The SCET_II and factorization

We reformulate the soft-collinear effective theory which includes the collinear quark and soft gluons. The quark form factor is used to prove that SCET${}_{\mathrm{I}\mathrm{I}}$ reproduces the IR physics of the full theory. We give a factorization proof in deep inelastic lepton-hadron scattering by use of the position space formulation.