Is there some truth to the often told story that the running of couplings is the result of screening through virtual particles?

Question

It's a well established fact that coupling parameters changes with the energy scale at which we probe a given process:

A popular way to explain this phenomenon goes as follows. Particles are surrounded by clouds of virtual particles which screen (or anti-screen) the bare charge, analogous to what happens in a dielectric material.

As we probe the process at higher energies, we start to see more and more of these virtual electrons and thus the net charge that we observe becomes weaker.

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Virtual particles are, of course, a controversial topic. But I was wondering if there is some truth to this story?

Answer 1

Basically I think that your explanation works. I would add the following intuition about the RG - following Wilson (his Nobel lecture is a wonderful read), I think it is useful to think of the RG as averaging over length-scales. For long wave-lengths (corresponding to low-energy), we average over large distances, meaning that together with the particle we "pick up" a lot of the interactions around it, the virtual particles that interact with it constantly etc. Therefore we indeed get screening. At short wave-lengths (=high energy) we average only over the very vicinity of the particle, therefore getting less screening effects and having a direct access to the "bare" charge (which is just the coupling constant it has with the photons).

Answer 2

To give some context for what I have in mind, here's the best answer I came up with myself. Corrections, comments and better answers would be much appreciated.

The proper mathematical context to discuss this question are the renormalization group equations. For example, in $\phi^4$-theory we have: $$ \lambda_R(s_1) = \lambda_R(s_0) +C \ln \left( \frac{s_1 }{s_0}\right) \lambda_R^2(s_0) + \ldots $$

The idea is that we choose some reference scale $s_0$. By definition, the process is at this scale completely described by the simple single-vertex diagram with coupling $\lambda_R(s_0)$ at the vertex. But as soon as we probe the process at a different scale $s_1$, we must take corrections into account which are described by the renormalization group equation. Formulated differently, if we consider a perturbative expansion in the renormalized coupling at reference scale $s_0$, $\lambda_R(s_0)$, we only describe the process completely by the simple single vertex diagram at scale $s_0$. At any other scale $s_1$, we must take corrections due to additional diagrams into account. In this sense, the effects of virtual particles (which correspond to lines in the loop) become important at higher energy scales.

In particular, higher order correction become more and more important as we move farther away from $s_0$. This is a result of the logarithmic dependence on $s_1/s_0$. In this sense, the effects of virtual particles become even more important at higher energy scales. And, as a result, the charge becomes, at least in this case, more anti-screened.