Pion form factor from local-duality QCD sum rule

TL;DR

This paper uses local-duality QCD sum rules to analyze the pion elastic form factor, showing the dominant contribution of the O(1) term up to 20 GeV^2 and estimating a 10-20% systematic error through a quantum-mechanical model comparison.

Contribution

It applies local-duality sum rules including O(1) and O(α_s) terms to calculate the pion form factor across a broad momentum range, providing a model-independent insight.

Findings

O(1) term contributes over half of the form factor at Q^2 ≤ 20 GeV^2

Systematic error of the method estimated at 10-20% from quantum-mechanical model comparison

Results are applicable in a broad range of spacelike momentum transfers

Abstract

We present our recent results for the pion elastic form factor [1] obtained within a local-duality three-point sum rule (a Borel sum rule in the limit of an infinite Borel parameter). Our analysis includes the O(1) and O(\alpha_s) contributions and is therefore applicable in a broad range of spacelike momentum transfers. Our results demonstrate in essentially model-independent way that the O(1) term, which provides the subleading 1/Q^4 power correction at asymptotically large momentum transfers, contributes more than half of the pion form factor in the region Q^2 \le 20 GeV^2. To probe the accuracy of local-duality sum rules for form factors, we apply precisely the same procedures to extract the form factor in a quantum-mechanical potential model. Comparison of the exact form factor known in this model with the result of the sum-rule calculation gives a probe of the systematic error of the method. In our example this error is found to be at the level of 10-20%. We expect similar systematic errors for form factors obtained from local-duality sum rules in QCD.