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 ${Q}^{2}$.
Highlights
Light cone perturbative QCD has been applied to the calculations for many inclusive and exclusive hadronic processes
We study the effects on the γγà → π0 transition form factor in the framework of light cone perturbative QCD
Analyzing all constraints for the pion light cone wave function and distribution amplitude from considering the lepton and two-photon decays and experimental information for the quark transverse momentum, we found the probability for the pion to be in the 1S state is in the range of 25%–46%
Summary
Light cone perturbative QCD has been applied to the calculations for many inclusive and exclusive hadronic processes. The test of these calculations against available experimental data, for many exclusive processes, is usually retarded by the possible higher order and higher twist contributions to the theoretical calculations at low and medium regions of momentum transfer (Q2) and the limited availability of experimental data at high Q2. The measurements of the γγà → π0 transition form factor (TFF) [1,2], the simplest QCD process involving a hadron, posed a very interesting challenge to the theoretical calculations. We investigate the possible radial excitation of the quark-antiquark (qq ) pair in the π0 and study its contribution to the γγà → π0 transition form factor.
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