Diagrammatic mass factorization

We develop an analogy between mass factorization (concerning the mass equivalent collinear singularities) and multiplicative Bogoliubov-Parasiuk-Hepp-Zimmermann renormalization (concerning the ultraviolet singularities) with the role of the renormalization constant taken over by the operator matrix elements. By introducing Zimmermann's forest formula we demonstrate its use in constructing the deep-inelastic (DI)/Drell-Yan (DY) factorized parton cross sections and arrive at an all-order proof of mass factorization. The DY correction term is determined by similar reasonings. The noncancellation of the higher-order QCD infrared singularities is left apart