# I Virtual Particles and Energy Scales

#### jeffbarrington

Just a basic question which I will ask through an example:

An electron and positron can scatter by annihilating to form either a virtual Z or virtual photon, either of which can then pair produce to give an electron/positron pair (amongst an infinity of other processes whose contributions need to be summed up, of course). Firstly, am I correct in thinking the process involving the virtual Z can still occur when the CM energy is less than the mass of the Z (uncertainty principle allows energy to be 'borrowed' for a sufficiently short time)? Second, if this is the case, then if the CM energy is indeed much less than the mass of the Z, I can take this to mean that the contribution of the process involving the Z is negligible (which I think can be understood from the 1/(P^2-m^2c^2) factor in the propagator)?

Thanks in advance, really new to a lot of these concepts so my understanding is a bit of a jumble at the moment.

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#### mfb

Mentor
An electron and positron can scatter by annihilating to form either a virtual Z or virtual photon, either of which can then pair produce to give an electron/positron pair (amongst an infinity of other processes whose contributions need to be summed up, of course). Firstly, am I correct in thinking the process involving the virtual Z can still occur when the CM energy is less than the mass of the Z (uncertainty principle allows energy to be 'borrowed' for a sufficiently short time)?
It is not "either/or". You cannot look at a given collision and say "this was a photon" or "this was a Z".
Virtual particles are tools in calculations, they are not real.

If you plot the cross section against the invariant mass, you get a spectrum that looks like this (from here):

You can compare this spectrum to "what would happen in a world without Z", and then assign the difference to the Z, but that is not really fair. You can also ask "what would happen in a world without the photon". And here is the point: If you add those two results, you do not get what we observe: it is not "either/or".

#### jeffbarrington

It is not "either/or". You cannot look at a given collision and say "this was a photon" or "this was a Z".
Virtual particles are tools in calculations, they are not real.
So this is sort of what I'm getting at - I understand that it is not either/or. What I mean to say is, the total rate of some process involves summing up an infinite number of contributions from Feynman diagrams, higher order being much less significant (except with the strong force). Some of these diagrams include a Z, some just photons. My question is that when we do the calculations, do we still include the contributions from those diagrams which include the Z when the CM energy is less than the mass of the Z (I am fairly sure we do, just checking) and, if this is the case, do these contributions become smaller?

To reiterate - I understand that the diagrams are mathematical tools, but they do correspond to contributions to the overall rate calculation, and some of these diagrams include the Z, and some don't (which isn't to be taken as literally meaning a Z was 'definitely' there or not - as you say, they're virtual, we can't see them). I realise my wording was woolly there.

#### mfb

Mentor
My question is that when we do the calculations, do we still include the contributions from those diagrams which include the Z when the CM energy is less than the mass of the Z (I am fairly sure we do, just checking) and, if this is the case, do these contributions become smaller?
It is relevant below 90 GeV (as you can see from the plot above, it is a significant contribution starting at about 70 GeV), but the contribution in general gets smaller if you are further away from 90 GeV.

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