Wednesday, February 17, 2021

Can one regard leptons as effectively local 3-quark composites?

The idea about leptons as local composites of 3 quarks (see this) is strongly suggested by the mathematical structure of TGD. Later it was realized that it is enough that leptons look like local composites  in scales longer than CP2 scale defining the scale of the partonic 2-surface assignable to the particle.   

The proposal has profound consequences. One might say that SUSY  in the TGD sense has been   below our nose  for more than a century. The proposal could also solve matter-antimatter asymmetry since the twistor-lift of TGD predicts the analog of Kähler structure for Minkowski space and a small CP breaking,  which could make possible   a cosmological evolution in which quarks prefer to form baryons and antiquarks to form leptons. 

The basic objection is that the leptonic analog of Δ might emerge. One must explain why this state is at least experimentally absent and also develop a detailed model. In the article Can one regard leptons as effectively local 3-quark composites?  the construction of leptons as effectively local 3 quark states allowing effective description in terms of the   modes of leptonic spinor field in H=M4× CP2 having H-chirality opposite to quark spinors is discussed in detail.

See the article Can one regard leptons as effectively local 3-quark composites? and the chapter The Recent View about SUSY in TGD Universe.

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

Articles and other material related to TGD. 


Mitchell said...

According to this idea, p and e are both made of uud. But what is the actual difference between p and e, then?

Matti Pitkänen said...

The total quantum numbers of p and e^+ are same (recall that TGD color differs from QCD color in that color is angular momentum like, not spin-like and the colar partial waves has color representations correlation with em charge: tjhis is essential).

There are following differences.

a) The quarks in p are at different partonic 2-surfaces with distances of order proton size scale. This makes possible strange, charmed etc variants of baryons. The quarks in e areat the same partonic 2-surface with size of order 10^4 Planck lengths, the CP_2 size scale. For leptons one has only different generations corresponding to genus of the partonic 2-surface.

b) The color representation of U quarks are triplets but those of D quarks are not. The color wave functions of each D quark in proton is reduced to triplets by acting with super-Kac Moody type generators which are color octets. The super-Kac-Moody generators also increase the conformal weight to zero (masslessness). which is in general negative due to negative vacuum conformal weight.

In the case of e color neutralization is not carried out separately for quarks but for the entire 3 quark state.

c) For baryons the wave function in spin-isospin degrees is totally symmetric since color is antisymmetric (statistics).

For electron this could be also true. For neutrinos the color and spin-ew degrees of freedom must entangle since color wave function is not singlet antisymmetric under exchange of quarks.

Mitchell said...

I apologize in advance for my insufficient understanding of TGD. I have a simplified mental model of TGD which is probably wrong, hopefully you can correct me.

The simplified mental model is that for the color interaction, we have punctured 2-surfaces somehow interacting with modes of the CP_2 metric. The punctures are the quarks and SU(3) would come in the usual Kaluza-Klein way.

In terms of this model, the difference between proton and electron would be, that proton contains three 2-surfaces each with one puncture, while electron is one 2-surface with three punctures.

I have many other questions. But first I need to correct this mental picture!

Mitchell said...

I just remembered that in string theory, one doesn't get the forces in "the usual Kaluza-Klein way". So probably that isn't what happens in TGD, either!

Matti Pitkänen said...

Your view about baryons and leptons is correct. I answered already early or at least wrote the answer. Sorry for slowness.

*Only color interaction is analogous to Kaluza-Klein.

*Electroweak connection is projection of CP_2 spinor connection. Bundles induction is standard notion but colleagues have not found it for some reason. Stringy picture is different: the gauge fields emerge by spontaneous compactifications.

* In TGD standard model gauge potentials and gravitational field emerge when many-sheeted space-time is replaced with slightly curved region of Minkowski space. Standard model gauge potentials are sums of components of spinor connection for sheets and projections of Killing vectors of SU(3).

*At M^8 level local color gauge group emerges as a subgroup of G_2 acting as octonionic automorphisms. Co-associativity condition for space-time surfaces implies that space-time surface is obtained by local G_2 transformation acting on flat M^4. SU(3) gauge potentials do not reduce to gauge.