Graduate Why do we know that an elementary particle is a point particle?

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Elementary particles are considered point particles because, in high-energy collisions, evidence of internal structure only appears when the de Broglie wavelength is larger than the particle size, suggesting they lack substructure. Quantum Field Theory (QFT) describes particles as states that transform under symmetry groups, with no inherent size, challenging the classical notion of point particles. While protons and neutrons are composite and exhibit size due to their quark structure, electrons and neutrinos are treated as fundamental, lacking size in experimental observations. The concept of "point particle" is nuanced; it reflects the precision of measurements rather than a classical definition, as particles like electrons do not possess a sharp mass and are better understood as integrals over representations in QFT. Ultimately, the classification of particles remains complex, and while measurements can yield precise locations, they do not confirm classical point-like behavior.
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A. Neumaier said:
It is a stable infraparticle, which means that it has an additional mass degree of freedom, which behaves like an additional momentum dof.
Here is more on infraparticles. For more on the branch point of the electron propagator, see, e.g., section II of
 
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