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I am wondering, in patricle physics, when we have an annihilation vertex, we always have a particle and an antiparticle annihilating. Why is that ?

Let me make an example to be clearer. Let's take a weak interaction vertex. We know an electron and an electronic antineutrino can annihilate each other on a weak interaction vertex to give a W- boson. Why is this not possible with an electron and an electronic neutrino ?

I understand in some cases it is forbidden by conservation of charge, that is why an electron and positron can annihilate but not 2 electrons. But in the example above, I fail to see which conservation is violated, if there is one. Or is this annihilation rule an experimental postulate ?

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Lepton number would be violated. – Lewis Miller 5 hours ago
    
Lepton number conservation would be violated. – Raziman T. V. 5 hours ago
    
But it seems to me that this lepton number is introduced somewhat artificially ? Is there a deeper reason ? Electric charge is for example observed by its effect on the QED interaction. Does lepton number arise anywhere else than this conservation ? – Frotaur 5 hours ago
    
@Frotaur you can't write down a Lorentz-invariant and gauge-invariant QFT Lagrangian which would give you such an interaction vertex. This is the deeper reason. – Solenodon Paradoxus 5 hours ago
up vote 6 down vote

One has to realize that words in physics have a definite meaning. This meaning, for words used in physics, is dependent on the specific mathematical model that uses it.

The mathematical model for particle physics is called the standard model

elempart

All matter and energy emerges from interactions and composites of these particle. The model encapsulates the large number of particle data measured over the last half century.

In all particle interactions , particles may transmute at the vertices changing quantum numbers and identity as defined in the table. Changing identity is not called annihilation. The basic definition of annihilation as used in particle physics is that after the interaction all the quantum numbers of the initiating particles add up to zero. The particles coming out of the vertex add up to zero, and thus new pairs can appear with different quantum numbers.

Thus we get, as an example, e+e- annihilating into a quark antiquark pair, which have completely different quantum numbers than the electron positron pair, but their addition adds up to zero.

In your example an electron_antineutrino scattering on an electron will make the lepton number zero but not the charge, so it is not within the definition of "annihilation". It is merely an interaction.

Of course an electron_neutrino on an electron gives a lepton number of 2.

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up vote 1 down vote

Lepton number (which is negative for ant-leptons) - if they still use that, what with neutrino oscilations. Chirality is also largely conserved.

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