Radiative Transitions and the Quarkonium Magnetic Moment

I discuss heavy quarkonium radiative transitions and the related issue of the quarkonium magnetic moment inside effective field theories. Differences in set up and conclusions with respect to typical phenomenological approaches are outlined. Heavy quarkonium radiative transitions have been studied for long time in the framework of phenomenological models 1–14 (for a recent review see 15). In a typical set up 7 , the starting point is a relativistic Hamiltonian whose dynamical fields are heavy quarks and photons; gluons are integrated out and replaced by a scalar and a vector interaction. The non-relativistic nature of heavy quarkonia is exploited by performing a Foldy–Wouthuysen transformation. Anomalous magnetic moments are added as if the system was made of two particles independently interacting with the external electromagnetic field. Such an approach, despite phenomenological success, has an obvious limitation: its connection with QCD is unclear. More precisely, while it relies on a systematic (non-relativistic) expansion to describe the electromagnetic interaction of the heavy quarks, it does not to describe their strong interaction. As a result, the nature of the binding potential between the two heavy quarks and of the couplings of the heavy quarks with the electromagnetic field remains elusive. In particular, one may wonder if the heavy quarkonium anomalous magnetic moment gets contributions from the interaction of the heavy quarks in the bound state and if, in the non-relativistic expansion, the many couplings between the heavy quarks and the electromagnetic field, allowed by the symmetries of QCD, really orga