Vision about unification of strong and weak interactions

The considerations of the article About Platonization of Nuclear String Model and of Model of Atoms) inspire a unified vision about strong and weak interactions.

1. At the level of H=M⁴ × CP₂, the color group SU(3) acting as isometries of CP₂ would describe the perturbative aspects of color interaction and give rise to color confinement. The non-perturbative aspects of strong interactions would correspond to the holonomy group of CP₂ and weak interactions for weak bosons which are either dark or p-adically scaled variants of ordinary weak bosons and massless below the scaled up Compton length.

   The large value of h_eff would make the perturbation theory for these weak interactions convergent (see this). Strong isospin can be identified as weak isospin. Both p-adic and h_eff hierarchies of length scales are required in the proposed vision.

2. At the level of M⁸ = M⁴ × E⁴, SU(3) corresponds to a subgroup of octonionic automorphisms and U(2) could be identified as a subgroup of isometries leaving invariant the number theoretic inner product in E⁴. This inspired the proposal that strong isospin corresponds to U(2) and hadron-parton duality corresponds to M⁸-H duality basically.

This picture explains various poorly understood aspects of strong interactions.

1. In the good old times, when strong interactions were not yet "understood" and it was also possible to think instead of merely computing, strange connections between strong and weak interactions were observed. The already mentioned conserved vector current hypothesis (CVC) and partially conserved axial current hypothesis (PCAC) were formulated and successful quantitative predictions emerged.

   Strong isospin is equal to weak isospin for nucleons but heavier quarks did not fit the picture. (c,s) and (t,b) dublets were assigned quantum numbers such as strangeness and charm, and they are not quantum numbers of weak interactions.

   When perturbative QCD became the dominating science industry, low energy hadron physics was forgotten. Lattice QCD was thought to describe hadrons but the successes were rather meager. Lattice QCD has even mathematical problems such as the description of quarks and the strong CP problem which lead to postulate the existence of axions, which have not been found.

2. In TGD these connections can be understood elegantly.

   1. The topological description of family replication phenomenon implies that strangeness and charm are not fundamental quantum numbers and the identification of weak and strong isospins makes sense.
   2. Strong interactions in long length scales for hadrons become p-adically scaled dark weak interactions. The flux tubes correspond to possibly p-adically scaled mesons or equivalently weak bosons in a generalized sense predicted by the TGD based explanation of family replication phenomenon. Tensegrity is the basic construction principle for hadrons and nuclei and even atoms, for which color octet excitations of leptons define the counterparts of mesons.

Also the fractality inspired ideas related to p-adically scaled up variants of strong and weak interactions organize to a beautiful picture.

1. p-Adic fractality inspired the idea that both strong and interaction physics appear as p-adically scaled variants. In particular, M₈₉ hadron physics would be a p-adically scaled up version of the ordinary hadron physics assignable with M₁₀₇ and would correspond to the same p-adic length scale as weak bosons. Various forgotten anomalies support this proposal (see this and this).

   But why both weak and strong interaction physics with the same p-adic length scale (or actually scales)? Both weak bosons and mesons would be described as string-like entities. How can one distinguish between these?

2. There is no need for both! Weak bosons and their predicted exotic counterparts implied by the family replication phenomenon are nothing but the mesons of M₈₉ hadron physics. TGD explanation of the family replication phenomenon indeed predicts the analog of family replication phenomenon for weak bosons basically similar to that for mesons. From the known spectrum of mesons of ordinary mesons one can predict masses of both M₈₉ mesons, or equivalently the masses of ordinary and exotic weak bosons. There is already evidence for the dark counterparts of M₈₉ mesons with scaled up Compton length equal to that for M₁₀₇ mesons. Also M₈₉ baryons are predicted.

3. Higgs would be the counterpart of sigma meson. There is evidence of the pseudoscalar counterpart of Higgs identifiable as a counterpart of M₈₉ pion. Weak bosons would be counterparts of ρ meson. Also axial vector weak mesons are predicted as counterparts of ω.

   The exotic weak mesons as counterparts of kaon, charmed mesons, etc.., are predicted but their p-adic length scale is shorter. Also for these there is some evidence (see this and this). In particular, there are indications for the existence of Higgs-like states decaying into e-μ pair (see this). This particle might correspond to kaon, which is pseudoscalar rather than scalar. All masses can be predicted from hadron physics by scaling apart from the p-adic prime defining the mass scale and satisfying the p-adic length scale hypothesis.

See the article About Platonization of Nuclear String Model and of Model of Atoms or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.