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The classic charge radius formula $r$ is used commonly to calculate the radius of electrons(assuming they are spherical). My problem is: can the same formula be used to calculate radii of muons or taus and other leptons and fermions. And if not, what are the radii of muons and taus and how are they calculated? $$r=\frac{e^2}{4πε_0mc^2}$$ I want to know the radii of muons and taus, and I wonder if the classic charge radius formula given above can be used.

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You can calculate it, but it will mean as little as it does for the electron. In modern physics, such as the Standard Model, elementary particles are point particles, not little spheres. As Wikipedia says, “Attempts to model the electron as a non-point particle have been described as ill-conceived and counter-pedagogic.”

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  • $\begingroup$ I'm not sure that's entirely fair. The classical radius of an electron is a guide as to the distance (i.e. energy) at which renormalisation effects become important. It's a reasonable question whether the classical radius of the muon and tau have the same significance. $\endgroup$ – John Rennie Aug 20 at 16:56
  • $\begingroup$ The classical radius of charged particles is also used in cross section definitions, for example the Klein-Nishina formula : en.wikipedia.org/wiki/Klein%E2%80%93Nishina_formula $\endgroup$ – Cham Aug 20 at 17:24
  • $\begingroup$ Yes, that distance appears in physics, but it isn’t the radius of a spherical particle. It just tells you how close you have to get to the point particle before some effect is significant. $\endgroup$ – G. Smith Aug 20 at 18:02
  • $\begingroup$ Are there any recent work measuring the radii of muons and taus then?@G.Smith $\endgroup$ – MichaelPhysica Aug 21 at 6:12
  • $\begingroup$ I’m not personally aware of such experiments. But if any experiment (for example, at CERN’s LHC) had ever revealed the electron, muon, or tau to have a finite radius, it would be huge news, since the Standard Model says that they and all other elementary particles are point particles. The fact that such a discovery would almost certainly get an experimenter a Nobel makes me confident that physicists are avidly looking for any such deviations from the Standard Model. They just haven’t found any yet that can attributed to finite size. $\endgroup$ – G. Smith Aug 21 at 6:27

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