Analysis of the Pion Electromagnetic Form Factor with Next-to-Next-to-Leading Order QCD Corrections

TL;DR

This paper refines the theoretical prediction of the pion electromagnetic form factor at high momentum transfer by applying the Principle of Maximum Conformality to NNLO QCD calculations, reducing scale ambiguities and improving agreement with experiments.

Contribution

It introduces the use of the Principle of Maximum Conformality to NNLO QCD calculations of the pion form factor, enhancing prediction precision by eliminating renormalization scale ambiguities.

Findings

PMC reduces renormalization scale uncertainties.

Improved predictions align better with experimental data.

Enhanced understanding of pion structure through precise QCD calculations.

Abstract

NNLO QCD corrections for the pion electromagnetic form factor at large momentum transfer have been recently performed in [Phys. Rev. Lett. 132, 201901 (2024); Phys. Rev. Lett. 134, 221901 (2025)], revealing that the NLO and NNLO contributions are positive and sizeable. Unfortunately, these predictions have been obtained using the conventional scale-setting method and thus they are plagued by large renormalization scale ambiguities. In this paper, we analyze the pion electromagnetic form factor at NNLO by applying the Principle of Maximum Conformality (PMC), which is introduced with the aim of resolving renormalization scheme and scale ambiguities. By applying the PMC, a more precise perturbative QCD (pQCD) prediction for the pion EMFF \(Q^2F_\pi(Q^2)\) without conventional renormalization scale ambiguity can be achieved. This improved pQCD prediction is highly beneficial for the precise determination of the pion light-cone distribution amplitude. We then conduct a comprehensive comparison between theoretical predictions and experimental measurements of the pion EMFF \(Q^2F_\pi(Q^2)\).