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

arivero

In any case, I agree that the "seed top" idea is interesting. The squarks we have are different, as they change barion number. But the diagram at the end of the paper almost fits with the chains from koide, we have also a t-->b-->c and then a b-->c--->s, and the point of having the lepton sector hanging separately b--->tau c--->mu s--->e could be similar to the orthogonality.

mitchell porter

I have been reluctant to play the game of conventional MSSM phenomenology - too many possibilities, too much history of "this time, it's just around the corner" - but I have found a psychological starting-point from which to approach this exercise: think in terms of starting with a "supersplit" spectrum in which all the superpartners are at some ultra-high scale. You don't start out with the assumption that supersymmetry is the answer to the hierarchy problem or to anything else, and you are spared all the further problems-to-be-solved that are caused by assuming low-scale supersymmetry. Initially you regard it just as a feature of final-stage unification, extremely remote from experiment...

Then you think "what if one, two, or a few of these particles have small enough masses to be relevant to observable physics after all", and e.g. try to construct a Koide cascade from a He-Volkas-Wu-type theory. And only then do you start thinking about how to get your Koide-MSSM from a GUT, from the heterotic string, etc. (The idea of gauge-top unification, or even gauge-Higgs-top unification, looks interesting.) If it's worth it, you're even "allowed" to include ideas from conventional super-phenomenology, in a specific Koide-MSSM model. But in constructing a Koide-MSSM, I think it's imperative to start philosophically as if you were just extending the SM, and not the MSSM as conventionally conceived.

mitchell porter

We may have our first step in a MSSM top-seeded mass cascade: a right-handed down-type squark. Dobrescu and Fox (2008) present a model somewhat in the spirit of He, Volkas, and Wu, in which a leptoquark scalar they call "r", and a color-octet weak-doublet scalar, and some vectorlike fermions, produce a mass cascade in which, starting with a tree-level mass for the top, they obtain bottom and tau at one loop, charm at two loops, and strange at three loops; and muon at three loops and electron at four loops. On pages 9-10 they note that the down-type squark could play the same role as the "r" - "in supersymmetric models with R-parity violation the squarks may have leptoquark couplings" - though with differences in the details.

There has been a lot of work on radiative generation of SM fermion masses in the MSSM - e.g. hep-ph/9601262, hep-ph/9902443, hep-ph/0107147, arxiv:1108.2424 - but it's focused on other sources of mass, e.g. massive gauginos. Nonetheless I think all that work offers a useful context for a detailed development of MSSM top-cascade models, e.g. Crivellin (arxiv:1105.2818). There's work on starting just with top, bottom, and tau masses, so if we cut that back to just top, and then put in place a modified Dobrescu-Fox cascade, we might get somewhere.

Of course, since we're ultimately trying to explain a cascade of Koide relations, just parameter-fitting and showing the phenomenological viability of such a model would not be enough. If this really is how things work, one has to suppose that the Koide relations have an origin outside the MSSM. I suppose it would be convenient if e.g. one introduced extra symmetries to the MSSM just to set non-top yukawas to zero and to get the right structure of couplings for the cascade, and those extra symmetries alone were sufficient to produce Koide relations. But I wouldn't be surprised if we have to go very deep. For example, think of the topological expansion in string theory, in which e.g. a tree-level scattering of n open strings becomes a disk with n insertions on its boundary, and the k-loop correction is a disk with k holes. It's conceivable that the Koide relations have their origins in the properties of amplitudes at such a remote level of description.

arivero

About the point of "Assuming that the leptons and quarks other than top are massless at tree level", I still kept a thinking that the M2-brane and M5-branes should have a role to justify this masslessness. Either that, or something having an 84 irrepr.

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: 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

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 QCD 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 (slide 20). 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

[itex]<\bar Q_L \cdot Q_R> = <\bar u_L u_R + \bar d_L d_R + \cdots>[/itex]

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 [itex]<\bar q_{jL} q_{kR}>[/itex], j and k flavor indices), and that the quark fields would be defined as the operator basis which diagonalizes the matrix.