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

## TL;DR

This paper reexamines the proof of QCD factorization for certain exclusive meson processes at twist 3, clarifying previous misconceptions and confirming the validity of the factorization theorem after correcting earlier errors.

## Contribution

It identifies and corrects the improper use of Fierz identities in previous proofs, reaffirming the factorization theorem at the two-parton twist-3 level.

## Key findings

- Residual collinear divergences are due to improper Fierz insertion.
- Factorization holds at twist-3 after correction.
- Clarifies the theoretical foundation of exclusive meson processes.

## Abstract

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.