Monday, March 14, 2011

Some TGD inspired comments about Higgs, ew symmetry breaking, and SUSY

In the following still some comments about TGD based view about symmetry breaking, Higgs, electroweak symmetry breaking, and SUSY. There are several unclear issues at the level of detais. This is thanks to my unforgivable laziness in writing down the details. The results from LHC are however so fascinating that they force me to win my laziness. In the following I try to clarify my thoughs.

1. Is the earlier conjectured pseudoscalar Higgs there at all?

Spin 1 gauge bosons and Higgs differ only by different spin direction of fermions at opposite wormhole throats. For spin 1 gauge bosons the 3-momenta at two wormhole throats cannot be parallel if if one wants non-vanishing spin component in the direction of moment. 3-momenta are most naturally opposite for the massless states at throats. This forces massivation for all gauge bosons and even graviton and this in turn requires Higgs even in the case of gluons.

Question: Could the parity properties of the couplings of gauge boson and corresponding Higgs transforming like 3+1 under SU(2) (this is due to the special character of imbedding space spinors) be exactly the same? Higgs would couple like a mixture of scalar and pseudoscalar to fermions just as weak gauge bosons couple and the mixture would be just the same. If there are no axial variants of vector gauge bosons there should exist no pseudoscalar Higgs. The nonexistence of axial variants of vector gauge bosons is suggested by quantum classical correspondence: only gauge bosons having classical space-time correlates as induced gauge potentials should be allowed, nothing else. Note that color variant of Higgs would exist and would be eaten by gluons to get mass.

2. Could Higgs mechanism lead to the disappearance of also Higgsinos?

The similarity of the construction of gauge bosons and Higgsinos as pairs of wormhole throats containing fermion and antifermion encourages to think that Higgs mechanism is invariant under supersymmetries. If so, also Higgsinos would be eaten and one would have massive super-symmetric gauge theory with fermions with photon and other massless particle possessing a tiny mass. This looks very simple. The testable implication would be that only weak gauginos should contribute to muon g-2 anomaly.

3. Electroweak symmetry breaking

The recent view about electroweak symmetry breaking is less than year old. The basic realization was that wormhole throats carrying elementary particle quantum numbers possess Kähler magnetic charge (in homological sense-CP2 has non-trivial second homology). This magnetic charge must be compensated and this is achieved if the particle wormhole throat is connected to a second wormhole throat by a magnetic flux tube. The second wormhole would carry a weak charge of neutrino pair compensating the weak isospin of the particle so that weak interactions would be screened above the weak length scale. For colored states the compensation could also occur in longer length scale and corresponds to color confinement.

This does not actually require the length scale of flux tubes associated with all elementary particles to be the weak length scale as I have thought. Rather, the flux tube length for a particle at rest could correspond to the Compton length of the particle. For instance, for electron the maximal flux tube length would be about 10-13 meters. For particles not at rest the length would get shorter by length contraction. For very light but massive particles such as photon and graviton the maximum length of flux tube would be very long. The interaction of very low energy photons and gravitons would be essentially classical and induced by the classical oscillations of induced gauge fields induced by a long flux tube connecting the interacting systems. For high energy quanta this interaction would be essentially quantal and realized as absorption of quanta with flux tube length -essentially wave length of quantum- much shorter than the distance between the interacting systems. Gravitational waves would interact essentially classically even when absorbed since absorption would mean that the flux tube would connects two parts of the measurement apparatus. For large hbar gravitons the length of flux tube could correspond to the distance between interaction systems.

A fascinating possibility is that electronic Cooper pairs of superconductors with large value of hbar, could correspond to long flux tubes with electron's quantum numbers at both ends. Maybe this takes place in high Tc super conductors.

4. Some details of the SUSY predictions

TGD SUSY differs from the standard SUSY in many respects.

  1. All fermionic oscillator operators assignable to the wormhole throats generate supersymmetries. These oscillator operators differ from ordinary ones in that they do not have momentum label and momentum can be only assigned to the entire state. Therefore the interpretation of all states assignable to wormhole throats as large SUSY multiplet is possible. This SUSY is badly broken and there is hierarchy of breakings defined by the interactions inducing the breaking in turn define by the quantum numbers of SUSY generators. For quark generators the breaking is largest and the smallest breaking is associated with the oscillator operators assignable to right-handed neutrinos since they have only gravitational interactions.

  2. The symmetry generators are not Majorana spinors and this does not lead to any difficulties as has been found. Only if one would try stringy quantization trying to define stringy diagrams in terms of stringy propagators defined by stringy form of super-conformal algebra, one would end up with difficulties. Majorana property is also excluded by the separate conservation of baryon and lepton number.

    For single wormhole throat one can see the situation in terms of N=2 SUSY with right handed neutrino and its antiparticle appearing as SUSY generators carrying conserved fermion number. One can classify the superpartners by their right-handed neutrino number which is +/-1. For instance, for single wormhole throat one obtains fermion and its partner containing νR pair, and fermion number 0 and fermion number 2 sfermions. In the case of gauge bosons and Higgs similar degeneracy is obtained for both wormhole throats.

  3. Since induced gamma matrices and modified gamma matrices are mixtures of M4 and CP2 gamma matrices right handed neutrino is mixed with the left handed neutrino meaning breaking of R-parity. The simplest decays of sparticles are of form P→P+ν and can be said to be gravitationally induced since the mixing of gamma matrices is indeed a characteristic phenomenon of induced spinor structure. Also more complex decays with neutrino replaced with charge lepton are possible. The basic signature is lonely lepton not possible in decays of weak bosons.

  4. The basic outcome of SUSY QFT limit of TGD (see this) is that wormhole throat can carry only spin 0,1/2,1 corresponding to fermion and fermion pair if one wants to obtain standard propagator: otherwise one obtains 1/pn, n>2 and this is not an ordinary particle pole. The reason is that one cannot assign to fermionic oscillator operators independent momenta but only common momentum so they propagate effectively collinearly.

    One can criticize this argument as being inconsistent with the twistorial approach combined with zero energy ontology implying that wormhole throats are massless even for on mass shell states. In this approach one in principle avoids completely the use of propagators which would of course diverge for on shell wormhole throats. Also for twistor diagrams the counterparts of virtual particles are massless and off shell. The so called region momentum replaces momentum in Grassmannian twistor approach and has a direct counterpart as eigenvalue of the modified Dirac operator so that the analog of propagator exists in TGD framework. Since QFT limit must be a reasonable approximation to the full theory, one might hope that the QFT based argument makes sense when one replaces momentum with region momentum (or pseudo momentum as I have called it in TGD framework).

  5. Should one allow both nuR and its antiparticle as SUSY generators? This would mean more states as in standard SUSY for which only anti-nuR would be allowed for fermion. This would assign to a given wormhole throat with fermion number 1 spin 1 and spin 0 super partner and companion of fermion containing nuR-anti-nuR pair. For this state however propagator would behave like 1/p3 should that again strong SUSY breaking would occur for this extended SUSY. Only one half of SUSY would be broken weakly by the mixing of M4 and CP2 gamma matrices appearing in modified gamma matrices: the mixing would not involve weak or color interactions but could be said to be gravitational but not in the sense of abstract for geometry but induced geometry. The breaking of symmetries by this mechanicsm would be a beautiful demonstration that it is sub-manifold geometry rather than abstract manifold geometry that matters. Again string theorists managed to miss the point by effectively elimating induced geometry from the original string model by inducing the metric of space-time sheet as an independent variable. The motivation was that it became easy to calculate! The price paid was symmetry breaking mechanisms involving hundreds of three parameters.

  6. Single wormhole contact could carry spin J=2 and give rise to graviton like state. If one constructs from this gravitino by adding right-handed neutrinos, and if SUSY QFT limit makes sense, one obtains particle with propagator decreasing faster at either throat so that gravitino in standard sense would not exist. This would represent strong SUSY breaking in gravitational sector. These results are of utmost importance since the basic argument in favor dimension D=10 or D=11 for the target space of superstring models is that higher dimensions would give fundamental massless particles with higher spin.

    Note that the replament of wormhole throats by flux tubes having neutrino pair at the second end of the flux tube complicates the situation since one can add right handed neutrino also to the neutrino end. The SUSY QFT criterion would however suggest that these states are not particle like.


At 9:15 AM, Blogger Ulla said...

You lazy ???? Not enough.


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