Extracting Hadron Parameters from Dispersive Sum Rules

TL;DR

This paper critically examines the accuracy of dispersive sum rules in QCD by using an exactly solvable quantum-mechanical model, revealing systematic uncertainties and limitations in standard extraction procedures.

Contribution

It demonstrates that traditional sum-rule methods can underestimate bound-state parameters and that their claimed precision is often unreliable, highlighting the need for caution.

Findings

Sum-rule estimates underestimate decay constants by about 4%.

Form factors are underestimated by nearly 15%.

Systematic uncertainties are larger than correlator accuracy.

Abstract

Puzzled or surprised by the almost incredible accuracy occasionally claimed in the literature to be achievable for numerical outcomes of QCD sum-rule analyses, we scrutinized the usual procedure employed for the extraction of the parameters of individual bound states from dispersive sum rules by taking advantage of the exact solvability of a quantum-mechanical harmonic-oscillator model: It turns out that the determination of the ground-state parameters (that is, decay constant and form factor) by requiring independence from the Borel mass in its stability window does not necessarily yield their exact numerical values. For instance, the comparison of the sum-rule predictions for bound-state parameters with their numerical values known precisely in our harmonic-oscillator model reveals that standard sum-rule procedures underestimate the ground-state decay constant by some 4% and its form factor by almost 15%; such systematic uncertainties cannot be inferred from our correlators' accuracy better than 1% in the window of Borel stability: they are uncontrollable.