Cross-link relations between $\pi$ and $\rho$-meson channels and the QCD vacuum

TL;DR

This paper explores the theoretical connections between the $ ext{π}$ and $ ho$-meson channels within QCD, linking different vacuum descriptions and deriving relations that connect meson distribution amplitudes to measurable parton distribution functions.

Contribution

It introduces novel cross-link relations between meson channels derived from instanton physics and QCD sum rules, connecting meson DAs to parton distributions.

Findings

Derived linear relations between meson distribution amplitudes.

Linked scalar NLC effects to pion parton distribution moments.

Outlined implications for meson distribution amplitude scenarios.

Abstract

We discuss cross-link relations between the $\pi$ and $\rho$-meson channels emerging from two different descriptions of the QCD vacuum: Instanton physics and QCD sum rules with nonlocal condensates (NLC). We derive in both schemes an intriguing linear relation between the $\pi$ and the $\rho^\|$-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 non-singlet parton distribution function measurable in experiment -- a highly nontrivial result. The implications for the pion and the $\rho^\|$-meson DAs entailed by the obtained cross-link relations are outlined in terms of two generic scenarios.