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

N. G. Stefanis, W. Schroers+1 more|ArXiv.org|Dec 8, 1998

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper introduces an infrared-finite factorization and optimized renormalization scheme for exclusive processes in QCD, using an analytic, infrared-stable effective coupling αₛ(Q²) that removes Landau singularities via power corrections. Applied to pion form factors, the framework enhances hard scattering amplitudes by modifying the cusp and quark anomalous dimensions, leading to improved agreement with experimental data without suppressing transverse momentum effects.

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 $α_{s}(Q^{2})$ which removes the Landau singularity at $Q^{2}=Λ_{ m QCD}^{2}$ 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.

Motivation & Objective

• To resolve infrared divergences in exclusive QCD processes by constructing a finite, infrared-stable factorization scheme.
• To eliminate the Landau singularity in αₛ(Q²) at Q² = Λ²_QCD through a power-behaved correction.
• To enable the inclusion of transverse degrees of freedom in exclusive amplitudes without observable suppression.
• To optimize the renormalization scheme for exclusive processes like pion form factors and pion-photon transitions.
• To improve the phenomenological description of pion electromagnetic and transition form factors using perturbative QCD with enhanced hard scattering contributions.

Proposed method

• Introduce an analytic, infrared-stable effective coupling αₛ(Q²) that avoids the Landau pole by incorporating a power-law correction.
• Use this modified αₛ(Q²) to compute the cusp anomalous dimension and quark anomalous dimension in the Sudakov and evolution equations.
• Derive a modified Sudakov form factor and evolution kernel that reflect the infrared-finite structure of the coupling.
• Implement the new factorization and renormalization scheme in the calculation of exclusive amplitudes, particularly for pion form factors.
• Apply the framework to the pion's electromagnetic form factor and the pion-photon transition form factor, comparing results with experimental data.
• Ensure consistency with perturbative QCD while maintaining finiteness and physical behavior at low momentum scales.

Experimental results

Research questions

• RQ1 How can infrared divergences in exclusive QCD processes be systematically removed while preserving physical observables?
• RQ2 What is the impact of replacing the standard perturbative αₛ(Q²) with an infrared-finite analytic coupling on the hard scattering amplitude?
• RQ3 How does the modified cusp anomalous dimension affect the Sudakov form factor in exclusive processes?
• RQ4 To what extent does the inclusion of transverse momentum degrees of freedom remain viable in the new scheme without suppression?
• RQ5 Can the improved framework yield better agreement with experimental data for pion form factors compared to standard perturbative QCD?

Key findings

• The analytic coupling αₛ(Q²) successfully removes the Landau singularity at Q² = Λ²_QCD through a power-behaved correction, ensuring infrared finiteness.
• The modified cusp anomalous dimension leads to a significant enhancement of the Sudakov form factor, increasing the hard scattering amplitude.
• The quark anomalous dimension is altered in a way that modifies the evolution of distribution amplitudes, improving the description of exclusive processes.
• The framework allows for the consistent inclusion of transverse momentum effects without observable suppression, preserving physical amplitudes.
• The calculated pion electromagnetic form factor shows improved agreement with experimental data, particularly in the high-Q² regime.
• The pion-photon transition form factor is also enhanced in the new scheme, aligning better with experimental measurements than in conventional perturbative QCD.