Evolution of transverse momentum dependent distribution and fragmentation functions
A. A. Henneman, Daniel Boer, P. J. Mulders
TL;DR
This work derives the scale evolution of transverse-momentum dependent distribution and fragmentation functions that drive azimuthal spin asymmetries, using Lorentz invariance and QCD equations of motion. In the large-$N_c$ limit, the non-singlet and several twist-3 (including T-odd) sectors evolve autonomously with DGLAP-like kernels, linking moments of these functions to twist-2 and twist-3 operators. The results establish a consistent framework for Collins-related observables and other azimuthal effects, and reveal Gribov-Lipatov reciprocity for twist-2 channels while highlighting limitations from two-argument twist-3 contributions. Overall, the paper provides practical evolution equations to relate measurements across different energies in semi-inclusive processes.
Abstract
We use Lorentz invariance and the QCD equations of motion to study the evolution of functions that appear at leading order in a 1/Q expansion in azimuthal asymmetries. This includes the evolution equation of the Collins fragmentation function. The moments of these functions are matrix elements of known twist two and twist three operators. We present the evolution in the large N_c limit, restricting to non-singlet for the chiral-even functions.