Multipole expansion in quantum chromodynamics and the radiative decaysJψ→γ+ηandJψ→γ+π0

Abstract

A generalized formalism of QCD multipole expansion including constituent-quark-field quantization is proposed. It can be applied to study soft-gluon emission processes of heavy-quark-antiquark systems with quark-flavor changing or quark pair annihilation. As an application, the radiative decays $\frac{J}{\ensuremath{\psi}}\ensuremath{\rightarrow}\ensuremath{\gamma}+\ensuremath{\eta}$ and $\frac{J}{\ensuremath{\psi}}\ensuremath{\rightarrow}\ensuremath{\gamma}+{\ensuremath{\pi}}^{0}$ are studied in this framework. It is shown that $\frac{J}{\ensuremath{\psi}}\ensuremath{\rightarrow}\ensuremath{\gamma}+\ensuremath{\eta}$ is dominated by a vector-meson-dominance mechanism in which the vector mesons are $n^{3}S_{1}$ states of $c\overline{c}$ and the calculated rate is in agreement with the experiment. The decay $\frac{J}{\ensuremath{\psi}}\ensuremath{\rightarrow}\ensuremath{\gamma}+{\ensuremath{\pi}}^{0}$ is dominated by a different vector-meson-dominance mechanism in which the vector meson is ${\ensuremath{\rho}}^{0}$.