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Parton shower Monte Carlo event generators in which the shower evolves from hard splittings to soft splittings generally use the leading color (LC) approximation, which is the leading term in an expansion in powers of $1/N_\Lc^2$, where $N_\Lc = 3$ is the number of colors.
Z. Nagy and D. E. Soper, Parton showers with quantum interference: leading color, spin averaged
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