Accuracy of the pion elastic form factor extracted from a local-duality sum rule

TL;DR

This paper assesses the accuracy of local-duality sum rules in predicting the pion elastic form factor, using potential models and existing data, and finds improved accuracy at higher momentum transfers.

Contribution

It demonstrates that the local-duality sum rule approach becomes more accurate at Q^2 above 4-6 GeV^2, supporting its applicability to QCD predictions for the pion form factor.

Findings

Deviation from exact form factor peaks at Q^2~4-6 GeV^2

Accuracy improves rapidly for Q^2 > 6 GeV^2

Existing data suggest LD limit is reached at 4-10 GeV^2

Abstract

We analyze the accuracy of the pion elastic form factor predicted by a local-duality (LD) version of dispersive sum rules. To probe the precision of this theoretical approach, we adopt potential models with interactions that involve both Coulomb and confining terms. In this case, the exact form factor may be obtained from the solution of the Schroedinger equation and confronted with the LD sum rule results. We use parameter values appropriate for hadron physics and observe that, independently of the details of the confining interaction, the deviation of the LD form factor from the exact form factor culminates in the region Q^2~4-6 GeV^2. For larger Q^2, the accuracy of the LD description increases rather fast with Q^2. A similar picture is expected for QCD. For the pion form factor, existing data suggest that the LD limit may be reached already at the relatively low values Q^2=4-10 GeV^2. Thus, large deviations of the pion form factor from the behaviour predicted by LD QCD sum rules for higher values of Q^2, as found by some recent analyses, appear to us quite improbable. New accurate data on the pion form factor at Q^2=4-10 GeV^2 expected soon from JLab will have important implications for the behaviour of the pion form factor in a broad Q^2 range up to asymptotically large values of Q^2.