Identification of particles and anti-particles

The identification of an electron as a particle and the positron as an antiparticle is a matter of convention. We see lots of electrons around us so they become the normal particle and the rare and unusual positrons become the antiparticle.

My question is, when you have made the choice of the electron and positron as particle and anti-particle does this automatically identify every other particle (every other fermion?) as normal or anti?

For example the proton is a particle, or rather the quarks inside are. By considering the interactions of an electron with a quark inside a proton can we find something, e.g. a conserved quantity, that naturally identifies that quark as a particle rather than an antiparticle? Or do we also just have to extend our convention so say that a proton is a particle rather than an antiparticle? To complete the family I guess the same question would apply to the neutrinos.

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Proposal : if a left-handed matter spin $\frac{1}{2}$ "entity" is part of the weak interaction, it is a particle, otherwise it is an anti-particle – Trimok Oct 22 '13 at 17:02
@JohnRennie: re neutrinos, these would end up as particles via the lepton number; connecting to the quark sector is not as obvious, though there's (conjectired) stuff like B-L and leptoquarks – Christoph Oct 22 '13 at 17:27
@Christoph: ah, yes, good point. – John Rennie Oct 22 '13 at 18:22

Yes, to some extent. Once you choose which of the electron or positron is to be considered the normal particle, then that fixes your choice for the other leptons, because of neutrino mixing. Similarly, choosing one quark to be the normal particle fixes the choice for the other flavors and colors of quarks. But I can't think of a reason within the standard model that requires you to make corresponding choices for leptons and quarks.

In particle terms, you can think about it like this: say you start by choosing the electron to be the particle and the positron to be the antiparticle. You can then distinguish electron neutrinos and electron antineutrinos because in weak decay processes, an electron is always produced with an antineutrino and a positron with a normal neutrino. Then, because of neutrino oscillations, you can identify the other two species of neutrinos that oscillate with electron antineutrinos as antineutrinos themselves, and in turn you can identify the muon and tau lepton from production associated with their corresponding antineutrinos.

In terms of QFT, the relevant (almost-)conserved quantity is the "charge parity," the eigenvalue of the combination of operators $\mathcal{CP}$.

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Thanks. Christoph's comment made me realise that conserved lepton number automatically tells you what a neutrino is. For example in beta decay conservation of L tells you the accompanying neutrino must be an antiparticle. However I couldn't see any way to make a connection with the quarks. In SU(5)/SO(10) type models that unify leptons and quarks is there some way to link the two? Or is that a question for another day? – John Rennie Oct 22 '13 at 19:39
I think so, since GUTs group the quarks and leptons together into unified multiplets, e.g. $(e,\nu_e,u,d)$. But I'm not personally familiar with those theories so I couldn't tell you the details. That probably would be a good topic for another question. – David Z Oct 22 '13 at 20:00
@JohnRennie : In a $SU(5)$ model, it seems that particles and anti-particles may be mixed (if we look at the decomposition in $SU(3)*SU(2)*U(1)$), for instance the anti-symmetric representation $10$ decomposes as $10 \to (3,2,\frac{1}{6}) \oplus (3^*,1, -\frac{2}{3}) \oplus (1,1,1)$ (here all the particles/anti-particles have the same handedness). – Trimok Oct 23 '13 at 9:35
We call particles those that compose the ordinary matter that composes us. The neutron decays to: a proton , an electron and an electron antineutrino . The paraticle identification for the electron comes from this reaction, as also the antineutrino by conservation of lepton number. – anna v Nov 24 '13 at 8:08

Identification of particles and anti-particles

Good question. It's nice to see somebody thinking about physics. Shame it's an old question, but hey ho, it's never too late for physics.

The identification of an electron as a particle and the positron as an antiparticle is a matter of convention. We see lots of electrons around us so they become the normal particle and the rare and unusual positrons become the antiparticle.

Yes. It's a matter of convention. Not a matter of particle properties. Think of a 2 x 2 table and list the properties of the electron, the positron, the antiproton, and the proton.

My question is, when you have made the choice of the electron and positron as particle and anti-particle does this automatically identify every other particle (every other fermion?) as normal or anti?

No. Not unless you do physics "by convention" instead of looking at the hard scientific evidence.

For example the proton is a particle, or rather the quarks inside are.

Forget about the quarks. We've never seen a free quark:

Image credit CSIRO, see The Big Bang & the Standard Model of the Universe

Let's stick with hard scientific evidence. Let's focus on the four stable massive particles. One of which is the proton.

By considering the interactions of an electron with a quark inside a proton can we find something, e.g. a conserved quantity, that naturally identifies that quark as a particle rather than an antiparticle?

No.

Or do we also just have to extend our convention so say that a proton is a particle rather than an antiparticle?

No we don't have to. Of course, we could, and then we could wail about the mystery of the missing antimatter. We could sweep lepton asymmetry under the rug and marvel at baryon asymmetry, and put it on the cover of magazines.

To complete the family I guess the same question would apply to the neutrinos.

Forget the neutrino. People classify the neutrino as a lepton "by convention" instead of looking at the hard scientific evidence. The neutrino moves at c or so close to c that you can't tell the difference. Its mass is so close to zero that you can't tell the difference, and so is its charge. Let's see now, what particle does that remind you of? Ah, the electron!

As regards the thrust of your question, see this article about positronium which says "to a first approximation it can be regarded as a sort of light hydrogen atom". Positronium is a short-lived exotic atom, comprised of an electron and a positron. We call the electron matter, and we call the positron antimatter. And positronium is like light hydrogen. So why do we call hydrogen matter? Throw away that convention and you could justifiably say the proton is the antimatter and the antiproton is the matter, and then say hydrogen is an exotic atom too. Especially since baryon asymmetry is counterbalanced by lepton asymmetry. I rather think it's something like a game of mixed doubles in tennis. One side was always going to win, and did win. But then we called the winning team the matter. And now we wonder why the ladies lost, when actually, they didn't:

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Thanks. The point David makes is that the electron/mu/tau and the neutrinos all interchange so once we've defined any one of them as matter that fixes the definitions for all the others. Likewise defining any one of the quarks as matter fixes the definitions for all the others. The open question is whether defining an electron as matter allows us to extend the definition to the quarks. The Standard Model says no, but a GUT may say yes. – John Rennie Oct 7 '15 at 4:53
Neutrinos are a bit of an issue John. The Standard Model doesn't really cover neutrino oscillation. And we make electrons (and positrons) out of photons in pair production. And neutrinos are more like photons than they're like electrons. And there are issues with quarks too. So IMHO the question is more open than people think. – John Duffield Oct 7 '15 at 13:03