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As far as we know the quarks are not free not because of their fractional charges but because of the independent strong force interaction that grows with distance within the radius of the proton or neutron.

However, a valid observation IMO is also that free elementary particles with fractional charges are not observed so far to be possible.

Can it be that there is a correlation of the strong force with fractional charge and what would this relation be like?

Markoul11
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    Possible duplicate: https://physics.stackexchange.com/q/38137 – Nihar Karve Nov 03 '21 at 12:53
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    Here's an idea -- read the section on the Baryons about halfway down. Yes, I know it's probably a crackpot theory, but it's very relevant to your question nonetheless, maybe you'll at least find it interesting. – Adam Herbst Nov 03 '21 at 13:03
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    The question was already closed when I posted this comment, but in case it helps: The linked question was presumably deemed to be equivalent to this one because all quarks and leptons have integer charge in units of the down-quark's charge. The fact that we normally use units of the proton charge is an artifact of history. On the other hand, if you really are asking specifically why free elementary particles all have integer multiples of the proton's charge, then one answer could be the anomaly-cancellation requirement, depending on which details of the standard model you're keeping fixed. – Chiral Anomaly Nov 03 '21 at 13:26
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    @Markoul strong force interaction that grows with distance Can you give some references ? I always thought that any force, despite it's nature, decreases in magnitude with increasing distance, linearly or non-linearly. However, a valid observation IMO is also that free elementary particles with fractional charges are not observed so far to be possible Not true. Researchers have created quark-gluon plasma which is exactly what you are looking for. Also some quasi-particles has fractional charges. – Agnius Vasiliauskas Nov 03 '21 at 13:30
  • @Agnius Vasiliauskas https://en.wikipedia.org/wiki/Strong_interaction#Behavior_of_the_strong_force – Markoul11 Nov 03 '21 at 14:08
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    @Markoul11 It's not that simple. Quote from wiki The author states that the force between differently colored quarks remains constant at any distance after they travel only a tiny distance from each other a) Force change in a classical view is also tiny with tiny distance changes, so just maybe resolution of forces between quarks is not high enough ? b) Have you noticed that for that argument you need different quark colors ? So for neutron $udd$ quarks, this applies only for $ud$ quark pair if I have understood correctly. – Agnius Vasiliauskas Nov 03 '21 at 14:58

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