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Usually in particle physics larger mass refers to a smaller cross-section of a particle or atom thus a smaller sized particle.

How a so relative light mass particle only $511\,\mathrm{keV}$ can be so small thus dimensionless according to the Standard Model (SM) or at least $10^{-18}$m upper size limit?

Gert
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Markoul11
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    Mass is inversely related to Compton wavelength, but not cross sections. All particles in the SM chart are essentially pointlike, up to virtual dressing clouds around them. Neutrinos do not have appreciable sizes, despite their small mass. – Cosmas Zachos Apr 11 '22 at 16:15
  • @CosmasZachos Effectively yes but not physically. – Markoul11 Apr 11 '22 at 16:24
  • I making a guess now and hypothesis about a physical model: Assuming the answer is, it isn’t small. The physical charge dressed model of the electron gives a theoretical charge radius of the electron the reduced Compton wavelength 3.86E-13 m. So it is much bigger than the nucleus of an atom and its charge sphere (shell) is fully encompassing the nucleus from there also the expression comes from, “electron cloud”. The cloud is not because the alleged quantum superposition of a dimensionless point electron but instead the electron IS the cloud and its charge is fully encompassing the nucleus. – Markoul11 Apr 11 '22 at 17:08
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    @Markoul11 this site is about mainstream physics, not about science fiction and personal models,.The electron is a quantum mechanical entity and is described by a quantum mechanics wave function which depends on the boundary solutions of the specific problem. In mainstream physics it is a point particle and the probability of its location at x,y,z,t is dependent on the wavefunction solution. The probability loci are the famous "cloud" . Yes, there is a probability for the electron to be on the nucleus and that is how, in mainstream physics electron capture happens if quantum numbers – anna v Apr 11 '22 at 17:30
  • can be conserved. https://en.wikipedia.org/wiki/Electron_capture . – anna v Apr 11 '22 at 17:31
  • Dear @annav effective theories explanations, describing physical interpretations of phenomena despite of their success in predicting experimental results sometimes can be also science fiction :) – Markoul11 Apr 11 '22 at 18:15

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How a so relative light mass particle only 511keV can be so small thus dimensionless according to the Standard Model (SM) or at least 10−18m upper size limit?

Because an electron is a point particle with no internal structure (as far as we can tell).

When a composite "particle" (like an atom) has internal structure, the size and energy can often be closely related.

For example, the "size" of a hydrogen atom (e.g., the mean inverse radius $<1/r>$ of the electron in the ground state) is about an inverse angstrom, which (in units where $e=\hbar=m=1$) is about the same as the energy required to remove an electron from the ground state. (They differ by a factor of 2, so we say they are the same order of magnitude).

hft
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