Chimera distribution amplitudes for the pion and the longitudinally polarized $\rho$-meson

Abstract

Using QCD sum rules with nonlocal condensates, we show that the distribution amplitude of the longitudinally polarized $\rho$-meson may have a shorttailed platykurtic profile in close analogy to our recently proposed platykurtic distribution amplitude for the pion. Such a chimera distribution de facto amalgamates the broad unimodal profile of the distribution amplitude, obtained with a Dyson-Schwinger equations-based computational scheme, with the suppressed tails characterizing the bimodal distribution amplitudes derived from QCD sum rules with nonlocal condensates. We argue that pattern formation, emerging from the collective synchronization of coupled oscillators, can provide a single theoretical scaffolding to study unimodal and bimodal distribution amplitudes of light mesons without recourse to particular computational schemes and the reasons for them.Comment: 13 pages, 4 figures. In v2 a typo in Eq. (12) corrected. V3 contains clarifications in text; typos corrected; Table expanded; new references included and discussed; conclusions unchanged; matches version to be published in Nucl. Phys. A. V4: typos in AdS/QCD entries in Table I and in text, bottom of page 5, corrected. In v6 typo in expression for gauge link below Eq. (1) correcte