Simplification of higher-twist evolution in the large $N_c$ limit: why and why not

Abstract.

Working in the light-cone gauge, we find a simple procedure to calculate the autonomous one-loop $Q^2$ evolution of the twist-three part of the nucleon $g_T(x, Q^2)$ structure function in the large-$N_c$ limit. Our approach allows us to investigate the possibility of a similar large-$N_c$ simplification for other higher-twist evolutions. In particular, we show that it does not occur for the twist-four part of the $f_4(x, Q^2)$, $g_3(x, Q^2)$ and $h_3(x, Q^2)$ distributions. We also argue that the simplification of the twist-three evolution does not persist beyond one loop.