Can this neutrino be detected via a CC weak interaction?

[Kara386]

Homework Statement

A tau neutrino with energy 1GeV interacts with a stationary neutron. Can the neutrino be detected via a charged current interaction?

Take the mass of tau to be 1784MeV/c$^2$, 105MeV/c$^2$ for the muon and 939MeV/$c^2$ for the neutron.

Homework Equations

The Attempt at a Solution

I've got no idea what the criteria for detection via a weak interaction are, and it proved very difficult to google. Is there an energy threshold the neutrino has to reach to be detectable? As in should I be saying something like: it doesn't have 83GeV of energy, i.e. the equivalent of the mass of a W boson, so it can't create one? I know tha's wrong, the boson is virtual so doesn't have to have that mass - do I use the uncertainty principle to work out what the energy of the virtual boson would be?

I feel like I've missed some really important concept here, any help would be much appreciated. :)

 

[Orodruin]

Hint: There is an energy threshold for the CC interaction to be possible.

 

[jtbell]

Don't even think about the W here. Just consider the initial versus final particles.

A virtual particle does not have a well-defined mass. In this case, the "mass" of the W can be a lot different from the mass of a real (non-virtual) W.