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Or if a symmetry does exist what is it?

If possible could you compare this to a symmetry that leads to a conservation?

Qmechanic
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Adrien Amour
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1 Answers1

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The nature of charged weak interaction couplings in the SM does not respect generations, quark or lepton, since fermions of one generation couple to differently charged fermions outside this generation: this is called weak CKM mixing, for quarks, and PMNS mixing for leptons. So flavor is not a good, conserved, quantum number, only an approximate one predicated on the weakness of the weak interactions.

In the case of leptons, e.g., you may write loop diagrams underlying the unobserved, extremely rare, conjectural process, $\mu\to e\gamma$. (They involve coupling to virtual neutrinos.)

If, for some freakish reason, all mixing angles in the CKM and PMNS matrices vanished, quark and lepton flavors would be valid accidentally conserved quantum numbers.

Cosmas Zachos
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  • Thanks thats really helpful! Why would they be "accidentally conserved" as opposed to conserved quantities such as spin, what is there in the theory that stipulates that these contents should be conserved? – Adrien Amour Oct 28 '21 at 16:33
  • Accidental symmetry is one we do not fully understand.... in contrast to gauge symmetries. A small blemish of it at some scale will mar the symmetry at other scales, as well. Rotational invariance underlying angular momentum/spin conservation is a fundamental global symmetry, to be sure, so you have a point. – Cosmas Zachos Oct 28 '21 at 16:51
  • Link. – Cosmas Zachos Oct 28 '21 at 17:18
  • Thanks that really helps – Adrien Amour Oct 31 '21 at 15:56