Is the annihilation between an electron and an electron antineutrino possible. How much energy is needed for the annihilations. Could the annihilations be mutual and could this result in a pion if energies are high enough?
Is the annihilation between a positron and a electron neutrino possible. How much energy is needed for the annihilations. Could the annihilations be mutual and could this result in a pion if energies are high enough?
The cross-section for neutrino reactions with quarks is very small, for reactions with other leptons it's even smaller. You can increase the probability of a reaction by increasing the energy, but it takes a lot of energy because the W & Z bosons of the weak interaction are so massive, 80 & 91 GeV/c², respectively. Note that a proton's mass is only 938 MeV/c², and an electron's is 511 keV/c².
So, in principle, you could do $$e^- + \overline{\nu}_e \to W^-$$ but you have to accelerate the electron so its KE is around 80 GeV, relative to the antineutrino. And of course the $W^-$ won't last long, it will soon decay back to an electron & antineutrino again.
This analysis also applies to the reaction between a positron and an electron neutrino (which of course produces a $W^+$).
To get electron energies in that range you need a big accelerator, like the old Large Electron–Positron Collider, which achieved electron + positron collisions as high as 209 GeV. So if you collided an electron beam from the LEP with an antineutrino beam you could get collision kinetic energy in excess of 100 GeV.
On a related note, you could fire a beam of neutrinos head-on into a beam of antineutrinos and virtually nothing would happen. The beams would just pass through each other, unless the relative energies of the particles were insanely high. Even supernova neutrinos are "only" 10-30 MeV.
When talking about annihilation, one usually thinks of a particle and its antiparticle annihilating into a photon.
However under certain energetic conditions, we could observe electron and electron antineutrino annihilation, the final particle being a W (weak) boson which would then decay into another pair lepton - antilepton respecting some conservation rules, for example the conservation of charges, conservation of leptonic number.
You can find a good undergrad book on particles interaction named "Quarks and Leptons" by Halzen and Martin.
