Kinematics of current region fragmentation in semi-inclusive deeply inelastic scattering

Different kinematical regions of semi-inclusive deeply inelastic scattering (SIDIS) processes correspond to different underlying partonic pictures, and it is important to understand the transition between them. We find criteria in semi-inclusive deeply inelastic scattering (SIDIS) for identifying the current fragmentation region — the kinematical region where a factorization picture with fragmentation functions is appropriate, especially for studies of transverse-momentum-dependent (TMD) functions. This region is distinguished from the central (soft) and target fragmentation regions. The basis of our argument is in the errors in approximations used in deriving factorization. As compared with previous work, we show that it is essential to take account of the transverse momentum of the detected hadron, and we find a much more restricted range for genuine current fragmentation. We show that it is important to develop an extended factorization formulation to treat hadronization in the central region, as well as the current and target fragmentation regions, and to obtain a unified formalism spanning all rapidities for the detected hadron.