Proper factorization theorems in high-energy scattering near the endpoint

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.