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QCD and confinement specify that hadrons must be color-neutral. My understanding is that this means you can have mesons (quark + antiquark) or baryons with 3 quarks, one of each color: Red+green+blue=neutral. In a meson, does the color of the quark and antiquark matter? Must a red quark be paired with a red antiquark; or does the color change constantly due to the exchange of gluons which also carry color charg?

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The color charges are paired (color with anticolor), but there's no gauge invariant meaning to the identification of the color (RGB). And due to QM, the quark states are a superposition over all the colors (and antiquarks over the anticolors). The wikipedia page is pretty clear: http://en.wikipedia.org/wiki/Color_charge. As it notes, you also can't distinguish a color from a certain superposition of the two non-complementary anticolors (e.g., R from a combination of anti-G + anti-B).

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