Can Virtual Particle Lifetimes Be Calculated?

[edpell]

Is it possible to calculate the lifetime of a virtual particle? For example is an electron and a proton form a virtual neutron that is off shell by 0.8Mev how long will it last? Is this something we can calculate?

At first I would think it would be short lived because of the 0.8MeV energy shortage but then I think about the 80,000MeV needed to produce the W (charged vector boson) to allow the decay and think it might take awhile.

 

[Vanadium 50]

It's not something that we can calculate and it's not even something that makes sense to ask. It's simply not a property that they have.

 

[Bill_K]

edpell, A virtual particle is always an intermediate stage - you can't say: let's create a virtual neutron, and then ask what happens to it. This is turning things inside out. You first describe a process by giving its end products, then you can ask what virtual particles were involved.

Well first of all, proton plus electron makes neutron plus neutrino, so let's not forget that. You also have to decide on the level - are you going to talk in terms of protons and neutrons or in terms of quarks and W's.

So, one possibility is that the neutron beta decays the usual way into proton plus electron plus antineutrino. If there's only enough energy in the initial collision to create a neutron that is off shell by 0.8 MeV, then indeed it will exist over a very short time given by Heisenberg. However the probability of the process is also extremely small. The net result is a proton-electron scatter plus the creation of a neutrino-antineutrino pair, and whether an intermediate neutron was briefly present is not important.

Another possibility is that the neutron reabsorbs the original neutrino, producing proton plus electron again. This process would be coherent with elastic scattering and contribute slightly to it. In this case you have an internal loop and must integrate the neutron and neutrino over all energies.