Effective Continuum Thresholds for Quark-Hadron Duality in Dispersive Sum Rules

TL;DR

This paper proposes a modified approach to dispersive sum rules in nonperturbative QCD by allowing effective continuum thresholds to depend on Borel parameters and momenta, improving accuracy in hadron property predictions.

Contribution

It introduces a method where effective continuum thresholds depend on Borel parameters and momenta, enhancing the precision of QCD sum rule predictions.

Findings

Effective thresholds depend on Borel parameters and momenta.

Thresholds are non-universal and vary with correlators.

Method aligns with quantum-theoretical potential models.

Abstract

Modifying the standard approaches to nonperturbative QCD based on Borel-transformed dispersive sum rules by allowing the effective continuum thresholds required for the implementation of quark-hadron duality to depend on the Borel parameters and on any relevant momentum promises to provide higher accuracy and reliable error estimates for the extracted predictions of hadron characteristics. A careful analysis reveals that the exact effective continuum thresholds do indeed exhibit dependence on the Borel parameter (and on external momenta) and that they are not universal but vary with the correlators under consideration. The striking similarity of our hadron-parameter extraction procedures in QCD, on the one hand, and quantum-theoretical potential models, on the other hand, calls for application of the proposed techniques in QCD.