Revisiting the factorization theorem for $\rho {\gamma }^{\ast }\to \pi (\rho )$ at twist 3

We revisit the proof of the perturbative QCD factorization for the exclusive processes $\rho {\gamma }^{\star }\to \pi (\rho )$ at the two-parton twist-3 level. It is pointed out that the residual collinear divergences observed in the literature, which break the factorization of the above processes at the considered accuracy, are attributed to the improper insertion of the Fierz identity for factorizing the fermion flow. We show that the factorization theorem indeed holds at the two-parton twist-3 level after the mishandling is corrected.