Can protons and neutrons be completely converted into Leptons?

Question

In beta decay, a neutron releases an electron and turns into a proton. The inverse happens, though usually not naturally, in positron emission, where a proton emits a positron and becomes a neutron. As the electron has mass, approximately 1/1836th of a proton, I was wondering, for how long this could go on? Could we, in theory, let a proton or neutron completely decay into only electrons, positrons, and energy? Or, more generally speaking, leptons, like neutrinos and such. I know, because protons are very stable, they won't just naturally decay, but if you put a lot of energy into it, could this happen? And if not, why?

Answer 1

Protons and neutrons are members of a class of particles called baryons; and according to the Standard Model of particle physics, baryon number is conserved. Protons and neutrons both have baryon number 1; leptons and photons have baryon number 0. So if you start with some protons and neutrons (baryon number not equal to zero), you cannot end up with no baryons.

The proton is the lightest baryon, so in general, free neutrons (and other more exotic baryons) will eventually decay to protons. But the proton cannot decay, since there is no lighter baryon for it to turn into. Conversely, if I took a bunch of protons and neutrons and put a bunch of energy into them somehow, I might get some more exotic baryons; but I will never end up with just leptons and photons.

There are hypothetical extensions to the Standard Model that would, if true, allow for the baryon number of a system to change. Experiments have been done to look for such violations, most notably looking for proton decay. However, no such experiment to date has observed the baryon number of a system change.