A comprehensive revisit of the $\rho$ meson with improved Monte-Carlo based QCD sum rules

TL;DR

This paper enhances Monte-Carlo based QCD sum rules by introducing a rigorous sum rule window and a Breit-Wigner spectral function, enabling unbiased predictions of hadronic parameters, demonstrated on the rho meson with results aligning with experiments.

Contribution

It introduces a novel, assumption-free method for QCD sum rule analysis using H"older inequalities and Breit-Wigner parametrization, improving the accuracy of hadronic property predictions.

Findings

Predicted rho meson mass and width consistent with experimental data.

Method applicable to other hadronic channels.

Inclusion of alpha_s corrections improves sum rule reliability.

Abstract

We improve the Monte-Carlo based QCD sum rules by introducing the rigorous H\"older-inequality-determined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function. In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum.Therefore an unbiased prediction can be obtained for the phenomenological parameters (the hadronic mass and width etc.). We test the new approach in the $\rho$ meson channel with re-examination and inclusion of $\alpha_s$ corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels.