Pion form factor at spacelike momentum transfers from local-duality QCD sum rule

TL;DR

This paper investigates the pion form factor at spacelike momentum transfers using local-duality QCD sum rules, highlighting the dominance of nonperturbative effects up to high momentum values without relying on the pion distribution amplitude.

Contribution

It introduces a calculation of the two-loop double spectral density for the $<AVA>$ correlator, enabling predictions of the pion form factor without referencing the pion distribution amplitude.

Findings

Nonperturbative contributions dominate up to Q^2 = 20 GeV^2.

The O(1) term provides over half of the form factor at high Q^2.

Nonperturbative effects significantly influence the pion form factor at large momentum transfers.

Abstract

We study the pion form factor in a broad range of spacelike momentum transfers within the local-duality version of QCD sum rules. We make use of the recently calculated two-loop double spectral density of the $<AVA>$ correlator including O(1) and $O(\alpha_s)$ terms, which allows us to give predictions for the pion form factor and to study the interplay between the nonperturbative and perturbative contributions to the pion form factor without any reference to the pion distribution amplitude. Our results demonstrate the dominance of the nonperturbative contribution to the form factor up to relatively large values of the momentum transfer: namely, the nonperturbative O(1) term, which provides the $1/Q^4$ power correction, gives more than half of the pion form factor in the region $Q^2 \le 20$ GeV$^2$.