GUTs from fermionic supergenerators.

[arivero]

This thread is to discuss a very non-standard opinion: that SUSY has indeed been observed time ago.

It draws on the "binary GUT" approach to SO(10), as stated by Zee in his book "Quantum Field Theory in a nutshell" and by F. Wilczek and A. Zee before. They observe that a SO(2 n) multiplet can be built as a product of SU(2) spinors, and they use this fact to generate the representations of GUT theories.

One can generate a SO(10) 16 spinor from a initial neutral two-component spinor |v> and four fermionic generators, let's call them Q+, Qr, Qg, Qb. The first of them has electric charge +1 and it is neutral for SU(3) colour, while the other three have electric charge -1/3 and they are coloured. We get

|v> : a neutrino, let's say.
Q+ v>, Qr v>, Qg v>, Qb v> : a positron and three down quarks.
Qr Q+ v>, Qg Q+ v> , Qb Q+ v>, Qg Qr v> Qb Qr v>, Qb Qg v>: three up quarks (charge +2/3) and three anti-up (charge -2/3).
Qg Qr Q+ v>, Qb Qr Q+ v>, Qb Qg Q+ v>, Qb Qg Qr v>: three anti-down and an electron.
Qb Qg Qr Q+ v>: the antineutrino

A problem of this idea is that we get the particles with different gradings. It can be solved by adding another neutral generator, Q0, so that we double the content of the multiplet. Now every fermionic component has the same grading, but we have got bosons too. And we need to look for them.

Here enters the main conjecture, proposed a couple years ago, and presented in hep-ph/0512065 (here attached).

It uses the fact that the top quark is unable to bind into mesons; with this property, it happens that the number of degrees of freedom of the standard-model fermions is the same, charge-by-charge, that the number of existing degrees of freedom for SU(3)-glued bosons.

So the standard model spectrum is composed of 96 fermionic degrees of freedom and 96 bosonic ones, matching in colour and electric charge.

The theory explains why the lepton masses and the hadronic masses are in the same range. A priory, the masses of muon and tau could have any value. Standard GUTs justify that the tau has a mass about one third of the bottom quark, but do not justify why such masses are in the hadronic rangue. And there is no model able to explain why the mass of the pion is so near of the mass of the muon.

The theory explains also why does Koide's equation, originally a preon based equation, work: because the fermions are not composite, but supersymmetric to composite particles.

From the 32 fermionic d.o.f. of the build above, we could try to add more neutral generators. One generator is not enough, but two generators drive us up to 128 d.o.f. instead of 96. So some symmetry breaking is needed. But it is interesting to note that we have started with 4 charged generators plus a neutral for the susy. And we seem to need two more, so we have a total of 7 generators acting in a two-component spinor. Perhaps do we need 8 generators acting in a "one-component" spinor?

I want to discuss this theory in the Independent Research subforum because the W-Z method very probably can be applied also in other alternative theories, and I would like to locate them and to see if they give some clues about the supersymmetric formalism.

 

[arivero]

since submision, some details of this research have been extended in http://arxiv.org/abs/0710.1526

I think that comments here
http://dorigo.wordpress.com/2006/09/14/a-mistery-behind-the-z-width/
and here
https://www.physicsforums.com/showthread.php?t=192457
can be related to this, at least for the lepton sector.

 

[Hans de Vries]

I think that comments here
http://dorigo.wordpress.com/2006/09/14/a-mistery-behind-the-z-width/
and here
https://www.physicsforums.com/showthread.php?t=192457
can be related to this, at least for the lepton sector.

Somehow I did miss this. I should pay more attention


Regards, Hans

 

[arivero]

let me add

http://dorigo.wordpress.com/2007/10/16/guest-post-alejandro-rivero-sbootstrap/

 

[arivero]

I really think that string theory could help with the most troublesome problem of this approach: to interpret the pairs cc, cu and uu, which are not obviously forbidden, forming three (and times color) degres of freedom with no obvious arrangement as Dirac fermions, and pretty exotic electric charge. They could be arranged in three chiral (and charged!) fermions, but then they are massless and can not be uplifted to the mass of the top quark. The hope is that the mechanism barring these particles out of existence is forced to be a chirality argument and then it introduces chirality in sBootstrap.

a related meditation is pure numerology: that the main numbers of string theory revolve around 8 and 24, with some secondary numbers being 26, 10, 10/2=5, and 2^5=32. The sBootstrap approach seems to visit similar places.

 

[arivero]

More on the pairs cc cu uu. If they are blind to any non axial charge, they are not only "electric neutral" but also "color neutral", because SU(3)xU(1) is vector, not chiral. So there are only three species of "up up" fermions, total of six degrees of freedom.

It could be interesting if we were trying harder to fit all the particles in a N=8 sugra multiplet.

We have 128 slots for fermions. Of these, the standard model fermions are 96. The gauginos fill 24, so a total of 120 and we are left with 8 for extra play. If we want MSSM mass generation, we need two higgs, so the higgsinos fill the 8 extant slots.

If we do not generate mass (via the higgs, anyway), then there is place for the gravitino, that is two slots, and six extra slots. Still, it could be non MSSM higgsino with 4 slots, and then 2 extra slots for a "spureusino". Or we could use the six extra slots for exactly the uu uc cc UU CC CU partners, making three chiral fermions, or any other group of three "familynos"

 

[arivero]

An objection to the previous comment: being blind to vector charge applies well to the fermion side, thus reducing to three species. But in the scalar side, we could still have the three different colours, so a "uu" familino would pair with red green and blue "uu" diquarks, instead of a single blind uu.

 

[arivero]

My comment in http://matpitka.blogspot.com/2010/10/quark-compositeness-nowhere-near-what.html :

I am not sure if quarks and leptons are composites, they could be. But I am almost certain that their superpartners are composite (as I explained in the sBootstrap theory time ago), so it could be that also the fermions themselves are composite.

Composite of light quarks joined with QCD.

With three generations of particles, it means that a scalarfermion is a composite of two coloured fermions from the set (u,d,s,c,b). You can check that the number of possible pairs is, exactly and charge by charge, the number of expected sfermions in three generations of the standard model. So the bootstrap.

With two or one generations, the number of pairs is less than the number of needed sfermions. With more than three, in the cases where you can find a exact match, you need a horribly huge quantity of very massive quarks, while for three you only need to give EW mass to the top quark. So the sBootstrap hypothesis predicts the number of generations.

Now, how does the compositeness of the sfermions translate to compositeness of the fermions themselves?. I have no idea. An approach could be to substitute the "integer spin string" of QCD, putting instead a half-integer spin string linked to the same fermions. Other approach should be to reintroduce the frontier conditions of Ramond strings. I do not see the exact method, and besides the composite fermion should have a compositeness scale a lot smaller than its bosonic partner. So I keep expecting results from experiments :-)

 

[CarlB]

Very nice!

It seems to me that the bootstrap principle doesn't have to imply that there's no subparticles. You'd get the same thing for an appropriate choice of preons.

 

[arivero]

Very nice!

It seems to me that the bootstrap principle doesn't have to imply that there's no subparticles. You'd get the same thing for an appropriate choice of preons.

Well, yes and not. There is the "anomaly matching condition", which restricts the choices of preons. But for colour and electromagnetism -non chiral forces- it could work.

 

[arivero]

Just in case someone is interested on quoting this idea and it is afraid of citing the internet forums, let me list the relevant papers in the arxiv.

The main corpus comes in three preprints:

http://arxiv.org/abs/0910.4793 Unbroken supersymmetry without new particles
http://arxiv.org/abs/0710.1526 Third Spectroscopy with a hint of superstrings
http://arxiv.org/abs/hep-ph/0512065 Supersymmetry with composite bosons

These preprints include some phenomenological information, leading to the suspect that something is going on in the low energy area. The two main puzzles are the Z decay width and the Koide identity, and there are some other minor coincidences. hep-ph/0507144 and hep-ph/0603145 are about this puzzle of Z decay and other electromagnetic decays. As a minimum, someone should have a theory explaining the correlation between the decay of neutral mesons (including sigma 0, perhaps as a pair diquark-quark). The Z scale could be a coincidence. Koide is first reviewed in hep-ph/0505220, framed in an internet campaign to lobby for this equation (Brannen has been very successfull with it).

Some minor hints about low energy come from Hans de Vries guessings. I reported about them in gr-qc/0603123 hep-ph/0606171 and hep-ph/0503104

 

[arivero]

See this new thread
https://www.physicsforums.com/showthread.php?t=457825
From 15=(1,3)+ (3,2) + (6,1), I suspect than I can relate the SU(3) sextet to quarks on one side and to the SU(2) triplet on another

Idea of the pairing:

top = bb,sd
charm= ss,bd
up = dd,sb
and the subgroup represented by the triplet ss, sd, dd
should be related to the triplet cc,cu,uu