6
$\begingroup$

Processes like the electron-positron annihilation are widely known and they give us the impression that "matter annihilates with antimatter." However, I am wondering if this repeated phrase holds for other kinds of reactions.

Can an electron and an antimuon annihilate each other into photons? If not photons, can they annihilate into other particle species? If yes, how is the process different from the electron-positron annihilation? How is it similar?

Clearly the lepton flavor number wouldn't be conserved if they annihilate into photons, so the weak interaction would have to be involved, but what exactly are the processes?

$\endgroup$
6
  • 2
    $\begingroup$ Are you aware that particles have quantum numbers associated with them and quantum number conservation is important in elementary particle reactions? hyperphysics.phy-astr.gsu.edu/hbase/Particles/parint.html $\endgroup$
    – anna v
    Dec 16, 2022 at 4:41
  • $\begingroup$ duplicate: physics.stackexchange.com/questions/403834/… $\endgroup$
    – kricheli
    Dec 16, 2022 at 4:56
  • $\begingroup$ @annav Yes I'm aware. As far as I understand, lepton number is counted as $\text{(number of leptons) - (number of antileptons)}$, which is zero in my described reaction. Particle flavor numbers, as I have noted, would not be conserved, but the weak interaction doesn't seem to care about that. Is my description correct so far? If there is any specific detail I am missing, I would be glad to be informed of it. $\endgroup$ Dec 16, 2022 at 5:18
  • $\begingroup$ So far, I accept @kricheli pointing out that any reaction I am describing does not fit the definition of annihilation. That's fair enough. $\endgroup$ Dec 16, 2022 at 5:19
  • $\begingroup$ Do you count K-capture? The electron doesn't survive. en.wikipedia.org/wiki/Electron_capture $\endgroup$
    – John Doty
    Dec 16, 2022 at 18:01

2 Answers 2

3
$\begingroup$

Yes, although this is fairly complicated. Lepton number symmetry is an anomalous symmetry of the Standard Model, which means that while it holds in the classical theory, it does not hold at the quantum level (Wikipedia mentions this). Hence, there are quantum processes that violate lepton number conservation, but I only know of this happening non-perturbatively in processes involving instantons and sphalerons. At ridiculously high energies (read: beyond the LHC) it is theorized within the Standard Model that you might get, for example, a proton and an electron annihilating into $W$ bosons through a non-perturbative process. Shifman's Advanced Topics in Quantum Field Theory has a discussion about this in Chap. 5.

This is fairly different than electron-positron annihilation. Electron-positron annihilation is something that happens at tree level, which means it is relatively common. This electron-proton annihilation, on the other hand, is an extremely suppressed effect that is expected to happen in the conditions of the primordial universe.

As for electrons and antimuons annihilating into bosons, I don't recall hearing anything about this. Since flavor symmetry is only an approximate symmetry (as noted by Wikipedia), I wouldn't be surprised if something like that exists—in QM, anything that isn't forbidden is mandatory. However, I can't think of an exact process.

$\endgroup$
3
  • $\begingroup$ Is 'annihilating' the term used for massive particle interactions that result in other massive particles? Would it be used in lower energy contexts, e.g. $p + \bar{\nu}_e \to n + e^+ $? $\endgroup$
    – g s
    Dec 16, 2022 at 5:47
  • 1
    $\begingroup$ @gs I understood "annihilation" as "results in bosons", especially since OP said "If not photons, can they annihilate into other particle species?". Shifman does use the term "annihilation" when discussing a proton and an electron leading to a bunch of $W$ bosons (Fig. 5.12, p. 230, on the 2nd edition) $\endgroup$ Dec 16, 2022 at 5:53
  • 2
    $\begingroup$ @gs The Wikipedia link in the answer by kricheli also calls "annihilation" processes such as an electron and an electron antineutrino incoming with an outgoing $W$ boson (although they qualify this use as informal). $\endgroup$ Dec 16, 2022 at 5:56
0
$\begingroup$

No. Particle annihilation is usually understood as a reaction of particle and anti-particle to leave only photons (possibly virtual) bosons, most probably photons. https://en.wikipedia.org/wiki/Annihilation

$\endgroup$
2
  • 2
    $\begingroup$ If you read carefully the Wikipedia page you linked, you'll realize that, although it is the most probable channel at low energy, photon decay of $e^+e^-$ is not the only possibility. $\endgroup$ Dec 16, 2022 at 5:41
  • $\begingroup$ Minor caveat: $p + \bar p$ is going to make charged pions, and they decay weakly leaving behind $\nu + \bar \nu$, which are matter and anti-matter. Not energy. Regarding neutrino / antineutrino annihilation....hmmm idk, the cross section is tiny, and what would they produce? lighter (anti)neutrinos...but then the whole mass-mixing thing kicks in. Sounds nuanced. $\endgroup$
    – JEB
    Dec 16, 2022 at 13:17

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.