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The binding of quarks in mesons baffles me. It's an Occam's Razor thing.

Since a meson is a colorless, the simplest way to bind its two quarks together is to use a $U(1)$ Cartan subalgebra of $SU(3)$. That is, the two quarks would bind by exchanging only gluons whose color and anticolor components cancel out.

But if those were the only types of gluon exchanges occurring in a meson, then the color and anticolor of the two quarks in the meson would remain unchanged and persistent over time. That in turn would imply the existence of three orthogonal "varieties" or polarizations of meson, e.g. $r\overline{r}$, $g\overline{g}$, $b\overline{b}$ and their compositions. There are more elegant ways to say that in group theory, but if you picture all the possible ways of orienting a symmetric stick in 3D space you've already captured the idea quite nicely.

By Occam's Razor, nothing beyond Cartan subalgebra binding is needed to explain the existence of mesons. And if the time slice is small enough, I do not easily see how at least some degree of transient color polarization in mesons can be avoided, e.g. while they are "exchanging" a gluon.

So, by Occam's razor there must exist experimental evidence in particle physics proving that mesons are not color polarized, or at least that they change their color polarization very quickly indeed.

So, three questions:

  1. Does anyone know references or keywords for finding theoretical and experimental articles on meson color polarization, or why it does not exist?

  2. If meson color polarization does exist, what studies have been done on the duration of color polarization in mesons?

  3. If meson color polarization does exist, how are meson-to-meson interactions affected when mesons with similar or diverse color polarizations encounter each other?


Relevant past questions:

What is the role of the color-anticolor gluons?

Does the color of a quark matter in a meson?

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  • $\begingroup$ Totally out of my depth here, but I would be surprised to learn that this "simplest mechanism" was all that was going on simply on Totalitarian Principle grounds. If it was the case I would instantly want to know why. $\endgroup$ – dmckee Dec 28 '13 at 19:58
  • $\begingroup$ You would have to explain why and how the $SU(3)$ color symmetry had been broken to a $U(1)$ symmetry, so it is not exactly Occam's Razor. $\endgroup$ – Trimok Dec 28 '13 at 20:45
  • $\begingroup$ dmckee, I agree. But Gell-Mann wasn't saying that the quantum world was structureless, only that all options will get explored. My question is about the structure. Trimok, you have some more subtle point I'm missing, but if there is symmetry breaking in my question I don't quite see where it is. A meson is not a baryon, and that should impact the details of how gluons are exchanged, not their fundamental symmetries. $\endgroup$ – Terry Bollinger Dec 29 '13 at 3:48
  • $\begingroup$ I don't know offhand of a specific reference, but my nuclear structure friends talk about "color magnetism." $\endgroup$ – rob Jun 5 '14 at 6:18
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1. Using $U(1)$ would just not result in color confinement. The 'simplest' model to achieve this was shown to be $SU(3)$. Thus Occams Razor is at work here.

Side note: A meson is NOT bound by the 'color-neutral' gluons only, as one might think. All 8 gluons can be interchanged, thus changing the colors of the quarks in a quantum-mechanical random way. Even if you start by interchanging color-neutral gluons only, as soon as more than one is involved, they will mutally interact by the other color-changing gluons, thus resulting again in the same non-linear effects, i.e. confinement.

If you set up a model using color-neutral gluons only, and took away the internal color of the color-neutral gluons, you would also remove confinement!

2. The internal color - even if we were able to preset it to e.g. $r\bar r$ - would thus be washed out on a timescale given by those gluon processes.

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