Quark Magnetic Moments andE1Radiative Transitions in Charmonium

Abstract

In the long-wavelength limit, $\Gamma ({\psi }^{\prime }\to \gamma +{\chi }_J)=\mathrm{const}\times \mathrm{}(2J+1)\mathrm{}{p_{\gamma }}^3$ and $\Gamma ({\chi }_J\to \gamma +\psi )=\mathrm{const}\times {p_{\gamma }}^3$. The corrections to these expressions of order $\frac{p_{\gamma }}{m_c}$ ($m_c$ is the mass of the charmed quark) are calculated. These corrections are found to be proportional to ${〈\overrightarrow{\mathrm{L}}·\overrightarrow{\mathrm{S}}〉}_{{\chi }_J}\times \kappa$, where ${〈\overrightarrow{\mathrm{L}}·\overrightarrow{\mathrm{S}}〉}_{{\chi }_J}=1,-1,-2\mathrm{}$, for $J=2,1,0\mathrm{}$, and $\kappa$ is the anomalous magnetic moment of the quark. Angular distributions of photons in the decays ${\psi }^{\prime }\to \gamma \chi$ and $\chi \to \gamma \psi$ also are predicted; small but probably measurable deviations from the pure $E1\mathrm{}$ limit are found.