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We study magnetic dipole (M1) transitions between two quarkonia in theframework of non-relativistic effective field theories of QCD. Relativisticcorrections of relative order v^2 are investigated in a systematic fashion.Non-perturbative corrections due to color-octet effects are considered for thefirst time and shown to vanish at leading order. Exact, all order expressionsfor the relevant 1/m and 1/m^2 operators are derived. The results allow us toscrutinize several potential model claims. In particular, we show that QCDexcludes both contributions to the anomalous magnetic moment of the quarkoniuminduced by low-energy fluctuations and contributions to the magnetic dipoleoperators of the type induced by a scalar potential. Finally, we apply ourresults to the transitions J/psi -> eta_c gamma, Upsilon(1S) -> eta_b gamma,Upsilon(2S) -> eta_b(2S) gamma, Upsilon(2S) -> eta_b gamma, eta_b(2S) ->Upsilon(1S) gamma, h_b(1P) -> chi_{b0,1}(1P) gamma and chi_{b2}(1P) -> h_b(1P)gamma by assuming these quarkonium states in the weak-coupling regime. Ouranalysis shows that the J/psi -> eta_c gamma width is consistent with aweak-coupling treatment of the charmonium ground state, while such a treatmentfor the hindered transition Upsilon(2S) -> eta_b gamma appears difficult toaccommodate within the CLEO III upper limit.Comment: 44 pages, 8 figures; typos corrected, one reference added; to appear  in Physical Review

Model-independent study of magnetic dipole transitions in quarkonium