Is $CP$ instead of $C$ responsible for changing a particle to its antiparticle?

Question

The charge conjugation operator $C$ reverses the charge of a state. But it may or may not convert a particle to its antiparticle. For example, consider a neutrino which is charge-neutral and left-handed while its antiparticle is also charge-neutral but right-handed. Therefore, charge conjugation is not sufficient to produce the antineutrino from a neutrino but CP is. $P$ is responsible for changing the chirality.

1. So is it not $CP$ instead of $C$ that is responsible for changing a particle to its antiparticle?

2. Is this fact related to the questions here and here?

Answer 1

Answer to part 1

There is no natural pairing between particles and anti-particles at the level of individual states (any such pairing is purely a matter of convention), but there is a natural pairing between particle species — that is, between species and their anti-species. That's because Poincaré symmetries don't permute species, even though they do permute states. This statement also applies to discrete Poincaré transformations like a space-reflection transformation P, in theories where P is a symmetry.

Once we agree that the natural pairing is between species, not between individual states, the answer to part 1 of the question is easy:

• In a theory that has both CP and C symmetry, they both permute species the same way. It's not either-or, it's both. That's because in a theory with both CP and C symmetry, P is also a symmetry, so particles related by P are the same species, by definition.

• To accommodate theories that don't have C (or P) symmetry, we can use CP to define the paring between species and their anti-species. This works whether or not the theory has C symmetry, and when it does, C symmetry gives the same pairing.

Even more generally, we could use CPT (instead of CP) to define the pairing between species and their anti-species, as Weinberg does in chapters 2 and 3 of Quantum Theory of Fields, volume 1. This provides some context for part 2 of the question...

Answer to part 2

Part 2 of the question asks whether part 1 is related to a couple of other questions about Sakharov's criteria for baryogenesis. Those criteria assert that to explain baryogenesis, the theory should not have either C or CP symmetry. The answer to

Why are both C and CP violation necessary for baryogenesis?

explains why this is so. It is also nicely explained in the comments following knzhou's answer to

What distinguishes the behaviour of particle from its antiparticle: C violation or CP violation?

To relate this to part 1 of the present question, note that Sakharov's criteria can be restated without referring specifically to CP or C, like this: To explain baryogenesis, the theory should not have any symmetries between particle species and their anti-species among all symmetries that preserve the time-orientation (which excludes CPT).