What is the maximum proton lifetime allowed by the standard model?

Question

Is some amount proton decay necessary in the standard model or is it possible for the proton lifetime to be infinite?

Answer 1

To answer your question, let me first concentrate on the first part "Is some amount proton decay necessary in the standard model (SM)?".

==> Well, proton decay or any processes are a consequence of a particular model, since so far proton decay is not observed experimentally in nature so it is certainly not necessary to incorporate in the SM . The SM and many extensions of it have proton decay, but the rate of the decay can vary significantly depending on the details of the model.

Let me now move to the second part of the question *** "is it possible for the proton lifetime to be infinite (in SM)?" ***.

==> Probably you already know that the SM has a $U_{B}(1)$ global symmetry, where $B$ is the baryon number. The consequence of this symmetry is, the lightest baryon, which is the proton is absolutely stable and this is why proton lifetime is infinity.

But note that, this is valid at the classical level. When quantum effects are taken in to account, this is not true. Quantum effects do break the baryon number conservation of the SM. This is done by the non-perturbative instanton effects. For a technical details see for example High Energy Behavior of Baryon and Lepton Number Violating Scattering Amplitudes and Breakdown of Unitarity in the Standard Model by Olivier Espinosa (pdf). At the quantum level the baryonic current is not conserved and one can compute to show that such non-perturbative processes has lead to both baryon and lepton number violations ($\Delta B=\Delta L =3$; L=lepton number) with a rate that is suppressed by a factor of $\sim 10^{-173}$.

So the bottom-line is, in the SM, at the classical level, proton is absolutely stable. But proton can decay due to quantum effects but the life time is extremely big but not infinity.