What about TGD interpretation?
- TGD predicts besides weak gauge bosons, Higgs, and pseudoscalar: about the prediction of pseudoscalar I became aware only now. This follows taking tensor products for spin-isospin representations formed by quarks but for some reason I had not noticed this. The mass scale of pseudoscalar Higgs is most naturally the same as that of scalar Higgs or of weak bosons and p-adic mass calculations allow to estimate its mass. Higgs mass 125 GeV is very nearly the minimal mass for p-adic prime p≈ 2k, k=89. The minimal mass for k=90 defining also the p-adic mass scale of weak bosons would be 88 GeV so that the interpretation as pseudo-scalar with k=90 might make sense (see this).
- This lower bound is somewhat smaller than 96 GeV but the estimate neglects effects related to isospin: doublet and complex doublet are actually predicted (or triplet and singlet when SU(2)w action is by automorphism on the 2× 2 matrix defined by the doublets rather than as left or right action on the doublets appearing as its rows/columns). Mass splitting looks natural and the neutral state might be the heavier one as in case of W,Z splitting.
- First of all, SUSY is there but it is very different from standard N=1 SUSY predicting Majorana fermions. The reason is that due to fermion number conservation theta parameters appearing in super-field must be replaced with fermionic - actually quark-like - oscillator operators. The simplest model predicts that theta parameters and their conjugates appearing in the super-fied correspond to quark oscillator operators in a number theoretic discretization of space-time surface. They thus anticommute non-trivially. Anticommutators are finite for cognitive representations for which space-time surface is replaced with a discrete set of points with preferred imbedding space coordinates in an extension of rationals.
- Super-spinor field is odd polynomial of creation operators and its conjugate is odd function of annihilation operators whereas the imbedding space coordinates appearing in bosonic action (Kahler action plus volume term) and modified super-Dirac action are replaced by imbedding space super-coordinates, which are polynomials in which super-monomials have vanishing total quark number and appear as sums of monomial and its conjugate to guarantee the hermiticity of the super-coordinate.
These assumptions guarantee that super-Dirac field describes local states with odd fermion number and propagators have the behavior required by statistics.
- In continuum variant of the theory the bosonic Wick contractions would give rise to infinities: this vanishing conforms with the vanishing of loops required quite generally by the number theoretical vision and implying discrete coupling constant evolution. This simplifies the analogs of Feynman diagrams appearing at the level of discrete "cognitive representations" to mere tree diagrams. In twistor approach the vanishing of loops means enormous simplification and implies behavior analogous to that in dual resonance models which initiated superstring models.
The vanishing of Wick contractions from super-space-time parts of the modified Dirac action and super-counterpart of classical action gives rise to conserved Noether currents having interpretation in terms of symmetries: the most natural interpretation is in terms of gigantic super-symplectic symmetries predicted by TGD. TGD predicts also their Yangian analogs multi-local symmetries.
- Super-symmetric vertices are just vacuum expectations of the action. In this picture leptons would be spartners of quarks as local 3-quarks composites. This little discovery I could have made four decades ago. The allowance of only quarks as fundamental fermions follows from SO(1,7) triality in number theoretic vision: here M8-M4×CP2 duality and the part of number theoretic vision involving classical number fields is needed. We would have been staring at super-symmetries for more than century! My heart bleeds for the unlucky colleagues still trying to find standard SUSY at LHC. I can only pray that these lost lambs of experimental and theoretical physics could find their way back to their shepherd.
- The quark numbers or protons and leptons would be opposite and matter antimatter asymmetry would mean preference of antiquarks to arrange into local triplets - leptons- whereas quarks would arrange to non-local triplets- baryons. Both (quark) matter and antimatter would have been in front of eyes all the time we have been producing literature about mechanisms possibly explaining the absence of antimatter.
CP breaking is necessary for this picture and twistor lift of TGD indeed predicts CP breaking term which would be due to the Kähler structure of Minkowski space required by twistor lift of TGD - also non-commutative quantum field theories predict it.
- What about SUSY breaking. It has been clear for a long time that the mass formulas could be same for the members of super-multiplet but that p-adic length scale could differ. I realized few weeks ago that the breaking of SUSY is universal and has very little to do with the details of dynamics. In the general case zero energy states are superpositions (mixtures) of states with different mass squared eigenvalues and M8-H duality allows to find an imbedding of M4 to M4 making mass squared vanishing for states without this mixing. For mixtures p-adic thermodynamics predicts the masses. That Minkowski space is a relative notion means obviously new view about the notion of mass.
For a summary of earlier postings see Latest progress in TGD.