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How do we determine if a decay is due to weak or strong interaction. Is it true that as long as any one of the 6 flavour numbers are not conserved, then it must be due to weak interaction? Is there a good general rule of thumb to determine this?

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Yes, this correct. The strong interaction cares only about the color charge, and doesn't care whether the color-charged objects are up quarks, charm quarks, or gluons. The electric interaction cares only about electric charge, which brings in the charged leptons. It's the weak interaction that segregates particles by their flavor.

You could say that only because the flavor interaction is weaker than the strong force or electromagnetism do we have the luxury of discussing particle flavor at all.

Experimentally there are other practical clues: weak decays tend to be much slower than strong or electromagnetic decays, and weak interactions strongly violate parity symmetry.

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