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

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

[tex]y_{u,d}\sim \lambda_{u,d}\lambda_q \sqrt {N/4\pi}[/tex]

? 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

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

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

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

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 [itex]b \bar b[/itex] and [itex]t \bar t[/itex]. 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

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