Unveiling the inner structure of the pion first excited state

TL;DR

This paper models the internal structure of the pion's first excited state using Bethe-Salpeter amplitudes, revealing nodal features in the distribution amplitude and a unimodal distribution function, enhancing understanding of mesonic excitations.

Contribution

It introduces an algebraic model linking Bethe-Salpeter amplitudes to parton distributions in excited mesons, providing new insights into their internal structure.

Findings

Distribution amplitude exhibits nodes at the hadronic scale.

Distribution function is unimodal with a peak at x=1/2.

Distinct concave and convex fluctuations observed in the valence region.

Abstract

By capturing the characteristics of the Bethe-Salpeter amplitude for the pion excitation state, we construct an algebraic model to provide the overall features of the pion first excitation state parton distribution amplitude and distribution function. We find that, at the hadronic scale, the distribution amplitude of the excited state exhibits nodes, while the distribution function is unimodal, with a peak at $x=1/2$ and distinct concave and convex fluctuations in the valence region. These findings provide new insights into the partonic structure of excited mesons and contribute significantly to our understanding of hadronic excitations.