Model-independent study of magnetic dipole transitions in quarkonium

We study magnetic dipole (M1) transitions between two quarkonia in the framework of nonrelativistic effective field theories of QCD. Relativistic corrections of relative order v2 are investigated in a systematic fashion. Nonperturbative corrections due to color-octet effects are considered for the first time and shown to vanish at relative order v2. Exact, all order expressions for the relevant 1/m and 1/m2 magnetic operators are derived. The results allow us to scrutinize several potential model claims. In particular, we show that QCD excludes both contributions to the anomalous magnetic moment of the quarkonium induced by low-energy fluctuations and contributions to the magnetic dipole operators of the type induced by a scalar potential. Finally, we apply our results to the transitions J/ψ→ηcγ, Υ(1S)→ηbγ, Υ(2S)→ηb(2S)γ, Υ(2S)→ηbγ, ηb(2S)→Υ(1S)γ, hb(1P)→χb0,1(1P)γ, and χb2(1P)→hb(1P)γ by assuming these quarkonium states in the weak-coupling regime. Our analysis shows that the J/ψ→ηcγ width is consistent with a weak-coupling treatment of the charmonium ground state, while such a treatment for the hindered transition Υ(2S)→ηbγ appears difficult to accommodate within the CLEO III upper limit.