Infrared-finite factorization and renormalization scheme for exclusive processes. Application to pion form factors

TL;DR

This paper introduces an infrared-finite factorization and renormalization scheme for exclusive processes, allowing the inclusion of transverse degrees of freedom and improving the calculation of pion form factors using a stable effective coupling.

Contribution

It develops an infrared-stable coupling scheme that removes Landau singularity and enhances the perturbative calculation of exclusive amplitudes, with applications to pion form factors.

Findings

Enhanced perturbative predictions for pion form factors.

Infrared-stable coupling removes Landau pole singularity.

Improved agreement with experimental data.

Abstract

We develop and discuss an infrared-finite factorization and optimized renormalization scheme for calculating exclusive processes which enables the inclusion of transverse degrees of freedom without entailing suppression of calculated observables, like form factors. This is achieved by employing an analytic, i.e., infrared stable, effective coupling $\alpha_{s}(Q^{2})$ which removes the Landau singularity at $Q^{2}=\Lambda_{\rm QCD}^{2}$ by a power-behaved correction. The ensuing contributions to the cusp anomalous dimension, related to the Sudakov form factor, and to the quark anomalous dimension, which controls evolution, lead to enhancement of the hard part of exclusive amplitudes, calculated in perturbative QCD. The phenomenological implications of this framework are analyzed by applying it to the pion's electromagnetic form factor and the pion-photon transition.