Why the Proton Doesn’t Decay
An isolated proton - one not bound inside an unstable nucleus - does not spontaneously transform into lighter particles. In other words, it is effectively stable. This stability arises from two key factors: a theoretical constraint in the Standard Model known as baryon number conservation, and the proton’s position as the most energetically stable baryon.
Baryon Number Conservation
Within the Standard Model of particle physics, there is a conserved quantity called the baryon number $B$, defined as:
- Each baryon (such as a proton or neutron) has $B = +1$.
- Each antibaryon has $B = -1$.
- All other particles (leptons, photons, etc.) have $B = 0$.
Both the strong and weak interactions - the forces responsible for most particle transformations - strictly conserve baryon number.
In other words, a process is only allowed if the total baryon number before and after the reaction is identical.
For a free proton to decay, the final state would need to include other particles with the same baryon number, $B = +1$.
But since the proton is the lightest baryon, there is no lighter $B = +1$ state into which it could decay.
$$ m_p \approx 938.27 \ \text{MeV}/c^2 $$
All other baryons (such as the neutron or the $\Delta$ resonances) are more massive. The lighter, stable particles we know of - electrons, neutrinos, photons - carry $B = 0$, so producing only those would violate baryon number conservation.
Thus, in the Standard Model, the proton is stable simply because it is the lightest possible baryon.
Even if baryon number conservation were not enforced, there is no combination of lighter, stable particles into which a proton could decay without also violating energy conservation.
Note. Certain beyond - Standard Model frameworks - such as Grand Unified Theories (GUTs) - predict that baryon number is not an exact symmetry. In these scenarios, the proton could in principle decay through channels like: $$ p \rightarrow e^+ + \pi^0 $$ $$ p \rightarrow e^+ + \gamma $$ Extensive experimental searches, however, have placed extremely stringent limits: the proton’s mean lifetime must exceed $10^{34}$ years - vastly longer than the current age of the universe ($\sim 1.4 \times 10^{10}$ years). To date, no evidence of proton decay has ever been observed.
