Radial excitation of light mesons and the $\gamma {\gamma }^{\ast }\to {\pi }^0$ transition form factor

Abstract

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

Comments: 10 pages, 4 figures; to appear in Phys. Rev. D