Semi-inclusive DIS: Factorization

There has been considerable experimental and theoretical interest in semi-inclusive hadron production in deep inelastic scattering (SIDIS) processes. For example, by studying the polarized and unpolarized SIDIS, one will be able to identify the sea quark distribution and polarization in nucleon, and the experimental results from the HERMES collaboration have revealed nontrivial sea structure in nucleon [1]. More recently, SIDIS opened a new window to study the transverse momentum dependent (TMD) parton distributions and fragmentation functions from the low transverse momentum hadron production. The transverse momentum distribution of the final state hadron is directly related to the transverse momentum dependence of the parton distributions and fragmentation. These studies will provide new opportunities to explore the partonic structure of nucleon, especially the threedimension distribution of partons inside nucleon. The DIS experiments, including HERMES, COMPAS, and JLab Hall B collaborations, have studied various azimuthal asymmetries in SIDIS. In particular, the HERMES collaboration found sizable single spin asymmetries in these processes involving nontrivial QCD effects and hadron structure. On the theory side, there has been great progress in the last few years too. In this short talk, it is impossible to cover all these important physics. Rather, I would like to focus on one of the questions concerning applying the QCD to the description of the semi-inclusive DIS, in particular, the QCD factorization for SIDIS. Unlike the inclusive DIS process, SIDIS is more involved because of additional hadron measurement in the final state. We can classify the SIDIS processes into three different categories. First, if we integrate out the transverse momentum of the final state hadron, these SIDIS will be similar to the inclusive DIS, and a collinear factorization is applicable. The cross section can be written as a convolution of the integrated parton distribution and fragmentation function and the hard partonic cross section which can be calculated from perturbative QCD. Second class is the large transverse momentum SIDIS. When transverse momentum is large enough (in order of Q, the virtuality of the virtual photon), again a collinear factorization shall be used to analyze the cross section. The third class is the low transverse momentum hadron production, where a collinear factorization approach may not be applicable because the transverse momentum of the final state hadron is small compared to the hard scale Q. In order to describe this class of processes, we have to introduce a new factorization theorem, involving the transverse momentum dependent parton distribution and fragmentation functions. Rigorous theoretical studies in this direction started from the classical work on semi-inclusive processes in e+e− annihilation by Collins and Soper [2], where a QCD factorization was proved, and ∗This work was supported in part by the U.S. Department of Energy under contract DE-AC0205CH11231. We are grateful to RIKEN, Brookhaven National Laboratory and the U.S. Department of Energy (contract number DE-AC02-98CH10886) for providing the facilities essential for the completion of this work.