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I read something here http://cosmology.princeton.edu/~mcdonald/examples/EP/lee_pr_9_143_74.pdf

The observed CP violation is assumed to be due to the spontaneous symmetry-breaking mechanism; the Lagrangian is CP invariant but its particular solution is not.

I think that Higgs Potential is only a particular way which physicists took advantage of to explain this difference to export a mass function (exist also negative mass, not only 'positive' mass) not to explain real difference between CP violation and spontaneous symmetry breaking deeper.

Higgs Potential is a set of matrix/equations solutions that physicists borrowed for using spontaneous symmetry breaking to explain a mechanism that can be 'exported' (or valued like in Computer Science) to enhance a particular extension of Vector Field: a mass (a scalar), in fact: (I don't know if negative mass -2kg can be explained using Higgs Potential)

** I read from wiki

The Higgs field, through the interactions specified (summarized, represented, or even simulated) by its potential, induces spontaneous breaking of three out of the four generators ("directions") of the gauge group U(2). This is often written as SU(2) × U(1), (which is strictly speaking only the same on the level of infinitesimal symmetries) because the diagonal phase factor also acts on other fields in particular quarks

Higgs Potential $\rightarrow$ induce a SBS but to have a CP violation we need to change SOMETHING about Higgs Potential to have a new, extended Higgs Potential: CP-Violating Higgs Potentials

So, if also Higgs Potential can be CP violated :

  1. What role plays spontaneous symmetry breaking if SBS is explained by Higgs Potential ?
  2. Is CP violation a Homomorphism of Higgs Potential ?
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The CP violation observed in particle physics is attributed to the complex phase in the CKM matrix. This does not come from the Higgs potential. It is a global property of the yukawa couplings between the quarks and the Higgs, only possible because there are three generations of fermions. The paper by T.D. Lee was written just before the third generation was discovered and does not address this possibility.

There are various ways in which additional CP violation might be created by presently unknown physics. One of these is for the Higgs potential to contain CP-violating interactions. The question seems to be asking whether that example of CP violation would be "a homomorphism of the Higgs potential". Well, there might be homomorphisms somewhere, but I would like to better understand the question's motivation before I go looking for them.

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  • $\begingroup$ your answer is very good, mm.. I was wondering if, by turning the potential of Higgs, we could explain mass as a particular shape of a spin but represented as a topological space. The particles have 3 fundamental properties: mass, charge and spin (mcs). But I want to consider only 2 properties, charge and spin (cs), so I need to explain particle mass through 2 fundamental properties, not 3, therefore, the problem seems to lead us back to the integral geometry, the transformations and the morphisms of the same potentials that are used to explain, discriminate different properties. $\endgroup$
    – user332153
    Feb 17, 2018 at 19:17

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