particle physics - Pair production of neutrinos

I learned that neutrinos have a much lower energy than electrons. Pair production of electrons occurs when the photon energy is above 2 times the energy of an electron. So I am wondering if pair production of neutrinos wouldn't be even more common and occur at much lower energy levels?

Answer

Pair production of electron/positron happens in the electric field of the atoms to satisfy conservation laws and the same will be true for off mass shell Z0 going into a neutrino antineutrino pair, interacting with the weak field of the atoms.

The equivalent to the photon weak interaction mediator is the Z0 and neutrino antineutrino pairs can be formed that way. The weak interaction is orders of magnitude smaller than the electromagnetic one, and thus the probability of getting pairs of neutrinos-antineutrinos is high only in special situations as in the Big Bang or in a Super Nova explosion where the density of matter is high and there is energy available.

The weak couplings lower the probability of interaction drastically so the advantage of a smaller neutrino mass with respect to the electrons is lost for experiments possible in the laboratory.