Magnetic dipole transitions in quarkonia

Amplitudes for allowed and hindered $M1\mathrm{}$ transitions are analyzed in a theory in which relativistic effects are taken into account to order ${\left(\frac{v}{c}\right)}^2$. Relativistic effects are small for allowed transitions. For hindered transitions, on the other hand, retardation and relativistic effects and coupled-channel mixing are important. We have calculated retardation and relativistic effects, and find strong cancellation between the various contributions. Results are given for ${\psi }^{\prime }\to {\eta }_c\gamma$ and for both allowed and hindered transitions in the $\Upsilon$ system. When coupled-channel mixing is taken into account in the ${\psi }^{\prime }\to {\eta }_c\gamma$ case, we find that theory and experiment agree within error.