As I saw Tommaso's posting about quark compositeness I was for a moment absolutely sure that quark compositeness in the sense of TGD has been discovered. Unfortunately my wishful thinking (or rather feeling!) was wrong. What has been found that there is no substructure at energy scales below 4 TeV. In any case it is worth of summarizing what compositeness would mean in TGD framework since the concept of substructure is a delicate notion.
The weak form of electric-magnetic duality, last summer's big theoretical discovery in TGD, forces to conclude that elementary particles in TGD Universe correspond to "weak strings", which are essentially magnetic flux tubes carrying opposite magnetic charges at their ends. The fermion at the first end is accompanied by a neutrino antineutrino pair at second end. The neutrino pair neutralizes weak isospin and in this manner causes weak confinement and screening which closely relates to TGD counterpart for particle massivation. I have explained at my blog gauge boson massivation based on this picture: see this.
One highly suggestive conclusion is that also photon gets massive by eating the remaining component of Higgs ( consisting of SU(2) triplet and singlet as gauge bosons rather than complex doublet) so that there would be no Higgs to be found at LHC.
What should be found (among other things) would be compositeness of both quarks, leptons, and intermediate gauge bosons. All of them would be string like objects -magnetic flux tubes with wormhole contacts with two throats at their ends of length of order weak scale. The weak string tension is the crucial parameter which does not however make itself visible through the masses of elementary particles which correspond to the lowest states. The first guess is in terms of weak mass scale in which case new physics would be easy to observe and might have been already observed. The second natural guess is that Mersenne prime M_89 characterizing weak bosons determines the tension. If so the tension would be 29=512 times hadronic string tension and by p-adic length scale hypothesis would correspond to about 512 times 1 GeV = .5 TeV.
I have also proposed that ordinary hadron physics characterized by Mersenne prime M107 has a scaled up variant of characterized by M89 with about 512 GeV string tension. The proposal is inspired by the observation that Mersenne primes seem to correspond to hadron like physics in TGD Universe: leptons e and tau correspond to Mersenne primes M127 and M107 and muon to Gaussian Mersenne with k=113 and there is evidence for leptopion like states formed by color octet excitations of these states for all three leptons. For electron evidence comes from seventies, for tau CDF anomaly provides the evidence, and there is also evidence in case of muon. It remains to be seen if both M89 hadronic physics and/or weak stringy physics is or neither of them are there. For details see this.
What makes the situation exciting since I do not have enough understanding to conclude whether the results say anything about the notion of weak string. One can say that below the length scale one would see quarks and leptons as particles without the weak screening is this what we have seen already for a long time above weak energy scale. Only time will show.
23 comments:
I have made a background picture for Keas research, and you are there also quite a lot. Hope it isn't miserably bad.
http://zone-reflex.blogspot.com/2010/10/on-background-of-matter.html
You are invited to talk for your scaling theory? Why electron:proton = 1:10? It is a bit difficult for me.
http://www.galaxyzooforum.org/index.php?topic=272147.msg504871#msg504871
Graham: "We do not need to complicate matters I think, although you are most welcome to try, by advocating an allo Planck distribution otherwise you have to change h, and c and address the required allo photon within the first generation of matter."
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 and in what sense. This is a delicate question. Topologically or at Fock space level and in what sense at Fock space level. In my own approach twistor program fixes the details to high degree.
All particles would however reduce to many particle states of elementary fermions with collinear light-like momenta at partonic 2-surfaces: this Fock space would have interpretation as a big SUSY multiplet. This is like building particles from legos. Also gravitons would reduce at fundamental level to bound states of fermions.
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 :-)
Interesting suggestion. The representations of SU(3) 3x3 give 6+3bar and you get antitriplet for a given pair of quarks. This would give 6x6 color triplets and you must get rid of 30 color triplets. You must also get electromagnetic and weak charges correctly. This must give additional conditions. For instance, you must drop charges 4/3 and -2/3 away so that you can have only UD and DD type pairs. This gives 9+9 pairs and you must drop still 13 unlucky ones from consideration;-). Maybe statistics helps here?
I do see not why fermions should be composite in this framework. Why compositeness of sfermions should require this?
In my own approach super-multiplets are obtained in rather analogous manner: simply as Fock states with parallel -actually identical light-like momenta- and ordinary fermion corresponds to the state with single oscillator operator for modes of spinor field at the light-like orbit of partonic 2-surface.
This forces a generalization of SUSY formalism to a a situation in which N can be large- even infinite. The componets of super field correspond to the Fock states. In this formalism the states with total F+Fbar =n have propagator proportional to 1/p^n. n>2 corresponds to a particle for which propagator decays faster than 1/p^2 so that these states do not correspond to ordinary particles.
This effectively reduces the SUSY to N=1 required by experiments. Right-handed neutrino would generate this SUSY.
Yes, statistics helps a lot for SU(3) colour. From 3x3bar=8+1, you can choose the singlet, and from 3x3 you go with 3bar. So a, say, ud combination admits tree colours via the 3bar, while uD is in the colour singlet, so neutral.
in the flavour side, you can see it as a SU(5) flavour game. For the colour singlets, you use 5x5bar=24+1. It you check the electric charges of the 24, you will see 6 +1, 6 with -1 and 12 neutrals. Bingo in this side.
For the colour triplets, it is 5x5=15+10, and the same with 5barx5bar. The representation here is the 15, and if you look again at the electric charge, you will see that it contains 6 states of charge -2/3 (pairing the U antiquarks) and 6 states of charge +1/3 (pairing the D antiquarks). Barring the adhoc dropping of the 4/3 charge, the pairing is amazingly perfect, and as I said, it needs a minimum of 3 generations and it becomes horrible (physical and group theoretically) for the solutions with more than 3 generations. Here the only requisite is to give a high mass to the top quark, so that it does not have bound states.
Yes, the formalism does not require compositeness to the fermions themselves. Still, it is tempting to try the same trick in the way you explain, by formalising it in Fock space in a way abstract enough. I have been unable to do it, so my initial claim "I am not sure... they could be".
(Clarification: With "pairing the U antiquarks", I mean that these states should be the superpartners of the tree U antiquarks, but of course when you build a Dirac fermion you want to combine particle and antiparticle, thus the 15 and the 15bar irreps here)
With this clarification in mind, we can look to the only serious problem of the sBootstrap: the six states UU,UC,CC,uu,uc,cc. First I considered two radical options: first option was to disregard them, second option to hope for a truncation mechanism putting them out of the spectrum. They are coloured and charged, so if they account for 18 states they really put a lot of pressure in model building.
But the more fascinating thing, I noticed lated, is that when you consider sypersymmetry you can not organize these suspected sfermions to partner with Dirac fermions. You could use four of them, and still you should have two unpaired. Or you could still think in generations, and then you have three generations of what? Fermions of two components.
Weyl or Majorana, but no Dirac. This is key, because both colour and electromagnetism are pure vector (no axial-vector) interactions, and Dirac is is requisite.
I did not understand the SU(5) but then noticed that you do not consider t quark at all. I do not understand why you drop it from consideration.
The following trial assumes all families-also t.
One can try to understand statistics by the constraints posed on scalar property, color triplet property and symmetry properties in family index which in TGD framework gives rise to dynamical SU(3) with fermion families forming a triplet. DD and UD give the correct charges so that the consideration can restricted to these. Electroweak degrees of freedom are frozen.
For UD type states you antisymmetrize in color to give antitriplet, antisymmetrization in spin gives scalar, you can antisymmetrize also in the index labeling three families so that you have dynamical SU(3). Electroweak degrees of freedom are frozen so that you get three antisymmetric representations and total antisymmetry. States are of form U_iD_j-U_jD_i in family index.
For DD type states antisymmetrization does not however work in family index. Therefore the states would be symmetric and break statistics. I do not know how to proceed.
Yep, you are right, the family index does not work. It was a surprise to discover that the trick was to use the flavour index instead of the family index. Honestly, I have not checked the underlying mechanism telling that we must choose the 24 in 5x5bar = 24 +1 and the 15 in 5x5=15+10. I was happy enough after finding that representation theory was producing the correct answer.
Why SU(5) and not, you ask, SU(6) flavour? Because the first five quarks are massless from the point of view of the electroweak scale, while the last one, the top, is massive. If this argument is not enough, you can bring a dynamic one, involving the QCD scale, the Weak scale and the mass of the top: the halflife of the top quark, decaying via weak boson, is shorter than the halflife of top mesons, decaying via strong interaction. Or, to say it short, any quark more massive than about 150 GeV does not produce bound states.
It is possible to allow for any number of "very massive quarks" and ask the pairing to be exact. If one considers the neutrinos, the solution becomes unique. And if one forgets about them and allows for any number of neutral particles, there is an infinite of solutions but they are really awful. For instance, the next solution would be to have 14 generations but a "light flavour" group of 7 "down" and 2 "up" quarks.
The most horrible consequence of the conjecture of compositeness of superpartners is that it can cause a Damascus Road Conversion. It happened to me and I still feel pain. I strongly dislike string theory. For St Paul it was easy, to go from the dominant majority to the opressed and pursued minority. For a person in the minority - Non Commutative Geometry - it is sad to be pushed towards the research line of the majority.
By the way, I noticed that my argument excluding DD type states was wrong! D_iD_j-D_jD_i are of course possible by anticommutativity. The situation is exactly similar to antisymmetrization in color.
One must however assume symmetry in electroweak isospin and this means that one has all states DD, UU, and UD+DU and this gives also states with charge 4/3 and-2/3 so that the states are not related by N=1 SUSY to quarks.
Compositeness is a delicate concept since it can have many meanings. In TGD framework it seems
that compositeness in the sense that particles are wormhole pairs is the most natural and perhaps even unavoidable. For fermions one however excepts that in excellent approximation they behave like single wormhole throat whereas bosons would behave like single wormhole contact. Second wormhole throat/ contact would only take care of screening of weak interactions at length scales longer than weak scale.
Supersymmetry in the sense that wormhole throat carries parallely moving fermions is mathematically equivalent to the description in terms of a generalization of super fields and these particles for which propagators decay faster than 1/p or 1/p^2 are the only prediction.
You mentioned that you belong to non-commutative minority. Be happy: you are not after all the only member of your minority as I am;-)!
I do not know much about non-commutative geometry. I only know that hyper-finite factors relate closely to this mathematics and HFFs have a very natural place in TGD since the spinors of the world of classical worlds correspond to many fermion Fock states, which define hyper-finite factor of type II_1. I have written some chapters in my attempts to understand their physical and mathematical role. Some key points about physical interpretation,
a) HFFs and non-commutative geometry for spinors would have nothing to do with Planck scale.
Rather, the inclusions of HFFs would have interpretation in terms of finite measurement resolution in TGD framework. The action of included factor creates states which do not differ in the measurement resolution used.
b) Non-commutative variants of finite tensor powers of ordinary spinors would correspond to factors spaces defined by HFF factor defined by included HFF.
c) Braids would be the space-time correlate for finite measurement resolution and would define naturally effective discretizations of light-like 3-surface with strands carrying fermion number. They would define TQFTs and thus also quantum groups. One can say that the many-fermion states at the light-like orbits of partonic two surfaces give rise to a topological QFT and Universe is a topological quantum computer even at elementary particle level. Anyonic physics could correspond to large hbar and macroscopic partonic 2-surfaces.
One amusing finding suggesting a connection between TGD and Connes's approach to standard model.
a) Connes's idea about Higgs involves what I would call Z_2 bundle over Minkowski space. Wormhole contacts indeed reduce to pairs of M^4 points at the point like limit.
b) Massivation in this approach follows without any mention of Higgs expectation and wormholes as pairs of wormhole throats is essential for this. In fact, Higgs field as also gauge boson fields are only fictive concepts used when one zooms out and neglects the compositeness in TGD sense.
c) More concretely, gauge bosons are pairs of massless wormhole throats (wormhole contacts) and since fermion and antifermion at opposite throats must have parallel spin projections, their 3-momenta must be antiparallel: therefore massivation unavoidably occurs. Also photon seems to become massive and would eat the neutral Higgs (SU(2) triplet + singlet in TGD framework).
What is frustrating for a physicist like me is that the mathematics of HFFs is extremely difficult and tor obvious reasons there exists no vocabulary from mathematics to physics.
I don't want to disturb this discussion, but a simple question. I read about asymptotic degrees of freedoms, how the strength of gluons diminish with an increasing branching at high energies. (Wilzcek) How can this be related to wormholes?
Hmm, -2/3 is right. It is the charge of an up antiquark. And the colour charge, properly symmetrized, is also the charge of an antiquark. I do not see any problem on this point.
4/3 _IS_ a problem, but perhaps also a feature, as I told above. Count the combinations, you only have three of them (and three of -4/3, of course). You can not do three families of Dirac Spinors as superpartners, you need to try Weyl or Majorana, with the paradox that colour and electromagnetism can not work on them, these forces need to have Dirac particles. So either the 4/3 fermion partners are truncated away, or they are paradoxically neutrals.
Indeed the Z2xSpaceTime idea is a good introduction to NCG, and a lot of people did it as a training. And even published it. In fact my first intro to NCG was via a lecture of Coquereaux using such example.
Funny you mention the vocabulary problem. Connes approach to didactics is to do "vocabulaty tables" traslating from ordinary geometry to NCG. A lot of operators have a role as differential forms and/or infinitesimal objects, traces appear as integration, etc...
Let me note that part of the problem when trying to read TGD is also the vocabulary, because you have named objects as you advanced in your research, and it is not intuitive. For instance, a "wormhole" is exactly a solution to Einstein equations connecting two distant parts of space? Or just something that "looks as a wormhole" because it implies such connection? Nor to speak of the name itself, TGD :-) I would say that these "vocabulary improvements", needed as they could be, have at the end backfired.
Myself, I was tempted one or two times of giving a name to these rare 4/3 states, and I have not yet decided to use one, neither from the commonly known particles nor from my own personal impressions. Probably it is better to left them unnamed as they are, till more research.
I tried to understand Connes's basic idea about identification of ds as Dirac operator but failed completely. I understand that if operator has vanishing trace for HFF of type II_1 (trace of unit operator equal to 1) it represents infinitesimal in operator sense. But why infinitesimal distance should be Dirac operator.
This language barrier is nasty. I have been too lazy to build a systematic vocabulary so that I explain again and again same things. You mentioned wormholes. Wormhole contacts are only topologically like their general relativistic cousins called Einstein-Rosen bridges. Indeed, the induced metric inside the contact has however Euclidian signature implies which unique 3-D light-like throats at which the signature of the metric changes. These throats are carriers of elementary particle numbers.
Manyfermion states at throats define the spinors in the world of classical worlds. Small deformations of the throats are analogous to bosonic degrees of freedom analogous to stringy degrees of freedom. Light-like 3-dimensionality implies the extension of super-conformal symmetries of super-string models.
Wormhole throats define the lines of generalized Feynman diagrams. They meet at partonic 2-surfaces defining the fundamental vertices.
The size of throat is in CP_2 directions about 10^4 Planck lengths, CP_2 radius. In M^4 degrees of freedom it can be larger. A concrete model for the region of Eudlian signature is as a small deformation of CP_2 type vacuum extremal which has light-like curve as 1-D M^4 projection. Metrically it is its equivalent with CP_2. Hawking and others discovered CP_2 as gravitational instanton. M^4xCP_2 geometry explains elementary particle quantum numbers if family replication is due to the genus of the partonic 2-surface.
Topological Geometrodynamics was suggested by Wheeler who wrote a referee statement about my first published article which became my thesis around 1982.
Wheeler, now that you mention it I think I read about the origin of the name in some paper of you time ago.
About NCG, there is an intermediate "step" between a infinitesimal operator and dirac operator: F=D/|D|, having only the topological information but losing the metric one. So we have three levels: measure theory - topology - geometry.
I think Connes means with Dirac operator something different from the ordinary one. The zero modes of D are problematic in F and I understand that these are just the interesting ones from the topological point of view (difference n_+-n_- of the positive and negative eigenvalues as carrier of topological information).
For standard Dirac operator in CP_2 right-handed neutrino correspond to SUSY and also to non-trivial second homology of CP_2 implying also homological magnetic monopoles which turned out to crucial for understanding elementary particles.
In TGD framework the simplest Dirac operator for induced spinor structure is obtained by identifying gamma matrices as projections of imbedding space gamma matrices. Spinors are imbedding space spinors. There is however internal consistency condition requiring that space-time surfaces are minimal surfaces in this case: this guarantees that D_mu Gamma^mu=0 guaranteeing hermiticity. This also guarantees super-symmetry.
Since Kahler action defines the dynamics one must modify the Dirac by replacing contravariant gammas by modified gammas obtained by contracting canonical momentum densities of Kahler action with imbedding space gammas.
At light-like wormhole throats modified Dirac operator cannot involved metric and Chern-Simons term for Kahler gauge potential indeed gives a well-define Dirac operator whose generalized eigenvalues correspond to pslash for Dirac operator in M^4.
An attractive interpretation for the effective metric defined by the anticommutators of the modified gamma matrices for Kahler action in space-time interior (distinct from the induced metric) is in terms of condensed matter physics. The eigenvalues of the effective metric have interpretation in terms of effective light velocities in three orthogonal directions identified in terms of velocities analogous to sound velocities. Therefore condensed matter physics could be interpreted in terms of holography.
My understanding (btw, the Red Book is now freely available in Connes website) is that F is prior to D, the division being a kind of mnemotecnic trick.
A good bunch of the NCG mainstream is dedicated to proof index theorems, so I'd guess that the use of zero nodes is well understand. Again, they have a language problem when traslating to theoretical physics, because there is a lot of stuff on analytical vs topological indexes, which is unusual in hep-th, even in math-ph.
Yes, I loaded Connes's book for few years ago and read some parts of it.
Neither ATLAS nor CMS can find quark compositeness if quarks are composed of light fermions. There is a long list of problems of the Standard Model that points towards quark compositeness. The first one is a HUGE problem: How to explain the internal electric charge distribution of the nucleons (found by Hofstadter in 1956) with 3 point-like quarks? Please, find more information in the paper The Higgs-like Bosons and Quark Compositeness (submitted to publication in Frontiers in Science). the paper is available on the web.
Thank you for the link, Mario.
The low energy sector hadron physics is still poorly understood. We do not understand non-perturbative QCD: even its mathematical existence is questionable.
My immediate reflex-like counter argument to your proposal is question. How quark compositeness - a phenomenon at very short distances below weak scale - might help in a problem related to long scales of order hadron size scale? There are more than two orders of magnitudes between these scales.
My own expectation would be that the non-trivial structure of space-time - hadron space-time sheets and parton space-time sheets - could be the resolution of the problems related to hadron length scale. Also I expect however new short scale physics: scaled up variant of hadron physics with mass scale 512 times higher than that of hadron physics. This does not however mean quark compositeness but zooming as phase transitions transforming quarks of two different hadron physics to each other - very roughly.
The findings from RHIC and now from LHC suggest that string like objects - mesons of the new hadron physics - decaying to ordinary hadrons by a sequence of phase transitions increasing their p-adic length scale might indeed be there.
It is amusing that the relevant anomalies allowing to proceed from the recent dead end in particle physics (naturalness problem due the non-existence of SUSY at recent LHC energies, see http://www.math.columbia.edu/~woit/wordpress/?p=5946) could have been available already 7 years ago! We are conservative and see only what we expect to see. If there is something our left brain quickly cooks up a narrative explaining the anomaly: now the narrative saving standard QCD relies on some loose arguments involving AdS/CFT correspondence.
Post a Comment