The conservation law requires that Baryon number be conserved; that is, the sum of the Baryon number before and after a reaction/ decay must always equal the sum of the Baryon number after the reaction. This sounds fairly simple and I thought I've understood it until an example from my text made me question my understand

$$p\rightarrow e^{+} + \pi^{0}$$ Why is this proton decay conserved?

I see that proton has a Baryon number of 1. Positron has a Baryon number of 0 and pion naught have a Baryon number of 0. Clearly, the Baryon number is not conserved. But an example from my notes says it is a conserved decay. What am I missing?


Within the standard model, protons don't decay.
As you've pointed out, it doesn't conserve baryon number, and you can see it doesn't conserve lepton number either.
However, it does conserve their difference, and in some Grand Unification Theories (Theories which at high energies describe the electromagnetic interaction, weak interaction and strong interaction as one, similar to what has been done for the electroweak theory), this is the conservation law required.

See this for B-L conservation and this for some basic information on GUTs.

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