Virtual Particles and Energy Scales

In summary, the process of electron and positron scattering by annihilating to form either a virtual Z or virtual photon can also lead to pair production of an electron and positron. This is one of many processes that contribute to the overall rate calculation, and the contribution from the Z can still occur even when the center of mass energy is less than the mass of the Z due to the uncertainty principle. These contributions become smaller as the center of mass energy moves further away from the mass of the Z. However, it is important to note that virtual particles are mathematical tools and are not actually present in the collision.
  • #1
jeffbarrington
24
1
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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  • #2
jeffbarrington said:
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):

Zres1.png


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".
 
  • #3
mfb said:
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 realize my wording was woolly there.
 
  • #4
jeffbarrington said:
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.
 

FAQ: Virtual Particles and Energy Scales

What are virtual particles?

Virtual particles are particles that exist briefly as fluctuations in energy in the vacuum of space. They are not observable directly, but their effects can be seen in the behavior of other particles.

How are virtual particles related to energy scales?

Virtual particles are closely tied to energy scales because their creation and annihilation is governed by the uncertainty principle, which is directly related to energy. Higher energy scales can lead to the creation of more massive and short-lived virtual particles.

Can virtual particles be observed?

No, virtual particles cannot be directly observed. They exist on a subatomic level and are only detectable through their effects on other particles.

What is the role of virtual particles in quantum field theory?

Virtual particles play a crucial role in quantum field theory, where they are used to explain interactions between particles. They are also important in calculations and predictions of particle behavior.

Do virtual particles violate the law of conservation of energy?

No, virtual particles do not violate the law of conservation of energy. They may briefly appear to have energy, but this energy is balanced out by their short lifespan and does not violate the overall conservation of energy in the universe.

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