Can we meaningfully talk about the size of an elementary particle irrespective of its quantum state?

Question

Elementary particles such as the electron are quantum mechanical fuzzy objects described by quantum states or wavefunctions. They are not classical billiard balls with some fixed radius. Can we assign a notion of a natural "size'' of the electron irrespective of the state it is in? The only length associated with the electron that I can think of is the Compton wavelength, $\frac{\hbar}{m_ec}$. But I am not sure if it will be proper to refer that as the size of the electron. I don't have a definite answer. Thanks.

Answer 1

Elementary particles in the standard model of particle physics are axiomatically posited to be point particles, see table. The standard model successfully describes most of existing data and is successful in predictions for new studies, so all the beyond the standard model theories trying to fit the few unexplained data up to now, necessarily embed the standard model . At themoment all measurements are consistent within errors with the hypothesis in the model that electrons, neutrinos, etc are point particles.

Because they are quantum mechanical entities, they are fuzzy because their location follows their wavefunction description whose complex conjugate squared gives the probability of finding the point particle at (x,y,z,t). This probability locus is used to describe charge distributions, but the particle itself is a point, as far as accuracy of measurement presently goes.

For example, experiments that are trying to measure the size of the electron, with the hope of finding discrepancies with the standard model, are at the moment giving limits.