Radial excitation of light mesons and the γγ*→π0 transition form factor

Abstract

We investigate radial excitation of the quark-antiquark pair in the ${\ensuremath{\pi}}^{0}$ meson and its effects on the $\ensuremath{\gamma}{\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}$ 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 $|q\overline{q}⟩$ in the ${\ensuremath{\pi}}^{0}$ 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 $\ensuremath{\gamma}{\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}$ 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 ${Q}^{2}$.