What is the Leading Color Approximation in QCD?

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In summary, "Leading color" in QCD refers to the large-Nc approximation, where Nc ∼ Nf ≫ 1. This allows for the neglect of terms with 1/N in certain algebraic relations in SU(N). According to 't Hooft's first paper on large-Nc, only planar diagrams contribute in this limit, meaning there are no diagrams with crossing quark lines.
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earth2
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Hey folks,

i recently stumbled across the notion "leading color" in some qcd paper. What puzzles me is, how can the color structure in qcd give rise to leading terms? Does any of you have an example for this? Or an explanation?

Thanks!
earth2
 
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Leading color approximation is defined as Nc ∼ Nf ≫ 1; sometimes you will find leading color = large-Nc. This may be slightly different.

In the large-Nc approximation you make use of the fact that in certain algebraic relations in SU(N), e.g. in contractions of SU(N) matrices, you get terms with 1/N which you neglect in this limit. The first paper on large-Nc from 't Hooft (A planar diagram theory for strong interactions. Nucl. Phys. B72 (1974) 461 - 473.) shows that for large-Nc only planar diagrams contribute; planar means that there are no diagrams where two quark lines cross.
 

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