If the singlet gluon existed (and I realize it doesn't)

[Zarathustra0]

OK, here's a question that's unusual in that it regards a particle state that's pretty much taken to be nonexistent. Nonetheless, my curiosity is piqued. I've read from multiple sources that if the singlet gluon existed, it would couple with equal strength to all baryons because they are also color singlets. This coupling of course really must consist of coupling between the singlet gluon and the constituent quarks of the baryon since baryons are not elementary particles (or have I gotten part of that wrong?). That said, it seems that the quarks in the baryon are themselves not color singlets. Does a quark in a baryon somehow know that it is part of a color-singlet composite particle, i.e., does it carry this information inside it (e.g., as a quantum number although I assume not) such that the singlet gluon can couple to it--or does the singlet gluon somehow couple to the whole baryon? Obviously it doesn't couple at all because it doesn't exist, but I'm speaking hypothetically here.

 

[Bill_K]

Interesting question. I believe a singlet gluon would behave quite differently from the octet. Never mind the baryons, it would couple to quarks, and presumably all quarks equally.

The nonabelian nature of the color gauge group is what makes the Lagrangian nonlinear. This leads to the gluon-gluon interactions that cause the color force to strengthen at greater distances and hence to color confinement. But a singlet gluon would be associated with an abelian gauge symmetry, and would appear very similar in fact to electromagnetism. You'd basically have a long-range vector coupling. Since the 'charge' for this interaction would be the same for all quarks, it would lead to a repulsive force between them.

 

[Zarathustra0]

Thanks--in that case, would the force between antiquarks also be repulsive and that between a quark and an antiquark attractive?