Fractional Analytic Perturbation Theory in QCD and Exclusive Reactions

TL;DR

This paper develops a fractional analytic perturbation theory approach in QCD, ensuring scheme and scale invariance for exclusive reactions like the pion form factor by extending the Analytic Perturbation Theory to fractional powers of the coupling.

Contribution

It introduces a generalized fractional analytic perturbation theory in QCD that maintains analyticity and scheme independence for exclusive process calculations.

Findings

Results are insensitive to scheme and scale choices.

The approach generalizes APT to fractional powers of the coupling.

Enhanced stability in QCD calculations of exclusive reactions.

Abstract

Different ``analytization'' procedures for the factorized pion form factor are discussed in comparison with the standard QCD perturbation theory at NLO. It is argued that demanding the analyticity of the exclusive amplitude as a \emph{whole}, entails insensitivity of the results on all scheme and scale-setting parameters, including the factorization scale. This enables us to develop an approach of optimized perturbation theory within the MS-bar scheme and to generalize the Analytic Perturbation Theory to non-integer (fractional) powers of the strong running coupling in the complex Q^2 plane