Magnetic dipole transitions in quarkonia

Amplitudes for allowed and hindered $M1$ transitions are analyzed in a theory in which relativistic effects are taken into account to order ${(\frac{v}{c})}^{2}$. 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 ${\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}\ensuremath{\gamma}$ and for both allowed and hindered transitions in the $\ensuremath{\Upsilon}$ system. When coupled-channel mixing is taken into account in the ${\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}\ensuremath{\gamma}$ case, we find that theory and experiment agree within error.