How accurate is the local-duality model for the pion elastic form factor?

Abstract

We study the accuracy of the pion form factor, obtained with a local-duality version of dispersive sum rules. To probe this accuracy, we make use of a potential model, where the exact form factor may be calculated from the solution of the Schrödinger equation and confronted with the local-duality form factor. The deviation between these quantities is found to be below 20% in the region of momentum transfers Q > 2 − 3 GeV, independently of the specific form of the confining potential. We argue that the local-duality model for elastic form factors in QCD has at least this level of accuracy.

Recent results in QCD sum rule calculations of heavy meson properties

“…(i) The effective continuum threshold depends on the Borel parameter and, for the form-factor case, also on the momentum transfer [3,4,5,6,7]. In QCD, the effective threshold depends in addition on the renormalization scale.…”