Cautious conclusions concerning gauge boson massivation

The discussion of TGD counterpart of Higgs mechanism gives support for the following general picture.

1. p-Adic thermodynamics contributes to the masses of all particles including photon and gluons: in these cases the contributions are however small. For fermions they dominate. For weak bosons the contribution from Euclidian Higgs is dominating as the correct group theoretical prediction for the W/Z mass ratio demonstrates. The mere spin 1 character for gauge bosons implies that they are massive in 4-D sense. By conformal invariance Euclidian pion does not have tachyonic mass term in the analog of Higgs potential and this saves from radiative instability which standard N=1 SUSY was hoped to solve. Therefore the usual space-time SUSY associted with imbedding space in TGD framework is not needed, and there are strong arguments suggesting that it is not present. For space-time regarded as 4-surfaces one obtains 2-D super-conformal invariance for fermions localized at 2-surfaces and for right-handed neutrino it extends to 4-D superconformal symmetry generalizing ordinary SUSY to infinite-D symmetry.

2. There are several conjectures related to ZEO.
   1. The basic conjecture related to the perturbation theory is that wormhole throats are massless on mass shell states in imbedding space sense: this would hold true also for virtual particles and brings in mind what happens in twistor program. The recent progress in the construction of n-point functions leads to explicit general formulas for them expressing them in terms of a functional integral over four-surfaces. The deformation of the space-time surface fixes the deformation of basis for induced spinor fields and one obtains a perturbation theory in which correlation functions for imbedding space coordinates and fermionic propagator defined by the inverse of the modified Dirac operator appear as building bricks and the electroweak gauge coupling of the modified Dirac operator define the basic vertex. This operator is indeed 2-D for all other fermions than right-handed neutrino.

   2. The functional integral gives some expressions for amplitudes which resemble twistor amplitudes in the sense that the vertices define polygons and external fermions are massless although gauge bosons as their bound states are massive. This suggests perturbation at imbedding space level such that fermionic propagator is defined by longitudinal part of M⁴ momentum. Integration over possible choices M²⊂ M⁴ for CD would give Lorentz invariance and transform propagator terms to something else. As a matter of fact, Yangian invariance suggests general expressions very similar to those obtained in N=4 SUSY for amplitudes in Grassmannian approach.
   3. Another conjecture is that gauge conditions for gauge bosons hold true for longitudinal (M²-) momentum and automatically allow 3 polarization states. This allows to consider the possibility that all gauge bosons are massless in 4-D sense. By above argument this conjecture must be wrong. Could one do without M² altogether? A strong argument favoring longitudinal massivation is from p-adic thermodynamics for fermions. If p-adic thermodynamics determines longitudinal mass squared as a thermal expectation value such that 4-D momentum always light-like (this is important for twistor approach) one can assume that Super Virasoro conditions hold true for the fermion states. There are also number theoretic arguments and supporting the role of preferred M². Also the condition that the choice of quantization axes has WCW correlates favors M² as also the construction of the generalized Feynman graphs analogous to non-planar diagrams as generalization of knot diagrams.

The ZEO conjectures involving M² remain open. It the conjecture that Yangian invariance realized in terms of Grassmannians makes senseit could allow to deduce the outcome of the functional integral over four-surfaces and one could hope that TGD can be transformed to a calculable theory.

For details and background see the new chapter Higgs or something else? of “p-Adic Length Scale Hypothesis and Dark Matter Hierarchy”, and the article Is it really Higgs?.