A Week's Worth Of Science: Four Papers To Browse
By Tommaso Dorigo | November 1st 2009 05:35 AM | 10 comments | Print | E-mail | Track Comments

I am an experimental particle physicist working with the CMS experiment at CERN. In my spare time I play chess, abuse the piano, and aim my dobson...

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A Sunday morning browsing through preprints recently posted in the Cornell Arxiv revealed interesting reading material. If you have a couple of hours to kill next week, why not having a look at the following papers ? It will definitely hurt you less than spending the time on your WII or watching Jerry Springer.

- Alejandro Rivero, "Unbroken Supersymmetry Without New Particles", 0910.4793: Alejandro is a friend and he already wrote in this blog about his "sbootstrap" theory. To tell you in two words what this is about, he moves from a startling numerical coincidence between the masses of charged leptons (the Koide' mass formula) to hypothesize that the role of Supersymmetrical particles in the Standard Model is taken by composite mesons. It is a bold speculation, and it is certainly worth ten minutes of your time, if you can read English and know the basics of group theory.

- Gautam Bhattacharyya, "A Pedagogical Review of Electroweak Symmetry Breaking Scenarios", 0910.5095: a quite well-written and comprehensive summary of the theory of electroweak symmetry breaking in the standard model, with explanations of models involving little Higgs or Higgless breakings. I found it a very useful resource, especially for experimentalists wishing to refresh their memory; but beware, the math is only as simple as possible, not simpler.

- Tilman Plehn, Gavin Salam, Michael Spannowsky, "Fat Jets for a Light Higgs", 0910.5472: a recipe for looking for the Higgs boson at the LHC, using the associated production $pp \to t \bar t h X \to t \bar t b \bar b X$ for low Higgs boson masses and "fat jets" plus triple b-tagging. The study is interesting, although I was rather puzzled to learn that "After long debates this signature has recently been abandoned by both LHC experiments". The authors quote as evidence for this claim the observation that the signature has been recently removed from the standard Higgs "discovery reach" plots of ATLAS and CMS, but I would like to remind them that this is a necessary, but not a sufficient, condition for what they claim. In fact, my group is still pursuing that signature, with a new technique. Since 30 to 100 inverse femtobarns of data are needed, however, it is clearly something on which we are taking our time...

- H. Pessard, "Status of the OPERA Neutrino Experiment", 0910.5701: a short review of the status of OPERA, a really cool experiment which aims to detect oscillations of muon neutrinos (from a CERN beam shot underground in the direction of the Gran Sasso underground facility) into tau neutrinos. Tau neutrinos are notoriously hard to detect: technically it is the last standard model fermion to have been directly discovered, although nobody could really doubt of their existence after the tau lepton discovery and the LEP measurement of the Z boson width. OPERA uses photographic emulsions to reach micrometric precision in the tracking of charged particles emitted when tau neutrinos hit nuclei, produce tau leptons, and the latter decays after a path of few microns in the emulsion. Have a look at a typical picture (this one shows acharmed meson decay though) on the right.
I think OPERA is cool because of its concept: bricks of emulsions where neutrino interactions are captured get removed from the detector progressively, and analyzed as data taking proceeds. It reminds me of HAL, the supercomputer in "2001, the Space Odyssey", being disassembled bit by bit by the vindictive astronaut the machine had tried to kill. For a previous account of OPERA, read here.

Hey, thanks for the publicity.

Yes, the paper is mainly an update of the comments in this blog, time ago. Perhaps I should quote the blog too ;-). Actually I should add some bibliography, as I am selling it as a conjecture of mine, while it happens that the proposal to interpret the Ramond sector as a quark sector and the bosonic sector as mesons was already in the papers of Schwarz in 1971; it was forgotten after the discovery of supergravity, where the whole mess was upgraded to Planck scale. Reading between lines, I guess that the idea was received with skepticism; in a graduate lecture in 1974, Mandelstam suggests that it is better to forget about the fermionic sector and see the whole as a "quark theory of the meson, without quarks". The problem, of course, is that you need to explain how a theory can include composites and elementary, or alternatively if you want the fermions to be composite, explain why they are point like.

I am also thinking about removing or rebuilding a point appearing first time in this paper, and needing more substance to be discussed seriously: The argument of the existence of two natural divisions of the standard model on 84+12. That of the top quark and that of the neutrino. This split appears when you consider descending from D=11 or 10 down to 10 or 9 (still weak, the argument here), and then in dimension 9 one should build the SU(3)xU(1)_EM part of the standard model. Moreover, one of the splits needs chirality (for the neutrinos), the other doesn't. Moreover, one of splits involves the most massive particle, the other the lightest. I invite your readers, even without reading the paper, to guess what I am after, here.

Tommaso said that Alejandro Rivero "... hypothesize[s] that the role of Supersymmetrical particles in the Standard Model is taken by composite mesons ...".
In his paper "Unbroken supersymmetry, without new particles" arXiv 0910.4793 [hep-ph] Alejandro Rivero refers to arXiv 0808.3667 [hep-th] by Luis J. Boya in discussing supersymmetry. In that paper, Luis J. Boya said:

"... the Minimal Supersymmetric Standard Model(MSSM) ... scheme requires ... 2^8 states ... 128 boson and 128 fermion states in two different sets, the ordinary particles and the Susy partners ...
We are fully aware of the incompleteness of our approach ...
gravitation has been deliberately left over in this essay ...
we believe octonions ...[which]... spring from the triality of the Spin(8) group ... should play a role in the “final theory” ...
the largest exceptional group E8 appears conspicuously in theoretical constructions ...
So we feel the ... omissions (gravitation and octonions, in particular E8) should go together. ...".

One way to use those omissions might be:

1 - Look at the three 8-dim triality representations of Spin(8):
8v = vector representation
8s+ = +half-spinor representation (physically interpreted as 8 fundamental first-generation fermion particles)
8s- = -half-spinor representation (physically interpreted as 8 fundamental first-generation fermion antiparticles)

2 - Note that 28-dim Adjoint(Spin(8)) = 8v /\ 8v = antisymmetric product
(or Clifford product with respect to the real Clifford algebra Cl(8))
and
physically interpret the 28 adjoint bivector generators as gauge bosons

3 - By the triality automorphism
8v /\ 8v = 8s+ /\ 8s+ = 8s- /\ 8s-
so that the 28 bivectors of Cl(8) can be considered to be composite made up of pairs of half-spinors analagous to Alejandro Rivero's "composite mesons"
thus
establishing a triality-based supersymmetry between the 28 gauge bosons and the 8 fundamental fermion particles (and the 8 fundamental fermion antiparticles)

4 - Take the tensor product of two copies of Cl(8)
Cl(8) x Cl(8) = Cl(16)
to see that
the half-spinors of Cl(8) are embedded in each the two
128-dimensional half-spinors of Cl(16),
thus accounting for Luis Boya's "... 128 fermion states ..."
and
the 28 bivectors of Cl(8) are embedded in the 120-dimensional bivectors of Cl(16),
thus accounting for 120 of Luis Boya's "... 128 boson ... states ...".

5 - Combine one of the 128-dim Cl(16) fermionic half-spinors with the 120-dim Cl(16) bosonic bivectors to construct 248-dim E8.

All this can be taken further in some detail (for example,
how to use 12 of the 28 bivectors as the 8+3+1 bosons of the Standard Model,
and how the 128 - 120 = 8 other Luis Boya bosonic things might represent an 8-dim Kaluza-Klein spacetime)
but as this is just a blog comment I will stop here.

Tony Smith

PS - In a comment, Alexandro Rivero points out two natural divisions of the Standard Model:

1 - the Neutrino, whose very low mass sets it apart from the other 7 fundamental fermions (Electron, Red Down Quark, Green Down Quark, Blue Down Quark, Red Up Quark, Green Up Quark, Blue Up Quark),
which might be related to an octonion representation where
the Neutrino is represented by the 1 Real Octonion
and the 7 massive fermions are represented by the 7 Imaginary Octonions

and

2 - the T-quark, whose very high mass sets it apart from the other 5 quarks (down, up, strange, charm, B-quark)
which might be related to some combinatorial consequeneces of representing the first generation fermions by Octonion basis elements
and
the second and third fermion generations by pairs and triples of Octonion basis elements.

Hi Tony,
A point of this paper is orthodoxy: to do not bring new ideas if we do not need it, to use instead the mechanisms already reported. The representations of SO(8) are orthodoxy: 8v are the Bose type I strings, 8 s+ are the Fermi type I strings, and so on. The tensor product generates type IIA, when both 8s+ and 8s- are involved, and type IIB, when only one kind of "half-spinor" is involved. The symmetrization of IIB produces Type I Chiral Sugra. I think all of this should be considered "standard notation", and it covers most of the contents in your steps 1-4. As for step 5, is basically the E8xE8 heterotic string trick, or most properly a "tensor square root" of it. I have neglected the string theories based on gauge groups (E8xE8 or SO(32)) because they are basically a 10D shadow of the 26 dim string. (With a caveat: it is true that 32 comes from n=2d, d+D=26, D=10, but it also appears natyrally in Type I as 2^D/2)

My greatest pain in all this approach is that I can not see any natural way for the flavour groups SU(5) > SU(3)xSU(2) in my paper to appear, as subgroups of SO(8) or whatever.

Ah, about my last paragraph, I leave open my question: "guess what I am after". Really I would enjoy to hear oppinions about the implied idea.

Alejandro, thanks very much for the nice correspondence of my (1-5) and orthodox string theory constructions.

As to your "... greatest pain in all this approach is that [you] can not see any natural way for the flavour groups SU(5) > SU(3)xSU(2) ... to appear ...",
maybe the problem is with the SU(3) "generations" symmetry.
Maybe the 3-generation structure is not on the same fundamental level as the supersymmetry and gauge group symmetries,
but
comes in at a different level and must be treated separately.
(I think that Garrett Lisi encountered similar difficulties when he tried to use triality to get 3 generations in his E8 model.)

Tony Smith

Maybe. It is true that the most natural place to look for three generations is the place I am disregarding in this approach: the jump between SO(8) and SO(24), ie between D=10 and D=26. Horava and Witten duality between E8xE8 and type IIA is relevant here.

In sBootstrap the flavour symmetry is at the same level than supersymmetry. But it seems to be a theory of open strings.

Alejandro, thanks for the reference in your fascinating paper. I'm working on getting a paper published so you could actually put in a reference instead of just a mention. :(

I've got a paper under review at Foundations of Physics that, at the request of the editor, has been revised which is supposed to give a derivation of Koide rules for mesons from the starting point of spin path integrals and mutually unbiased bases. And there's an earlier paper that gives a much longer list of Koide triplets in the hadrons which I intend on submitting to Phys Math Central after I get the first paper published.

Hi Carl, I am incorporating a reference to your PDF (and to this blog!) in the updated version. A minor reason to do not incorporate further references was to try keeping an academic formatting in the paper. A major one was to concentrate in content; there are a lot of opportunities for diversion in any bibliography.

I will update the paper tomorrow or past-tomorrow. I want to be clear about the T-duality between neutrino-world and top-world. Actually it is a poor result if it is going to be based in the naive estimate with the string scale at 1 GeV. Then the neutrino scale is too high, (1 GeV)^2/175 GeV= 5 MeV. It is a bit better if I use an string scale at 115 MeV, but even in this case is high; I can use the new scale to redo the seesaw, 0.115^2/175=M, M^2/1.77=3.2 eV, bad again. Other possibility is that the naive seesaw is modified when taking into account coupling constants and all that.

Alejandro, are you submitting this paper for publication? I'll add a citation to your paper in my next revision.

Carl, no, I am not submitting it. It is more a paper for a poster or a talk than for a publication.

References updated in v2 :-)

Also, some expansion on the 28 that Tony referred to, clarifying htat my bet from them is to be sfermions, at least the 21 part of them, when they decompose to 21+7 in SO(7).