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Semi-inclusive DIS: Factorization
Feng Yuan"2 *
1- Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
2- RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA
In this talk, we will present a QCD factorization theorem for the semi-inclusive deep-
inelastic scattering with hadrons in the current fragmentation region detected at low
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 collabora-
tion have revealed nontrivial sea structure in nucleon . 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 trans-
verse 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 three-
dimension 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 trans-
verse 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 theoret-
ical studies in this direction started from the classical work on semi-inclusive processes in
eC+e annihilation by Collins and Soper , where a QCD factorization was proved, and
*This work was supported in part by the U.S. Department of Energy under contract DE-AC02-
05CH11231. 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
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Yuan, Feng. Semi-inclusive DIS: Factorization, article, December 10, 2008; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc897140/m1/1/: accessed March 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.