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In the Standard Model, protons are considered to have an infinite lifetime. See https://en.wikipedia.org/wiki/Proton#Stability "The spontaneous decay of free protons has never been observed, and protons are therefore considered stable particles according to the Standard Model."

Now, according to wikipedia about $\beta^+$ decays,

https://en.wikipedia.org/wiki/Beta_decay#%CE%B2+_decay

the $\beta^+$ decay "may be considered as the decay of a proton inside the nucleus to a neutron" : $p\rightarrow n + e^+ + \nu_e$

Does it mean that there is really this decay that happens ? if so, how is that compatible with the fact that the lifetime of proton is expected to be infinite.

How could the fundamental law of authorized decay/forbidden decay be different inside the nucleus and outside nucleus ?

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An isolated proton can't undergo $p\to n+e^++\nu_e$; in its rest frame, energy would be created. But a proton in a suitable larger nucleus can so decay; the rest of the nucleus responds in a complicated way that ensure the conservation of energy and momentum.

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  • $\begingroup$ Thanks a lot. Would you know why $p\rightarrow n+ e^+ + \nu_e$ involve creation of energy ? $\endgroup$
    – Mathieu Krisztian
    Dec 12, 2021 at 21:31
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    $\begingroup$ @MathieuKrisztian The left-hand side only has $m_pc^2$ in the proton's rest frame, which isn't even enough for a neutron, let alone a positron and neutrino besides. $\endgroup$
    – J.G.
    Dec 12, 2021 at 21:32
  • $\begingroup$ An enormous thanks for having shared your knowledge. Everything is clear. $\endgroup$
    – Mathieu Krisztian
    Dec 12, 2021 at 21:32

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