Accuracy of bound-state form factors extracted from dispersive sum rules

TL;DR

This paper evaluates the accuracy of form factors extracted from dispersive sum rules using a harmonic-oscillator model, revealing significant systematic uncertainties exceeding 10%.

Contribution

It provides an exact correlator expression and compares sum rule extraction results with known values, highlighting limitations in current methods.

Findings

Uncontrolled systematic error in form factor extraction exceeds 10%.

Sum rule methods have larger uncertainties for form factors than decay constants.

Exact correlator expressions help assess the accuracy of sum rule extractions.

Abstract

We discuss the extraction of form factors from three-point sum rules making use of harmonic-oscillator model, where we derive the exact expression for the relevant correlator. We determine the form factor of the ground state by the standard procedures adopted in the method of sum rules, and compare the obtained results with the known exact values. We show that the uncontrollable uncertainty in the extracted value of the form factor is typically much larger than that for the decay constant. In the example considered, we find the uncontrolled systematic error in the extracted form factor to exceed the 10% level.