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

Abstract

We improve the Monte-Carlo based QCD sum rules by introducing the rigorous Hölder-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.

12 pages, 8 figures, accepted for publication in Chinese Physics C

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• QCD sum rules with spectral densities solved in inverse problems
• Determination of the up/down-quark mass within QCD sum rules in the scalar channel
• Constraint on the light quark mass $m_q$ from QCD Sum Rules in the $I=0$ scalar channel
• Dispersive analysis of excited glueball states
• Vector and Scalar Mesons' Mixing from QCD Sum Rules