Unprejudiced Look at Effective Continuum Thresholds in Borel Dispersive Sum Rules

TL;DR

This paper improves dispersive sum rules in QCD by modeling effective thresholds as functions of momenta, reducing systematic uncertainties and enhancing the accuracy of hadron feature predictions.

Contribution

It introduces a novel approach to effective thresholds in sum rules, transitioning from constants to functions, thereby refining the extraction of hadron properties from QCD.

Findings

Reduced systematic uncertainties in sum rule predictions.

Enhanced accuracy in hadron feature extraction.

Validated the applicability of the modified sum rules to QCD.

Abstract

Dispersive sum rules constitute long-standing tools for extracting hadron features from QCD. We estimate the systematic uncertainties induced by assuming quark-hadron duality and improve the accuracy of the resulting predictions by elevating the effective thresholds involved in this approximation from constants to functions of momenta and a parameter entering upon Borel transformation. A rigorous scrutiny of the applicability of our proposed sum-rule modifications to QCD gives us great confidence that our sum-rule alterations will prove to be fruitful for hadron phenomenology.