Pion Form Factor in QCD at Intermediate Momentum Transfers

TL;DR

This paper analyzes the electromagnetic pion form factor using light-cone sum rules, incorporating radiative and higher-twist effects, and compares results with experimental data to understand soft and hard QCD contributions at intermediate momentum transfers.

Contribution

It provides a detailed quantitative analysis of the pion form factor with radiative corrections, higher-twist effects, and clarifies the soft-hard contribution interplay at intermediate Q^2.

Findings

Data favors the asymptotic pion distribution amplitude profile.

Nonperturbative corrections are about 30% at Q^2 ~ 1 GeV^2.

Strong cancellation occurs between soft and hard contributions.

Abstract

We present a quantitative analysis of the electromagnetic pion form factor in the light-cone sum rule approach, including radiative corrections and higher-twist effects. The comparison to the existing data favors the asymptotic profile of the pion distribution amplitude and allows to estimate the deviation: $(\int du/u \phi_\pi(u))/ (\int du/u \phi^{\rm as}_\pi(u))=$ 1.1$\pm$ 0.1 at the scale 1 GeV. Special attention is payed to the precise definition and interplay of soft and hard contributions at intermediate momentum transfer, and to matching of the sum rule to the perturbative QCD prediction. We observe a strong numerical cancellation between the soft (end point) contribution and power suppressed hard contributions of higher twist, so that the total nonperturbative correction to the usual pQCD result turns out to be of order 30% for $Q^2\sim 1$ GeV$^2$.