Pion Form Factor in QCD Sum Rules with Nonlocal Condensates and in the Local-Duality Approach

TL;DR

This paper analyzes the pion electromagnetic form factor using QCD sum rules with nonlocal condensates and compares it to the Local-Duality approach, highlighting the importance of nonlocality and providing refined estimates of higher-order contributions.

Contribution

It introduces a method incorporating nonlocal condensates into QCD sum rules and refines the continuum threshold parameter in the Local-Duality approach for better accuracy.

Findings

Nonlocal condensates are crucial for nonperturbative contributions.

The continuum threshold $s_0(Q^2)$ is underestimated in the Local-Duality approach.

Estimated $O(\alpha_s^2)$ contributions with about 1% accuracy.

Abstract

We discuss the QCD sum-rule approach for the spacelike electromagnetic pion form factor in the $O(\alpha_s)$ approximation. We show that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor. We compare our results with the Local-Duality predictions and show that the continuum threshold $s_0(Q^2)$ parameter is highly underestimated in the Local-Duality approach at $Q^2\gtrsim 2$ GeV$^2$. Using our fit for this parameter, $s_0^\text{LD}(Q^2)$, and applying the fractional analytic perturbation theory, we estimate with an accuracy of the order of 1% the $O(\alpha_s^2)$ contribution to the pion's form factor.