Cross-link relations between π and ρ -meson channels and the QCD vacuum

Abstract

We discuss cross-link relations between the $\ensuremath{\pi}$ and $\ensuremath{\rho}$-meson channels emerging from two different descriptions of the QCD vacuum: instanton physics and QCD sum rules with nonlocal condensates (NLCs). We derive in both schemes an intriguing linear relation between the $\ensuremath{\pi}$ and the ${\ensuremath{\rho}}^{\ensuremath{\parallel}}$-meson distribution amplitudes in terms of their conformal coefficients and work out the specific impact of the scalar NLC in these two channels. Using a simple model with Gaussian decay of the scalar NLC, we are able to relate it to the moments of the pion nonsinglet parton distribution function measurable in experiment---a highly nontrivial result. The implications for the pion and the ${\ensuremath{\rho}}^{\ensuremath{\parallel}}$-meson distribution amplitudes entailed by the obtained cross-link relations are outlined in terms of two generic scenarios.