Q^2 Evolution of Chiral-Odd Twist-3 Distributions h_L(x, Q^2) and e(x, Q^2) in Large-N_c QCD
I. I. Balitsky, V. M. Braun, Y. Koike, K. Tanaka
TL;DR
It is proved that the twist-3 chiral-odd parton distributions obey simple Gribov-Lipatov-Altarelli-Parisi evolution equations in the limit of {ital N}{sub {ital c}}, and analytic results for the corresponding anomalous dimensions are given.
Abstract
We prove that the twist-3 chiral-odd parton distributions obey simple Gribov-Lipatov-Altarelli-Parisi evolution equations in the limit $N_c\to\infty$ and give analytic results for the corresponding anomalous dimensions. To this end we introduce an evolution equation for the corresponding three-particle twist-3 parton correlation functions and find an exact analytic solution. For large values of n (operator dimension) we are further able to collect all corrections subleading in N_c, so our final results are valid to $O(1/N_c^2\cdot \ln(n)/n)$ accuracy.