Pinched weights and duality violation in QCD sum rules: A critical analysis

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 left-right correlator and any particular pinched weight, taking advantage of our previous work [1], where the possible high-energy behavior of the left-right 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, ${\mathcal{O}}_{6}=(\ensuremath{-}{4.3}_{\ensuremath{-}0.7}^{+0.9})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\text{ }\text{ }{\mathrm{GeV}}^{6}$ and ${\mathcal{O}}_{8}=(\ensuremath{-}{7.2}_{\ensuremath{-}5.3}^{+4.2})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\text{ }\text{ }{\mathrm{GeV}}^{8}$.