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

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.

Comments: 10 pages, 3 figures, talk presented by the first author at Workshop "Recent Advances in Perturbative QCD and Hadronic Physics", 20--25 July 2009, ECT*, Trento (Italy), in Honor of Prof. Anatoly Efremov's 75th Birthday Celebration