# Difference between boundedness (electrons around nuclei) and color confinement (quarks)

How does the orbiting of electrons around nuclei START?

Bound electrons don't move, right?

Do different orbitals overlap in multielectron atom?

What is the difference between real orbital & complex orbital?

https://en.wikipedia.org/wiki/Bound_state

Why aren't quarks free?

Could quarks be free in higher-dimensional space than 3D?

https://en.wikipedia.org/wiki/Color_confinement

We now know that quarks cannot be found free in our world (at normal energy levels), they are always in a confinement in nuclei with gluons. This interaction is due to the strong force or color charge.

I understand that electrons are bound to the nuclei but they can also be found free. Now electrons' bound is due to the EM charge which is different from color charge.

Both electrons and quarks do have rest mass. Both electrons and quarks interact with each other.

Quarks are confined because they interact with each other and to pull them apart, you need to put infinite energy, and it is like a rubber band and if it snaps, the energy will be enough to create more quarks.

A free quark is like the free end of a rubber band. If you want to make the ends of a rubber band free you have to pull them apart, however the farther apart you pull them the more energy you have to put in. If you wanted to make the ends of the rubber band truly free you'd have to make the separation between them infinite, and that would require infinite energy. What actually happens is that the rubber band snaps and you get four ends instead of the two you started with.

Similarly, if you take two quarks and try and pull them apart the force between them is approximately independent of distance, so to pull them apart to infinity would take infinite energy. What actually happens is that at some distance the energy stored in the field between them gets high enough to create more quarks, and in stead of two separated quarks you get two pairs of quarks.

This doesn't happen when you pull apart a proton and electron because the force between them falls according to the inverse square law. The difference between the electron/proton pair and a pair of quarks is that the force between the quarks doesn't fall according to the inverse square law. Instead at sufficiently long distances it becomes roughly constant.

I don't think this is fully understood (it certainly isn't fully understood by me :-), but it's thought to be because the lines of force in the quark-quark field represent virtual gluons, and gluons attract each other. This means the lines of force collect together to form a flux tube. By contrast the electron-proton force is transmitted by virtual photons and photons do not attract each other.

And this is what is interesting, gluons are massless and photons too, and gluons do not possess EM charge, and photons either. Still, gluons attract each other, while photons do not. Still there are 8 types of gluons, while there is only one type of photon?

The main confusion is that quarks do have EM charge, just like electrons and protons (nuclei). And they have rest mass too. But gluons do not have EM charge or rest mass and photons do not either. There is pair production too in both cases, quarks-antiquark and electron-positron pairs can be created. Both cases seems to be alike.

The only difference could be if we could not find a free gluon. The answers are saying that free quarks cannot be found (at low energy levels) but I did not find anything about free gluons.

Question:

1. What is the main difference between boundedness and confinement? Is this only because we can't find free gluons (at low energies)? Is there any reason to talk about a difference or could they be the same thing at high energies?

The number of gluons corresponds to the number of generators of $SU(3)$. There are 8 unique generators, so there are 8 types of gluons. But how do we know that the group is $SU(3)$ specifically? We know that the group describing the strong force involves three colors because the cross-sections of various QCD processes involve a multiplication by a color factor that is determined by the number of colors. We get these cross sections wrong if we use a different number of colors. Assuming unitarity, we now have the possible group narrowed down to $U(3)$ or $SU(3)$. If the group was $U(3)$, there would be a color-singlet gluon (the ninth generator, giving the extra degree of freedom in $U(3)$), which could potentially be free; the fact that we do not observe free gluons means that the proper group is $SU(3)$, and thus that there are 8 gluons.