(3) interaction), and a subquark "h", also with subcolor charge. (The left-handed part of the doublets is a weak doublet, the right-handed part is two weak singlets.)

One generation of SM leptons consists of the subcolor-charged doublet coupled to an subcolor-antisymmetric combination of two "h" subquarks, producing a lepton which is a subcolor singlet. One generation of SM quarks consists of the color-charged doublet coupled to a subcolor-singlet meson "h-hbar", producing particles which are subcolor singlets but color triplets. Koide admits the model doesn't explain why the doublet and the meson are bound together.

Curiously, this is the reverse of the sbootstrap, in the following sense. In Rivero 2005, quarks are associated with diquarks and leptons with mesons. In Koide 1981, leptons are associated with di-preons and quarks with pre-mesons.

Can we build the sbootstrap out of subcolor, but with "diquarks" in quarks and "mesons" in leptons? Here one faces the usual stumbling block that in the sbootstrap, we seem to be building quarks out of themselves. So I propose to proceed as follows. We are to think of the SM as dual to a model containing six quarks only, which we shall label t', b', c', s', u', d'. We are to think of t' as massive and the other five as massless.

Finally, we suppose that these dual quarks all have subcolor charge as well as color charge, and that there is a further dual-quark doublet n1, n2 ("n" for neutral), with subcolor charge, but no color charge or electromagnetic charge.

Now we can proceed in imitation of Koide, but in reverse. SM leptons combine n1, n2 with ordinary-color dual-mesons, producing particles that are color singlets and subcolor singlets. SM quarks combine n1, n2 with color-antisymmetric dual-diquarks in the anti-triplet representation, producing particles that are also subcolor singlets, but which are color anti-triplets, just like the original form of "hadronic supersymmetry". Or rather, SM quarks are "partially composite"; they are mixtures of the original dual-quarks with these quark-like subcolor-baryons.

So we have a duality between a model with six "dual quarks", one heavy and five massless, and no leptons; and a model with six quarks and six leptons of various masses. If we think of these as superfields, one might even suppose that this is a duality between two models of mass generation discussed recently in the thread, the "radiative" model in which only the top has a tree-level mass and all other SM fermions get their masses through loop effects, and the "circulant" model in which there are 3 or 6 higgses (the emergent sleptons) producing circulant mass matrices. (And perhaps the n-quarks are subcolor gauginos, and perhaps there will be a stringy model of the "subcolor baryons".)

 

[arivero]

Mitchell, have you noticed in the bibliography on composite Higgs equations such as

$$y_{u,d}\sim \lambda_{u,d}\lambda_q \sqrt {N/4\pi}$$

? I guess that the lambdas are a kind of square roots of mass.

 

[arivero]

How does the condensation "technicolor" work for the electroweak group? If I understand it, we need to give mass to three vector particles and produce three goldstone bosons. Thus the real comparision is not to flavour SU(3), that produces an octect of goldstones, but to flavour SU(2), and then the triplet of pions should be a triplet of higgses H+, H-, H0, and another three degrees of freedom are eaten to give mass to the rho.

I think that the role of the "u,c terminated strings" in the sBootstrap is a even more retorted version of this, involving pairs of particles instead of particle/antiparticle, and some B-L juggling to adjust the charges. But it is amazing that then the top condensate is not involved ever in the Higgs mechanism. Does the sBootstrap have some hidden role for the top condensate, or we are really so strict about not allowing it to bind to any object in any situation?

 

[arivero]

"u,c terminated strings" ... and some B-L juggling to adjust the charges.

The point is that Q = T3 + (B-L)/2.

So if we uncouple B-L, a quark only offers an electric charge from T3, this is +1/2 for the up quark, -1/2 for the down. The T3 can be R or L.

So you see, uu, uc and cc could produce three Q=+1 bosons very nicely, and the antiparticles the corresponding Q=-1 But the problem is that we need to have two Q=0 bosons in the pack.

The most obvious way is to have one of them, say c, with a T3=-1/2. But then it should have B-L equal to 7/3 to compensate, for instance keeping B=1/3 but L=-2 instead of 0. Either that, or some other mechanism I am missing yet.

Had we such mechanism, we had a prediction of a higgs sector from condensates with a neutral H0 and two charged H+ H-

 

[mitchell porter]

I think the idea is unlikely. However, I will point out Mohapatra et al on an up-type sextet diquark Higgs. Your diquark Higgs might also need a B-L spurion to work.

There was a paper proposing that the 125 GeV boson is in fact a mixture of toponium and bottomonium. (Interestingly, the other mixed eigenstate has a mass close to 325 GeV, where there were anomalies last year.) One could look for a connection with topcolor, topcolor-assisted technicolor, and/or pion-Higgs models.

 

[arivero]

Mohapatra et al

Somehow the academics now how to get their stuff published. Not that they get more impact that us, although.

I am pretty sure that it is possible to do the first part, to get rid of colour and B-L on the argument that they are pure vector forces. The problem remains of genning a neutral boson out of it.

 

[arivero]

I think the idea is unlikely. However, I will point out Mohapatra et al on an up-type sextet diquark Higgs.

It is interesting that in this kind of models the uu diquarks have different mass scale than the dd. I guess that it is related to the different scales of electrons and neutrinos in the lepton side of the model.

 

[mitchell porter]

There is no fundamental dd diquark in that model. The "diquark" here is a scalar with a diquark coupling, not a QCD diquark.

If you follow the references back, the 2007 paper cites a 1998 paper which cites a 1980 paper which talks about Higgses made of bound states of fermions. It doesn't call them diquark Higgses. Actually I can't parse the figure in that paper; it seems the Δ_R,44 is the scalar with a VEV, then it has an interaction with three other scalars, and then they interact with quarks and induce a ΔB=2 transition. So the "diquarkness" might be hiding in that diagram somewhere. But that's the best I can do, in the search for a diquark Higgs which is a genuine QCD diquark.

Another consideration is that QCD diquarks are not gauge invariant. A diquark condensate breaks the gauge symmetry, it's involved with phenomena like color-flavor locking and color superconductivity. I can imagine that such exotic phenomena play a role in the appearance of QCD scales in the Koide triplets, e.g. maybe they help to hide a second confining SU(3) interaction, as in the amended version of Koide 1981 that I proposed. But I do think a chiral condensate (qqbar, not qq) is a more plausible way to get EWSB.

In sbootstrap language, diquark -> squark and meson -> slepton. There's a small literature on sneutrino Higgses, but I can't see anything at all about a "squark Higgs". (There is some stuff out there, about squark condensates and CFL in holographic QCD.) But this difference of opinion shouldn't be too much of a problem, the big picture probably involves both chiral condensates and diquark condensates and we'll have to understand both.

 

[lpetrich]

So this is about some particle in a 6 (20) representation of QCD SU(3)?

That is a symmetric square of the fundamental representation, 3 (10); its antisymmetric square is 3* (01).

Since hadron states are all color singlets (colorless), a 6 needs to combine with a 6* (02), like its antiparticle, or a 3 (10) and an 8 (11), like a quark and a gluon:

6(20) * 6*(02) = 27(22) + 8(11) + 1(00)
6(20) * 3(10) = 10(30) + 8(11)
8(11) * 8(11) = 10(30) + 10*(03) + 27(22) + 8(11) + 8(11) + 1(00)

To combine with the quarks and yield integer electric charges, it must have antiquark-like electroweak quantum numbers, with
(weak hypercharge) = (weak isospin) + 1/3 + (integer)

 

[lpetrich]

Let's see about Georgi-Glashow SU(5).

24(1001) = (8,1,0) + (1,3,0) + (1,1,0) + (3,2,-6/5) + (3*,2,6/5)
5(1000) = (3,1,-1/3) + (1,2,1/2)
10(0100) = (3,2,1/6) + (3*,1,-2/3) + (1,1,1)
10*(0010) = (3*,2,-1/6) + (3,1,2/3) + (1,1,-1)
5*(0001) = (3*,1,1/3) + (1,2,-1/2)

To get 6 and 6* QCD states, one can use
15(2000) = (6,1,-2/3) + (3,2,1/6) + (1,3,1)
15*(0002) = (6*,1,2/3) + (3*,2,-1/6) + (1,3,-1)
and similar decompositions for 40(1100), 50(0200), 45(1010), etc.

GG automatically makes every color singlet have integer electric charge.

One can go further, in the likes of SO(10) and E6, but one gets even more extra particles.

 

[arivero]

So this is about some particle in a 6 (20) representation of QCD SU(3)?

Yes and no. The particles in these articles come from usual GUT theory. The ones in the sBootstrap comes from a 15 of SU(5) flavour, still to be seen if it is relevant to see them also as SU(3) colour antitriplets.

 

[arivero]

Funny. The guy in the left corner in the Strings 2008 closing lecture (the one with the blue shirt) seems to be busy thinking about orientability of the worldsheet and diverse wrappings. I had not noticed it before.

http://cdsweb.cern.ch/record/1121966

 

[mitchell porter]

"A Higgslike Dilaton". There have been many such Higgs-vs-dilaton papers. This one examines the situation where the theory is supersymmetric and the SM fermions are partly composite (i.e. are mixtures of elementary and composite fields with the same quantum numbers), a scenario discussed several times in this thread.

 

[arivero]

"A Higgslike Dilaton". There have been many such Higgs-vs-dilaton papers. This one examines the situation where the theory is supersymmetric and the SM fermions are partly composite (i.e. are mixtures of elementary and composite fields with the same quantum numbers), a scenario discussed several times in this thread.

Big guys in the paper. And then it shows how half-baked our speculations are, if you consider the difficulties they have to formulate a decently realistic model. But it is encouraging that they consider partial compositeness as a part of the play.

 

[mitchell porter]

Ramond et al had a paper, "On Mixing Supersymmetry and Family Symmetry Breakings", in which "extra family partners of the Higgs particles act as messengers for both supersymmetry and family symmetry breakings". It's mildly interesting to contemplate how the waterfall and/or sbootstrap might be realized in a framework like this, because this is a serious, calculable field-theoretic model.

The first thing to note is that it talks about supersymmetry breaking, and also how it is accomplished. There are several new scalar fields in the Higgs sector, and one of them is postulated to be coupled to a hidden sector where supersymmetry is broken. This messenger field then acquires vevs which break susy (and family symmetry), and the breaking is then transmitted to the rest of the visible sector (MSSM plus new scalars). This transmission of susy-breaking from a whole new sector where the breaking originates is completely standard; it's "single-sector supersymmetry breaking" which is the unusual alternative to mediated susy-breaking.

By contrast, the papers which introduce the sbootstrap hardly talk about susy-breaking. In fact, among the inspirations for the sbootstrap are coincidences like the similarity of the muon mass and the pion mass. Another question hanging over the sbootstrap is how much of conventional thinking about supersymmetry it wishes to take on. In the conventional MSSM, the muon is the superpartner of certain sleptons, and the pion is still a QCD composite and has no relation to those sleptons at all. In the sbootstrap, one supposes that the muon is the superpartner of something decidedly pion-like (and in fact all the leptons are "superpartners" of pion-like quark-antiquark combinations). So it seems that something like the MSSM is supposed to be emergent from something like SQCD. (An alternative approach might be to say that the MSSM has its normal interpretation - sleptons and pions are fundamentally different - but that it has a peculiar hidden N=2 supersymmetry, with the sbootstrap correspondence being the emergent second supersymmetry.)

Second, let's consider the role that family symmetry plays in the sbootstrap and the Koide waterfall, and then in Ramond et al. Alejandro describes the sbootstrap as featuring an SU(5) global flavor symmetry, and family symmetries have also featured in many attempts to explain the Koide formula.

The family symmetry considered in Ramond et al is discrete and very simple, the permutation group S3, and so is the model; it's not even a three-generation model, there are only two "families". This isn't yet a serious phenomenological model, it's a toy model of how symmetry-breaking messenger particles (here, some of the new scalars) could carry flavor and yet not cause detectable flavor-changing neutral currents. The physics that results depends greatly on the specific vacuum and on renormalization-group effects. These technicalities would be relevant for any serious attempt to embed sbootstrap and waterfall in such a model, and at first glance they don't look very friendly for the generation of Koide-type relationships, but a real assessment on that score awaits a deeper analysis, especially of the "focusing mechanism" which, for certain vacuum alignments, produces phenomenologically convenient cancellations.

So overall this is an interesting class of model to examine, for potential implementations of sbootstrap and waterfall, because by design it addresses the issue (neglected by us) of how the symmetries get broken.

 

[mitchell porter]

Two unorthodox top/Higgs papers today. John Moffat continues his series suggesting that LHC's new boson is not a Higgs, but rather a pseudoscalar meson, a mixture of $b \bar b$ and $t \bar t$. And Christopher Hill, inventor of "topcolor", observes that the "top-Higgs system" has a susy-like dilatation symmetry, which he uses to explain a web of relations between the top yukawa, the Higgs mass, and the Higgs VEV.

These papers should be considered in conjunction with Bruno Machet's attempt to build Higgs doublets out of quark bilinear condensates (#149) and with "A Higgslike Dilaton" (#166). With respect to the sbootstrap, Moffat and Machet remind us that the "mesons" and "diquarks" of the correspondence might be condensates (but what is the superpartner of a condensate?), and Hill reminds us that an unorthodox "supersymmetry" may be at work. Also, these papers remind us that there remain many relatively elementary constructions that have never been considered.

One more thought. In Hill's paper, he argues that alongside top yukawa being close to 1, LHC has revealed that the Higgs quartic coupling is close to 1/4. Numerologically I am reminded of Yukinari Sumino's scheme for cancelling QED corrections to the Koide relation, which requires that the coupling of the new family gauge bosons is approximately 1/4 of the QED coupling. Sumino had no explanation for this relation; could Hill's new symmetry do the job?

 

[arivero]

Two unorthodox top/Higgs papers today.

Well, as a minimum, it shows that Perimeter and Fermilab have an allowance for exotic thoughts

 

[arivero]

The peculiar arrangement of SU(4), or U(1)xSU(3) multiplets noticed in the Koide thread

https://www.physicsforums.com/showthread.php?t=551549&page=6

could be related to the problems to put the higgs scalar under the same symmetries that the other scalars in the sboostrap.

Remember that we had to our disposal three scalars from the 15 and other three from the 15 irreps of SU(5). In our quark mnemonics, it is uu, uc, cc, uu, uc, cc (using the underscore to mean antiparticle). For such thing to be able to produce integer uncoloured charges, we need the mass/higgs mechanism to be blind to colour and blind to B-L, so that all the electric charge of these objects come from the electroweak isospin. Thus here is the first connection to the other thread: the multiplets of equal mass are for the charges for which the sBootstrap Higgs, if it is there, needs to be blind.

The second connection is even foggier: in the other thread, either the strange quark or the muon seem to need an opposite quantum number in order to fit in a SU(4) multiplet. Here it is either the up quark or the charm quark which seem to need some opposite value to sum zero in the uc combination.

 

[mitchell porter]

Two recent papers, by authors already mentioned in this thread, which derive a Higgs sector in a sbootstrap-friendly way:

Bruno Machet continues his series "Unlocking the Standard Model" (see #149), in which the idea seems to be that the Higgs will come from pion-like vevs. As discussed e.g. in #151, in a Higgsless SM, the W and Z will still acquire masses from pion vevs, but at the wrong energy scale. Machet nonetheless wants a version of this to work. In this, his third paper in the series, he considers two generations of quarks, and claims to get the Cabibbo angle from his Higgs-like condensates. Presumably future work will aim to get the whole CKM matrix from the quark bilinears of a three-generation model. Of the multitude of scalar and pseudoscalar mesons that appear, he states (page 4) that some of the scalars will be the Higgs, and the rest should correspond to the observed mesons.

Kitano and Nakai's "Emergent Higgs from extra dimensions" aims to get the Higgs (and the masses of the Higgs and the top) from a deconstructed compactification of the d=6 (2,0) theory to four dimensions. This paper is certainly replete with connections to interesting topics. The (2,0) theory is the worldvolume theory of the M5-brane, so it's central to current advances in theoretical QFT. Their deconstructed version (deconstruction here means that the extra dimensions are approximated by a lattice, so e.g. a circle becomes a ring of sites with a copy of the d=4 SM fields at each site, coupled via the links in the ring, as in a quiver theory) is said to resemble topcolor (see page 3). There's much more I could talk about and I may have to return to this paper. But for now I'll remark on the possibility that perhaps something like Machet's model, which naively shouldn't work, could be produced by a Kitano-Nakai scenario, in which new strong couplings occur at high energy. "As in the Nambu–Jona-Lasinio model for the chiral symmetry breaking, whether or not a condensation forms depends crucially on how the theory is cut-off, and thus discussion requires a UV completion of the theory."

 

[arivero]

The peculiar arrangement of SU(4), or U(1)xSU(3) multiplets noticed in the Koide thread
https://www.physicsforums.com/showthread.php?t=551549&page=6

Back to this, let's approach diquark masses with the mass of the heaviest quark, or the QCD mass if it is heavier than the quarks themselves. Then we can add mesons and diquarks to the "SU(4) arrangement".

$$\begin{array}{lllll} ?, t_{rgb}& & & & \\ ?, b_{rgb}& B^+,B_c^+ & bu, bc& bb, bs, bd & \\ \tau, c_{rgb} & D^+, D_s^+& sc,dc \\ \mu, s_{rgb} & \pi^+, K^+& su, du& ss, sd, dd \\ ?, d_{rgb} \\ e, u_{rgb}\end{array}$$

It is tempting to think that in this "midly broken susy", the two lower mass levels are actually massless, so that SUSY does not need to kept the pairing at the same mass; it could be that the partners of d are the charmed diquarks, while the partners of up have been lost in the same mixing that breaks t and c partners.

Adding neutrinos and the missed diquarks, the table is a bit more complex. With some small abuse of notation, we could write the "after mild breaking" sBootstrap as

$$\begin{array}{lllllll} &\nu_?, t_{rgb}& & & & \\ &\nu_?, b_{rgb}& B^+,B_c^+ & bu, bc& bb, bs, bd & \eta_b, \stackrel{b\bar s,b\bar d}{\bar bs,\bar bd} \\ \stackrel{\bar c\bar c}{cc},\stackrel{\bar c\bar u}{cu}&\tau, c_{rgb} & D^+, D_s^+& sc,dc & & \eta_c, \stackrel{c\bar u}{\bar cu}\\ \stackrel{\bar u\bar u}{uu}&\mu, s_{rgb} & \pi^+, K^+& su, du& ss, sd, dd & K^0,\pi^0, \stackrel{s\bar d}{\bar sd}\\ &\nu_?, d_{rgb} \\ &e, u_{rgb}\end{array}$$

It is sort of symmetric, in a pleasant way. Wish I knew what to do about it.

 

[mitchell porter]

We can adapt an earlier idea for the sbootstrap to Pati-Salam. The earlier idea is that there is a fundamental QCD-like theory with six flavors of quark, five light and one heavy; the five light quarks form fermionic composites, "diquarkinos" and "mesinos"; and the mesinos are the leptons, while the diquarkinos mix with the fundamental quarks to give us the phenomenological quarks.

For Pati-Salam sbootstrap, the prescription is almost the same, except that the leptons already exist as the "nth color" in the fundamental QCD-like theory, so in this version the mesinos are mixing with preexisting degrees of freedom, just like the diquarkinos.

It's probably best to think of the fundamental theory as having N=1 supersymmetry (at least), and to think of these composites as superfields.

 

[arivero]

http://higgs.ph.ed.ac.uk/sites/default/files/Higgs_RR.pdf

Rattazzi is near to discover the sBootstrap if he continues this kind of enquiries.