My attitude to Higgs has developed from original denial to almost acceptance and back to denial. This denial has nothing to do with bets: anyone can bet that Higgs exists or does not exist. Without genuine justifications this kind of statements contain just single bit of information or disinformation.
My original attitude was a denial based on following arguments natural in sub-manifold gravity.
- TGD does not allow Higgs as a scalar in 8-D sense: this state would be leptoquark: Minkowski scalars are always H-vectors and have generalized polarization.
- If Higgs is there it should behave like a SO(4) vector in CP2 tangent space with different directions analogous to polarizations. One can have 3+1 decomposition for tangent vectors of CP2 under electro-weak SU(2) but the problem is that there is no manner to build covariants or invariants in this manner. CP2 does not allow covariantly constant vector fields. The contractions of color isometry generators with the trace of second fundamental form would be general coordinate invariants but would give a color octet rather than complex electro-weak doublet (triplet plus singlet would results only if one identifies U(2) ⊂ SU(3) as electroweak gauge group).
The contractions of CP2vierbein vectors with the trace of the second fundamental form would give a candidate for Higgs and its contraction with CP2 gamma matrices appears in the Dirac equation for induced spinor fields and makes it inconsistent unless the trace of the second fundamental form and thus Higgs vanishes (minimal surface property). For non-minimal surfaces this identification would make Higgs contribution to mass square tachyonic. Thus this identification is not promising.
- Higgs is not needed to give mass for fermions since p-adic thermodynamics takes care of this. There are however some problems in the understanding of gauge boson masses. Some additional sources of mass seem to be necessary: p-adic thermodynamics in its basic form would give extremely small second order contribution to the gauge boson masses since the inverse integer valued p-adic temperature cannot be larger than T=1/2. For fermions one has T=1.
For these reasons I believed for a long time that TGD does not predict Higgs. I could have promoted this as a dramatic prediction of sub-manifold gravitation.
Could Higgs exist after all?
The last five years in blogs have been endless n-sigma talk related to rumors about Higgs and also now this kind of rumors are around. As a genuine skeptic I became skeptic also about my basic belief and asked whether Higgs might exist also in TGD Universe. I had also to understand the additional contribution to the mass of gauge bosons and how gauge bosons get their additional polarization state. Maybe Higgs might be necessary to achieve this. The identification of the basic objects as wormhole throats and contacts carrying quantum numbers was a decisive step of progress. The irony was that the progress began with the idea that Higgs could correspond to wormhole contact! Only later came the realization that this makes sense also for gauge bosons.
- Free fermions are in this picture wormhole throat pairs and topological condensation makes them massive. The throats formed in the topological condensation of fermions have vanishing magnetic charge. One has throat pair at both sheets but only the members of the second pair are connected by a Kähler magnetic flux tube.
- Bosonic emergence means that bosons consist of bound states of massless on mass shel fermion and anti-fermion associated with wormhole throats of wormhole contacts connecting space-time sheets. Also virtual particles consist of massless on mass-shell states in ZEO. Also bosons consist of two wormhole contacts since the total monopole charge must vanish. The throat pairs at both sheets are connected by Kähler magnetic flux tubes carrying monopole magnetic flux. Neutrino pair at the second wormhole throat neutralizes weak isospin for both bosons and fermions.
- Kähler magnetic flux tubes contribute to the mass of the particle stringy contribution. For elementary fermions the contribution from wormhole throat pair carrying fermion quantum numbers dominates the mass. In the case of hadrons the reconnection process for color magnetic flux tubes is responsible for non-perturbative aspects of hadron physics and making possible to understand what happens in the formation of jets and in hadronization. The physics in question involves new physics: contrary to the general belief jet QCD does not follow from QCD as QFT. Color magnetic flux tubes make themselves visible via what has become known as quark-gluon plasma. This terminology is misleading and based on wrong expectations: the attribute "strongly interacting" does not help much. In TGD Universe the ideal quark-gluon plasma in TGD is like a big hadron containing very many quarks and gluons rather than gas of partons as it would be in QCD proper.
- In TGD the possibly existing Higgs 4-plet would have same quantum numbers as electro-weak gauge bosons 3+1 as SU(2) multiplets. There would be a nice 1-1 correspondence between Higgses and gauge bosons in CP2 degrees of freedom. Only spin would be different. Sub-manifold gravity would be at work again.
- Higgses could be there but gauge bosons would eat them to get longitudinal polarizations. All Higgs components would become longitudinal polarizations of Higgs boson. Also gauge bosons which are usually regarded a massless would have a small mass. Same applies to graviton and all super-partners. The assumption that all physical particles have at least small mass resolves the infrared singularities and there are excellent hopes about a beautiful realization of twistorial approach in zero energy ontology (ZEO).
The problem is that one must postulate a lot of Higgs like particles and also their super-partners. And all of them would be eaten. Why the trouble of preparing all these Higgses if all of them end up to the plate?
Return to Higgs denialism
Now I am becoming a Higgs denialist again. There is no need for Higgs in TGD and TGD does not allow any natural mechanism transforming Higgs like states to longitudinal components of gauge bosons.
- In ZEO just the condition that boson has spin 1 implies that it is massive and has therefore also the third polarization. The argument is simple: if one wants the composite system of on mass shell massless fermion and antifermion to have helicity 1 one must assume that either the 3-momenta or energies have opposite sign or at least that the directions of 3-momenta are different. There is no need to assume that gauge bosons get the additional polarization state by eating Higgs. This applies to all states with spin.
- The recent advances in the formulation of generalized Feynman diagrams (see this) lead to the identification of the analog of the gauge condition eliminating unphysical polarizations. This condition allows three polarizations in the case of spin 1 states. Analogous conclusion applies in the case of higher spins.
- One can express the condition on polarizations more precisely. One can assign to each causal diamond (CD) a preferred sub-manifold M2 (2-D Minkowski space) of M4 defining preferred time direction and spin quantization axis: the are many choices and these correspond to non-equivalent CDs. This 2-plane defines the analog for the plane in which Feynman graphs live and allows to realize the vision about generalized Feynman graphs as sub-manifold braids. M2 corresponds in the number theoretical vision to hyper-complex numbers regarded as a 2-plane in the space of hyper-octonions.
- The gauge condition p• ε=0 is modified. The modified condition says that the allowed polarization vectors are orthogonal to the projection pM2 of the momentum of boson to M2: pM2• ε=0. Three polarization states are allowed instead of 2. All physical particles with spin are massive.
The conclusion is simple: no Higgs like states are needed! Just as I believed in the beginning. The prodigal son has returned back to his home! For reasons easy to understand, I am waiting eagerly the December 13:th. We know that 13 is the unlucky number but who will be the unlucky one? Higgs or me?
For more about Higgs see the chapter New Physics Predicted by TGD: Part I of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy". For background see also article Algebraic braids, sub-manifold braid theory, and generalized Feynman diagrams or the new chapter Generalized Feynman Diagrams as Generalized Braids of "Towards M-matrix".