Relativistic corrections to radiative transitions and spectra of quarkonia

Abstract

We calculate the energy spectrum and the one-photon $E1$ and $M1$ decays of charmonium and $b$-quarkonium including their first-order relativistic corrections, within the context of the Buchm\"uller-Tye potential. Results seem to suggest that the confining potential is predominantly scalar since this assumption gives good agreement for spectra and for $E1$ decay rates of $c\stackrel{-}{c}$ and gives reasonable results for $b\stackrel{-}{b}$. For $M1$ decays discrepancies persist unless the quarks have large anomalous moments, but the resolution of such discrepancies can probably be achieved by other means. As an interesting by-product of our investigations we find that for the nonrelativistically inhibited $E1$ decay ${\ensuremath{\Upsilon}}^{\ensuremath{'}\ensuremath{'}}\ensuremath{\rightarrow}{\ensuremath{\chi}}_{j}^{b}+\ensuremath{\gamma}$ of the $b\stackrel{-}{b}$ system, some rates are enhanced by a huge factor by first-order relativistic effects. When more data are available these decays should provide an additional testing ground for models of relativistic corrections.