  The widely used nonrelativistic QCD (NRQCD) factorization theory now
encounters some notable difficulties in describing quarkonium production. This
may be due to the inadequate treatment of soft hadrons emitted in the
hadronization process, which causes bad convergence of velocity expansion in
NRQCD. In this paper, starting from QCD we propose a rigorously defined
factorization approach, soft gluon factorization (SGF), to better deal with the
effects of soft hadrons. After a careful velocity expansion, the SGF can be as
simple as the NRQCD factorization in phenomenological studies, but has a much
better convergence. The SGF may provide a new insight to understand the
mechanisms of quarkonium production and decay.
