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Since the weak interaction violates CP symmetry but electromagnetism doesnt,does it mean that the electroweak fields also violates CP symmetry?Can a field which violates some symmetry be the product of a field at lower energies which doesnt violate the same symmetry?

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  • $\begingroup$ I'm puzzled by your question: electromagnetism preserves P, C, and CP at high and low energies, equally. Nothing about it gets it close to CP violation, which is a "fluke" inherent in charge current (charge altering) couplings of the weak interactions. Hell, you cannot violate it for weak neutral currents either! $\endgroup$ Commented Mar 21, 2023 at 15:09
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    $\begingroup$ @CosmasZachos the EM and the Weak interaction come from a more general field the Electroweak field.The seperation of the Electroweak field happens at low energy into the Weak and EM field.EM field preseves CP symmetry while Weak Interaction field doesnt. $\endgroup$ Commented Mar 21, 2023 at 15:12
  • $\begingroup$ Indeed, but there is nothing in weak mixing that "contaminates" photon couplings, which preserve charge, with CKM matrix elements which contain CP violation. Waving arms and expecting CP violation to jump into charge-preserving vertices can't work.... $\endgroup$ Commented Mar 21, 2023 at 15:15
  • $\begingroup$ Did you mean "the product of fields at higher (not lower) energies which doesn't violate the same symmetry"? Most people believe the U(1) and SU(2) symmetries are the "more fundamental cause" of electromagnetism and the weak force. If so @CosmasZachos I think the question is fine - it's asking if the high energy theory with a U(1) and SU(2) unbroken symmetry/force have CP violation. And I dont know the answer :(. You'd have to look at the high energy theory and see if there's a 3X3 matrix like the CKM matrix. $\endgroup$
    – AXensen
    Commented Mar 21, 2023 at 15:37
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    $\begingroup$ @Andrew Christensen At high energies there are no effects of the Higgs condensate to generate masses in the Yukawa's and give meaning to CKM mixing which underlies CP violation. ... $\endgroup$ Commented Mar 21, 2023 at 15:42

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I'll collect some of my comments above. The SM traces its CP violation to the complex phase of the three generation CKM mixing matrix quantifying fermion Yukawa couplings.

That is, CP violation is not a property of the gauge fields, but of their couplings to many (!!) fermions in currents with a discord between mass eigenstates and weak coupling (flavor) eigenstates. To have fermion masses, you need a Higgs v.e.v., so you might argue that CP violation is effaced at high energies.

  • But note, no matter what, the CKM matrix does not and cannot enter in gauge couplings to fermions of the same charge, so neutral bosons. Hence, it cannot enmesh CP violation with either the photon or the Z! Both electromagnetism and neutral current weak interactions respect CP. Weak mixing has nothing to do with CP violation...

You might then say that EM preserves CP at all energies.

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