Radial excitation of light mesons and the $\gamma \gamma^* \rightarrow \pi^0$ transition form factor

TL;DR

This paper explores how radial excitations of the quark-antiquark pair in the pion affect the transition form factor in light-cone perturbative QCD, revealing significant modifications at medium-large momentum transfers.

Contribution

It constructs the light-cone wave function for the first radially excited state of the pion and analyzes its impact on the transition form factor, highlighting the importance of radial excitations.

Findings

Radial excitation wave function has two nodes in $x$ at low $Q$.

Radial excitation significantly alters the $Q^2$ dependence of the transition form factor.

Radial excitation can modify predictions for the form factor in medium-large $Q^2$ region.

Abstract

We investigate radial excitation of the quark-antiquark pair in the $\pi^0$ meson and its effects on the $\gamma \gamma^* \rightarrow \pi^0$ transition form factor in the framework of light-cone perturbative QCD. The existing constraints on the light-cone wave function of the lowest Fock state $|q { \bar q} \rangle$ in the $\pi^0$ meson allow a sizeable radial excitation of the quark-antiquark pair. We construct the light-cone wave function for the quark-antiquark pair in the first radially excited state (the 2S state) using a simple harmonic oscillator potential. The distribution amplitude obtained for the 2S state has two nodes in $x$ at low scale of $Q$ and thereby has a much strong scale dependence than the 1S state. Contributions from this radial excitation to the $\gamma \gamma^* \rightarrow \pi^0$ transition form factor exhibit different $Q^2$-dependence behavior from the ground state and thus can modify the prediction for the transition form factor in the medium-large region of $Q^2$.