particle physics - Can a proton and an electron annihilate in a gravitational field?

According to this Physics.SE comment, it is gravitationally allowed, though very unlikely, for a proton and an electron to annihilate yielding two photons.

1. Is that correct?


2. If so, why? (In particular, why does semiclassical gravity allow nonconservation of baryon number?)

Do gravitational waves violate conservation of baryon number? is somewhat related, but the currently accepted answer discusses only black holes and the cosmological baryon asymmetry problem, neither of which is relevant to this question.

Answer

At first I thought that Ron Maimon is talking of the equivalent of the $β+$ decay which happens in proton rich nuclei, the energy taken from the binding energy balance:

$p -> n e^+ ν_e$

In the case of the answer to the question about Hawking and Unruh like radiation from large gravitational bodies that are not black holes, this should also be taken into account, with the energy provided by the gravitational field.This also is very improbable because of the tiny size of the gravitational coupling entering the necessary Feynman diagrams. In this case there is no baryon annihilation.

But the answer's "This eventually may happen when the proton decays," is based on GUTS theories. Protons do not decay in the standard model.

Ron is commenting on this sentence, and this implies GUTS.

So it is not effective quantized gravity which allows such a process , in GUTS protons decay, so there is no baryon number conservation. The process that Ron refers to (as also proton decay) can only occur within a GUTS theory.