Re: Is there any interaction between electron-neutrino and virtual electron ?

Hi Birol,

I'm sorry for taking so long to reply; it took me some time to think about how to answer this rather complex question. A deep analysis would be a lot of work and time for me, especially since the final answer to your question is a simple one: it is virtually impossible for a neutrino to interact with a virtual electron from an electric field to produce a real electron.

To begin with, although as you say the flux of neutrinos passing through the earth is very high, almost all of those neutrinos have energies well below 511 keV, the minimum energy necessary to produce a real electron. Here is a plot of the neutrino spectrum for reference.

The next problem (on top of the first one) is that you can't just produce a single electron. The incoming neutrino has zero electric charge, and since electric charge is conserved, you would need to produce an electron-positron pair (with total rest mass greater than 1 MeV). As you can see from the previous plot, this eliminates even more of the neutrino flux.

Finally - and most restrictively - the only way to produce an electron-positron pair is by the exchange of a virtual W boson. Since the W has a mass of over 80 GeV, you need a "hard" exchange (with a high momentum transfer) to make the cross section significant. Here is a possible Feynman diagram of such an exchange:

Asterix (*) indicates a virtual particle 

 nu_e - - - - - - +------- e+
                   \
                    W*
                     \
                      >------ nu_e
                     /
               *e-  /
                   /
gamma* ~~~~~~~~~~~<
                   \
                    \
                     \ e+


Note: Asterix (*) indicates a virtual particle 

In short, you're never going to see it happen. This is probably not exactly what you were hoping for, but I hope it's helped explain the real problems with neutrino scattering off of virtual electrons.

Best,
Sam