### The role of the right-handed neutrino in TGD based view about SUSY

The general ansatz for the preferred extremals of Kähler action and application of the conservation of em charge to the modified Dirac equation have led to a rather detailed view about classical and TGD and allowed to build a bridge between general vision about super-conformal symmetries in TGD Universe and field equations.

- Equivalence Principle realized as Einstein's equations in all scales follows directly from the general assatz for preferred extremals implying that space-time surface has either hermitian or Hamilton-Jacobi structure (which of them depends on the signature of the induced metric).

- The general structure of Super Virasoro representations can be understood: super-symplectic algebra is responsible for the non-perturbative aspects of QCD and determines also the ground states of elementary particles determining their quantum numbers.

- Super-Kac-Moody algebras associated with isometries and holonomies dictate standard model quantum numbers and lead to a massivation by p-adic thermodynamics: the crucial condition that the number of tensor factors in Super-Virasoro represention is 5 is satisfied.

- One can understand how the Super-Kac-Moody currents assignable to stringy world sheets emerging naturally from the conservation of em charge defined as their string world sheet Hodge duals gauge potentials for standard model gauge group and also their analogs for gravitons. Also the conjecture Yangian algebra generated by Super-Kac-Moody charges emerges naturally.

- One also finds that right handed neutrino is in a very special role because of its lacking couplings in electroweak sector and its role as a generator of the least broken SUSY. All other modes of induced spinor field are restricted to 2-D string world sheets and partonic 2-surfaces. Right-handed neutrino allows also the mode delocalized to entire space-time surface or perhaps only to the Euclidian regions defined by the 4-D line of the generalized Feynman diagrams.

In fact, in the following the possibility that the resulting sparticles cannot be distinguished from particles since the presence of right handed neutrino is not seen in the interactions and does not manifest itself in different spin structures for the couplings of particle and sparticle. This could explain the failure to detect spartners at LHC. Intermediate gauge boson decay widths however require that sparticles are dark in the sense of having non-standard value of Planck constant. Another variant of the argument assumes that 4-D right handed neutrinos are associated with space-time regions of Minkowskian signature and SUSY is defined for many-particle states rather than single particle states. It should be emphasized that TGD predicts that all fermions act as generators of badly broken supersymmetries at partonic 2-surfaces but these super-symmetries could correspond to much higher mass scale as that associated with the delocalized right-handed neutrino. The following piece of text summarizes the argument.

A highly interesting aspect of Super-Kac-Moody symmetry is the special role of right handed neutrino.

- Only right handed neutrino allows besides the modes restricted to 2-D surfaces also the 4D modes delocalized to the entire space-time surface. The first ones are holomorphic functions of single coordinate and the latter ones holomorphic functions of two complex/Hamilton-Jacobi coordinates. Onlyν
_{R}has the full D=4 counterpart of the conformal symmetry and the localization to 2-surfaces has interpretation as super-conformal symmetry breaking halving the number of super-conformal generators.

- This forces to ask for the meaning of super-partners. Are super-partners obtained by adding ν
_{R}neutrino localized at partonic 2-surface or delocalized to entire space-time surface or its Euclidian or Minkowskian region accompanying particle identified as wormhole throat? Only the Euclidian option allows to assign right handed neutrino to a unique partonic 2-surface. For the Minkowskian regions the assignment is to many particle state defined by the partonic 2-surfaces associated with the 3-surface. Hence for spartners the 4-D right-handed neutrino must be associated with the 4-D Euclidian line of the generalized Feynman diagram.

- The orthogonality of the localized and de-localized right handed neutrino modes requires that 2-D modes correspond to higher color partial waves at the level of imbedding space. If color octet is in question, the 2-D right handed neutrino as the candidate for the generator of standard SUSY would combine with the left handed neutrino to form a massive neutrino. If 2-D massive neutrino acts as a generator of super-symmetries, it is is in the same role as badly broken supers-ymmeries generated by other 2-D modes of the induced spinor field (SUSY with rather large value of
*N*) and one can argue that the counterpart of standard SUSY cannot correspond to this kind of super-symmetries. The right-handed neutrinos delocalized inside the lines of generalized Feynman diagrams, could generate*N=2*variant of the standard SUSY.

**1. How particle and right handed neutrino are bound together?**

Ordinary SUSY means that apart from kinematical spin factors sparticles and particles behave identically with respect to standard model interactions. These spin factors would allow to distinguish between particles and sparticles. But is this the case now?

- One can argue that 2-D particle and 4-D right-handed neutrino behave like independent entities, and because ν
_{R}has no standard model couplings this entire structure behaves like a particle rather than sparticle with respect to standard model interactions: the kinematical spin dependent factors would be absent.

- The question is also about the internal structure of the sparticle. How the four-momentum is divided between the ν
_{R}and and 2-D fermion. If ν_{R}carries a negligible portion of four-momentum, the four-momentum carried by the particle part of sparticle is same as that carried by particle for given four-momentum so that the distinctions are only kinematical for the ordinary view about sparticle and trivial for the view suggested by the 4-D character of ν_{R}.

- If ν
_{R}behaves as an independent unit not bound to the particle it would continue un-scattered as particle scatters: sparticle would decay to particle and right-handed neutrino. If ν_{R}carries a non-negligible energy the scattering could be detected via a missing energy. If not, then the decay could be detected by the interactions revealing the presence of ν_{R}. ν_{R}can have only gravitational interactions. What these gravitational interactions are is not however quite clear since the proposed identification of gravitational gauge potentials is as duals of Kac-Moody currents analogous to gauge potentials located at the boundaries of string world sheets. Does this mean that 4-D right-handed neutrino has no quantal gravitational interactions? Does internal consistency require ν_{R}to have a vanishing gravitational and inertial masses and does this mean that this particle carries only spin?

- The cautious conclusion would be following: if delocalized ν
_{R}and parton are un-correlated particle and sparticle cannot be distinguished experimentally and one might perhaps understand the failure to detect standard SUSY at LHC. Note however that the 2-D fermionic oscillator algebra defines badly broken large*N*SUSY containing also massive (longitudinal momentum square is non-vanishing) neutrino modes as generators.

**2. Taking a closer look on sparticles**

It is good to take a closer look at the delocalized right handed neutrino modes.

- At imbedding space level that is in cm mass degrees of freedom they correspond to covariantly constant CP
_{2}spinors carrying light-like momentum which for causal diamond could be discretized. For non-vanishing momentum one can speak about helicity having opposite sign for ν_{R}and ν_{R}bar. For vanishing four-momentum the situation is delicate since only spin remains and Majorana like behavior is suggestive. Unless one has momentum continuum, this mode might be important and generate additional SUSY resembling standard*N*=1 SUSY.

- At space-time level the solutions of modified Dirac equation are holomorphic or anti-holomorphic.

- For non-constant holomorphic modes these characteristics correlate naturally with fermion number and helicity of ν
_{R}. One can assign creation/annihilation operator to these two kinds of modes and the sign of fermion number correlates with the sign of helicity.

- The covariantly constant mode is naturally assignable to the covariantly constant neutrino spinor of imbedding space. To the two helicities one can assign also oscillator operators {a
_{+/-},a^{†}_{+/-}}. The effective Majorana property is expressed in terms of non-orthogonality of ν_{R}and and ν_{R}bar translated to the the non-vanishing of the anti-commutator {a^{†}_{+},a_{-}}= {a^{†}_{-},a_{+}}=1. The reduction of the rank of the 4× 4 matrix defined by anti-commutators to two expresses the fact that the number of degrees of freedom has halved. a^{†}_{+}=a_{-}realizes the conditions and implies that one has only*N*=1 SUSY multiplet since the state containing both ν_{R}and ν_{R}bar is same as that containing no right handed neutrinos.

- One can wonder whether this SUSY is masked totally by the fact that sparticles with all possible conformal weights n for induced spinor field are possible and the branching ratio to n=0 channel is small. If momentum continuum is present, the zero momentum mode might be equivalent to nothing.

- For non-constant holomorphic modes these characteristics correlate naturally with fermion number and helicity of ν

What can happen in spin degrees of freedom in super-symmetric interaction vertices if one accepts this interpretation? As already noticed, this depends solely on what one assumes about the correlation of the four-momenta of particle and ν_{R}.

- For SUSY generated by covariantly constant ν
_{R}and ν_{R}bar there is no neutrino four-momentum involved so that only spin matters. One cannot speak about the change of direction for ν_{R}. In the scattering of sparticle the direction of particle changes and introduces different spin quantization axes. ν_{R}retains its spin and in new system it is superposition of two spin projections. The presence of both helicities requires that the transformation ν_{R}→ ν_{R}bar happens with an amplitude determined purely kinematically by spin rotation matrices. This is consistent with fermion number conservation modulo 2.*N*=1 SUSY based on Majorana spinors is highly suggestive.

- For SUSY generated by non-constant holomorphic and anti-holomorphic modes carrying fermion number the behavior in the scattering is different. Suppose that the sparticle does not split to particle moving in the new direction and ν
_{R}moving in the original direction so that also ν_{R}or ν_{R}bar carrying some massless fraction of four-momentum changes its direction of motion. One can form the spin projections with respect to the new spin axis but must drop the projection which does not conserve fermion number. Therefore the kinematics at the vertices is different. Hence*N*=2 SUSY with fermion number conservation is suggestive when the momentum directions of particle and ν_{R}are completely correlated.

- Since right-handed neutrino has no standard model couplings, p-adic thermodynamics for 4-D right-handed neutrino must correspond to a very low p-adic temperature T=1/n. This implies that the excitations with higher conformal weight are effectively absent and one would have
*N*=1 SUSY effectively.

The simplest assumption is that particle and sparticle correspond to the same p-adic mass scale and have degenerate masses: it is difficult to imagine any good reason for why the p-adic mass scales should differ. This should have been observed -say in decay widths of weak bosons - unless the spartners correspond to large hbar phase and therefore to dark matter . Note that for the badly broken 2-D N=2 SUSY in fermionic sector this kind of almost degeneracy cannot be excluded and I have considered an explanation for the mysterious X and Y mesons in terms of this degeneracy (see this).

- LHC suggests that one does not have N=1 SUSY in standard sense. Could spartners correspond to dark matter with a large value of Planck constant and same mass? Or could 4-D right-handed neutrino exists only in the Minkowskian regions where they define superpartners of many particle states rather than single particle states? Could the reason be that for CP
_{2}type vacuum extremals modified gamma matrices vanish identically? Could this be used to argue that 4-D right-handed neutrinos cannot appear in the lines of generalize Feynman graphs which involve deformations of CP_{2}vacuum extremals?

For more details see the new chapter The recent vision about preferred extremals and solutions of the modified Dirac equation of "Quantum TGD as Infinite-Dimensional Geometry" or the article with the same title.

## 18 Comments:

You are busy.

Look here: http://www.physics.mcmaster.ca/ElementaryParticle/home/the-higgs

At CERN they have just provided the first experimental evidence that this picture of the vacuum having physical properties is right. They did so by exciting a wave in the vacuum, which in their experiment looks like a new type of particle.

At wikipedia there were the Higgs added yesterday, as scalar boson, removed today.

And http://www.physics.mcmaster.ca/ElementaryParticle/

Despite the great success the Standard Model has enjoyed when tested over the decades since its discovery, recent years have revealed signs of incipient failure. In particular, these new-found flaws indicate that it is very likely to fail at the distances that are just now becoming accessible at the highest-energy accelerators. The following paragraphs summarize the evidence that the Standard Model is now failing.

Almost everyone say that this means problems for SM. And they used a new statistical/analytical tool, not Monte Carlo. The same thing they tried with the 145 GeV bump, which failed.

People are realizing what the data really tell about Higgs. I was really surprised when Paula Eerola representing Finland in either CMS or ATLAS - I do not remember which - was completely convinced that it is Higgs. But for people who have made their professional career with Higgs, want strongly to retain their beliefs.

The most phanatic believers on Higgs seem to be Peter Woit and Lubos Motl. Woit because he desperately wants that no new physics is there. His blood enemy Motl because he believes on standard SUSY and superstrings and the underlying GUT paradigm.

In the middle of Higgsteria one easily forgets what really matters in theoretical physics. This is conceptual simplicity and elegance of the theory. This criterion is a real theory killer and is lethal for the mainstream theories developed during last decades.

I was lucky. After the latest successes I can rather safely conclude that TGD is an integrable theory, which means solvability, and I have more or less solved it. Einstein's theory as again and again demonstrated its power to survive experimental tests and this is due to one simple fact: GRT is based on deep principles. TGD generalizes these principles.

More or less? Hope the first :) It means more free time. This Higgs 'discovery' can be a good thing.

3:3:1 model?

http://arxiv.org/pdf/0801.0036

Look at this! http://arxiv.org/abs/1207.3612

To Ula:

The first link is about right handed neutrino. This is mystery particle of standard model but for some reason it has not received the attention that it deserves. Similar forgotten problem is the stability of proton: it should decay if GUT approach is correct but does not. After all, new physics begins from the problem of the old physics. These strange neglects of empirical facts reflect the deadly sin of theoreticians: arrogance, even arrogance towards Nature. And we know what the price of sin is: in this case it includes intellectual death.

How right handed and left handed neutrinos having no standard model couplings combine to a massive particle? This is one question. In TGD view about SUSY right handed neutrino as generator of the least broken conformal supersymmetries even extended to 4-D context has an absolutely central role in the construction of the theory. It gives for SUSY partners also a concrete interpretation.

http://phys.org/news/2012-07-source-anomaly.html

Look at this! Orbital angular momentum for photons! And they give different results depending on rotation! Spin 1 turns out to be odd with destructive interferens. Maybe this is simple, but not for me. So much work has been done on photon interference.

http://www.physics.gla.ac.uk/Optics/play/photonOAM/

I get a strong feeling the anyons tell us a very important story. Why are they intermediate? Because they are ground or minimal energy level for MATTER, half is imaginary.

Look also at http://arxiv.org/PS_cache/arxiv/pdf/1008/1008.4752v1.pdf

bosons condensed into the energy minima of an F-band of a bipartite square optical lattice. Momentum spectra indicate that a truly complex-valued staggered angular momentum superfluid order is established. The corresponding wave function is composed of alternating local F2x3−3x + i F2y3−3y-orbits and local S-orbits residing in the deep and shallow wells of the lattice, which are arranged as the black and white areas of a checkerboard.

Look at the picture e.

Compare http://mathworld.wolfram.com/Chessboard.html inverse chessboard and infinite chessboard reflected on a sphere.

Is really the sphere the vacuum point? The Higgs field in 1D? So we are chasing ghoasts? What does the 125 GeV correspond to? Some kind of resolution point? How does it behave with different amounts of energy input? Maybe it also changes?

And spin 2 particle, is it quasic? The chessboard formation is also seen in carbon lattice made of Dirac fermions.

This is probably stupid :)

You can delete it if it is too stupid. I thought it would be a good 'explanation' for the basic energy level and 'homeostatics'.

I think 'the chessboard formation' is not bad. It can also be linked to E8 and Golden ratio. And half imaginary it can be linked to DM.

The point is that IT IS NOT FLAT.

I try to look for a link p-adics and E8 but there is so much text. As instance a google search landed here.

http://tgd.wippiespace.com/public_html/pdfpool/rgflow.pdf

Can y tell more about it.

Matti, my blogspot today,

check it out and tell me from the TGD view if it is as important as I think it is- for me it confirms a lot of our approaches that already dwell within or beyond it in the new physics.

The PeSla www.pesla.blogspot.com

Ulla? what is not flat? :-)

http://www.sciencedaily.com/releases/2012/07/120719132949.htm

Oh, sorry, Ulla a direct link on science daily

Oh, and Ulla,

The chessboard stuff- well, that is what my quasics has been all about :-) Let us not let the established scientists take from people like Matti and Kea and others what we have seen all along.

PeSla,

Ye, I thought of you, and the quasic fields, actually. But these are only results of something deeper. E8 is a deep symmetry, linked to golden ratio, Fibonnaci etc.

I found the Lisi text hidden in a miscellanous file. http://tgdtheory.com/public_html/pdfpool/misc.pdf

3.fermions? 3-leptons? Note that magnetism (amd electricity ?) comes from interactions with bosons, and is de facto 'carrying' light without environmental influence. I have still difficulties understanding how that happen. Gravity (holography?) invoke on this. So maybe some of the bosons are transferred into the forces, creating mass that way? So, even photons can gain 'mass' in this way. Bosons are much misunderstood?

"something as mild as interacting waves could create something as extreme as a space-time singularity,"

also in Black holes

http://www.newscientist.com/article/dn22082-chemical-bond-discovered-that-only-exists-in-space.html

http://physicsworld.com/cws/article/news/2012/jul/20/new-chemical-bonds-possible-in-extreme-magnetic-fields

Magnetic body? The sphere has four halves? Superposition - quantization? Longitudinal and transvere lines, as Matti said. This is not always about angles only? But I need to study this question much more.

And to search for something special in the TGD texts are very troublesome. although I know it is there somewhere. So, I thought it was better to ask, sorry for that.

The NS link: Because the electrons in these bonded atoms occupied anti-bonding orbitals – which is forbidden in both types of known chemical bond – the researchers say this is a new type of bond. They have dubbed it

"perpendicular paramagnetic bonding".Ahh the perpendicular... good Ulla

The E8 idea (and all the good questions raised in that pdf TGD article of 2011) is much deeper than your pointing out how deep it is to me... after all this n-dimensional world I inhabited since at least 1964 long before string theory, even before common knowledge of quarks and quasars.

Synchronicity as it seems to be here (that perhaps a superperpendicularity of our bonds,

I do address today in my post Heart of the Matter some of the 136 issues and try to describe there is something beyond these merging of "dark atoms" in conception that are well, superdark structural cores going way beyond a simple four space chess board.

I await Matti's view and add a question, Fibonacci and all, can there be a 144 particle somehow in his system if it can be in a sense as concrete as his primes and these mean what going to infinity.

Note, my numbers are not simply the Lie group view- more finite and now more quasifinite. The maximum symmetery hidden or not is way beyond the idea of octonions even if the complex and real can meet if only in theory to the shockwave at the same ideal place.

The PeSla

Of course it is deep when it is a basic symmetry.

2-adic numbertrees are also quasic. http://en.wikipedia.org/wiki/Pontryagin_dual

http://www.maths.gla.ac.uk/~ajb/dvi-ps/padicnotes.pdf

The interesting thing would be if this directly can be linked to Carbon (as hexagon). This is obviously too simple for Matti.

http://en.wikipedia.org/wiki/E8_lattice

In string theory, the heterotic string is a peculiar hybrid of a 26-dimensional bosonic string and a 10-dimensional superstring. In order for the theory to work correctly, the 16 mismatched dimensions must be compactified on an even, unimodular lattice of rank 16. There are two such lattices: Γ8⊕Γ8 and Γ16 (constructed in a fashion analogous to that of Γ8). These lead to two version of the heterotic string known as the E8×E8 heterotic string and the SO(32) heterotic string.

Missing bosons are compactified??? Just like that?

Post a Comment

<< Home