Factorization of low-energy gluons in exclusive processes

TL;DR

This paper proves factorization in exclusive processes considering low-energy soft and collinear gluons, highlighting the role of color-singlet states and the limitations of soft-collinear effective theory.

Contribution

It provides a detailed proof of factorization including arbitrarily low-energy modes, clarifying the role of soft functions and collinear modes in exclusive processes.

Findings

Soft functions are free of collinear divergences in the factorization.

Cancellation of the soft function depends on the color-singlet nature of external hadrons.

Low-energy collinear modes can prevent soft function cancellation.

Abstract

We outline a proof of factorization in exclusive processes, taking into account the presence of soft and collinear modes of arbitrarily low energy, which arise when the external lines of the process are taken on shell. Specifically, we examine the process of e^+e^- annihilation through a virtual photon into two light mesons. In an intermediate step, we establish a factorized form that contains a soft function that is free of collinear divergences. In contrast, in soft-collinear effective theory, the low-energy collinear modes factor most straightforwardly into the soft function. We point out that the cancellation of the soft function, which relies on the color-singlet nature of the external hadrons, fails when the soft function contains low-energy collinear modes.