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I was making an exercise where I had to check if a decay is possible, so I checked if the baryon number, charge, energy, Lepton numbers, and spin are conserved. One of the decays is this one:

$\Sigma^0 \rightarrow \Lambda^0 + \gamma + \gamma$

All of the numbers were conserved except for the spin, so I thought that this meant that the decay was not possible. However, when I checked the solution, it didn't consider the spin. So my question is, should spin be conserved in a decay of elementary particles?

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  • $\begingroup$ How did you conclude the spin is not conserved? How did you add the spins? you recall the vector addition rules? $\endgroup$
    – Cosmas Zachos
    Commented Aug 3, 2023 at 0:29

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Spin of elementary particles was determined to be necessary and sufficient in order to preserve conservation of angular momentum in quantum mechanically modeled interactions. Or backwards, using the concept of a vector spin for the particles under study allowed a consistent quantum mechanical theory, consistent with conservation of angular momentum at the particle level and continuity between classical and quantum. For the history see this.

For your particular reaction the angular momenta vectors of the particles involved in the decay added (vectror addition) with the various spins conserve the total angular momentum. Spin is not an additive quantum number to be conserved, like charge, but a vector.

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