On the Pion Distribution Amplitude: Derivation, Properties, Predictions

Abstract

We provide an in-depth analysis of the π distribution amplitude in terms of two different Gegenbauer representations. Detailed predictions for the π − γ transition form factor are presented, obtained with light-cone sum rules. Various π distribution amplitudes are tested and the crucial role of their endpoint behavior in the form-factor analysis is discussed. Comparison with the data is given.

Chimera distribution amplitudes for the pion and the longitudinally polarized ρ -meson

“…Otherwise, the form factor would overshoot the data. And in fact, using the DSE DAs as nonperturbative input in a LCSR-framework, we have shown [5] that the predictions obtained herewith exceed the asymptotic limit even at the highest momenta around 40 GeV 2 probed in current experiments [46,47]. This is also obvious from Table I.…”

“…Comparison in earlier works, e.g., [5,7,28], of predictions for the pion-photon transition form factor obtained within the LCSR framework with all existing data, indicates that strict QCD scaling behavior at high Q 2 is very sensitive to the endpoint-behavior of the pion DA. This behavior is intimately related to the inverse moment x −1 π .…”

“…Note that the moments ξ N π coincide by construction with the central moments 2 at the edge of the NLC regime. The solid lines within both regions denote, respectively, the BMS model from [6] and the pk DA discussed in the text and in [4,5]. The broken lines show the unimodal DSE-DB DA (dashed), the DSE-RL DA (dashed-dotted) (both from [9]), and the asymptotic DA (dashed-dotted-dotted).…”

“…In particular the pion, the lightest bound state within Quantum Chromodynamics (QCD), provides a suitable "laboratory" for testing new ideas and techniques to catch the main ingredients of the underlying quark-gluon dynamics entering exclusive QCD processes (see [1][2][3] for reviews). In this paper we will present an amplification of the recent analysis by one of us in [4], continued in [5], for the pion and consider its extension to the longitudinally polarized ρ meson (ρ ). The new mode of thought in [4] is based on the ubiquitous phenomenon of synchronization (Sync for short) in complex systems and we will expand the status of this subject towards a deeper understanding of the meson DAs.…”

Spin effects in the pion holographic light-front wavefunction

“…Our predictions for the first two non-vanishing moments ξ 2 and ξ 4 as well as the inverse moment are shown in [47], renormalon model of Agaev [71], instanton vacuum models of Petrov et al [72] and Nam et al [73], Dyson-Schwinger Equations of Chang et al [78] in the rainbow-ladder (RL) approximation and using the dynamical chiral symmetry breaking improved kernel (DB) and finally the platykurtic DA of Stefanis et al [79,80].…”