Calculation of the pion-photon transition form factor using dispersion relations and renormalization-group summation

TL;DR

This paper develops a modified Fractional Analytic Perturbation Theory scheme combined with dispersion relations and renormalization-group methods to accurately compute the pion-photon transition form factor, especially at low energies.

Contribution

It introduces a process-specific boundary condition version of FAPT that improves low-momentum QCD calculations within the lightcone sum-rule framework.

Findings

Enhanced accuracy of the form factor calculation at low energies.

Improved inclusion of radiative corrections in QCD perturbation theory.

Demonstrated consistency with asymptotic QCD behavior.

Abstract

We consider the lightcone sum-rule description of the pion-photon transition form factor, based on dispersion relations, in combination with the renormalization group of QCD, in terms of the formal solution of the Efremov-Radyushkin-Brodsky-Lepage evolution equation, and show that the emerging scheme amounts to a certain version of Fractional Analytic Perturbation Theory (FAPT). In order to ensure the correct asymptotic behavior of the considered physical quantity, this modified FAPT version has to be supplemented by process-specific boundary conditions---in contrast to the standard one. However, it provides the advantage of significantly improving the inclusion of radiative corrections in the low-momentum regime of QCD perturbation theory using renormalization-group summation.