Pinched weights and Duality Violation in QCD Sum Rules: a critical analysis

TL;DR

This paper critically examines the effectiveness of pinched weights in reducing duality violations in QCD sum rules, demonstrating their limitations and proposing methods for precise determination of higher-dimensional operator contributions.

Contribution

It clarifies the limitations of pinched weights in duality violation reduction and provides a methodology to accurately extract dimension six and eight operator contributions in the LR correlator.

Findings

Pinched weights do not always reduce duality violations as commonly believed.

High-precision determination of O6 and O8 contributions is achievable using specific pinched weights.

The study offers a refined approach to analyze the LR spectral function at high energies.

Abstract

We analyze the so-called pinched weights, that are generally thought to reduce the violation of quark-hadron duality in Finite-Energy Sum Rules. After showing how this is not true in general, we explain how to address this question for the LR correlator and any particular pinched weight taking advantage of our previous work [1], where the possible high-energy behavior of the LR spectral function was studied. In particular we show that the use of pinched weights allows to determine with high accuracy the dimension six and eight contributions in the operator product expansion, O6=(-4.3^[+0.9}_{-0.7})*10^-3 GeV^6 and O8=(-7.2^{+4.2}_{-5.3})*10^-3 GeV^8.