What is the Leading Color Approximation in QCD?

[earth2]

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

 

[tom.stoer]

Leading color approximation is defined as N_c ∼ N_f ≫ 1; sometimes you will find leading color = large-N_c. This may be slightly different.

In the large-N_c 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-N_c from 't Hooft (A planar diagram theory for strong interactions. Nucl. Phys. B72 (1974) 461 - 473.) shows that for large-N_c only planar diagrams contribute; planar means that there are no diagrams where two quark lines cross.