  Consistent factorization theorems in high-energy scattering near the
threshold are presented in the framework of the soft-collinear effective
theory. Traditional factorization theorem separates the soft and collinear
parts successfully, but a final step should be supplemented if each part
encounters infrared divergence. We present factorization theorems in which the
infrared divergences appear only in the parton distribution functions and the
infrared divergence is removed by carefully separating and reorganizing
collinear and soft parts. The underlying physical idea is to isolate and remove
the soft contributions systematically from the collinear part in loop
corrections order by order. After this procedure, each factorized term in the
scattering cross sections is free of infrared divergence, and can be safely
computed using perturbation theory. This factorization procedure can be applied
to various high-energy scattering processes. We show factorization theorems in
Drell-Yan processes, deep inelastic scattering and Higgs production near the
endpoint.
