I don't have strong background in particle physics. Though, I had learnt a little of it. I have gone through the basic of these stuffs (pretty OK).
If I have done my homework right, color charge (R,G,B and their anti-colors) has nothing to do with "colors". They pair up in some fashion to form a gluon, which are 8 in number. Gluons are the force carriers between the quarks.
But my question is : "What exactly is the color charge? How do they name the colors? Is naming arbitrary?"
Question like this has been asked already here but I hardly think these answers address my question.
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6Possible duplicate of What IS Color Charge? – Salvatore Baldino Mar 22 '17 at 07:59
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I hardly think these answers address my question. Well the first of your questions certainly was addressed in the previous question. The latter two are generally off topic as per this Meta post. – Kyle Kanos Mar 22 '17 at 10:14
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Yes, color charge has nothing to do with "colors". The naming is indeed arbitrary; we could have called them yellow, blue, and cyan, or A, B, and C. What's important is that there are 3 of them.
As to your first question: the term "charge" carries a slightly different meaning in the context of QFT than in, say, classical EM. In the latter, the "amount of charge" is what determines the strength of the interaction. However in the context of QFT, we say a particle is charged if it transforms nontrivially under a gauge transformation. Using QED as an example, the charge nq (n an integer) determines how the field transforms under U(1) rotations - under a gauge transformation $$e^{iq\chi(x)}\in U(1)$$ the field transforms as $$\psi \rightarrow \psi '=e^{inq\chi(x)}\psi$$
(In group theory terms, the n determines the representation of the group. Note that if $n=0$, we get that $\psi '=\psi$, i.e. the field transforms trivially. This occurs when $\psi$ is uncharged under U(1).)
Similarly in QCD, the statement that quarks are charged is simply a statement that the quark fields will transform under SU(3) gauge transformations; replace the above $\psi$ with a 3-component field and the group with SU(3). But this is where terminology parts from classical EM: you speak of red, blue, green color charge, but it's not really a charge like q in the EM sense. In particular, if a quark is in a red state, or green state, or some superposition, it doesn't change the strength of the interaction the way adding more electric charge does in the classical sense.
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