We compute the magnetic dipole transitions between low-lying heavy quarkonium states in a model-independent way. We use the weak-coupling version of the effective field theory named potential nonrelativistic QCD, with the static potential exactly incorporated in the leading order Hamiltonian. The precision we reach is kγ3/m2×O(αs2,v2) and kγ3/m2×O(v4) for the allowed and forbidden transitions, respectively, where kγ is the photon energy. We also resum the large logarithms associated with the heavy quark mass scale. The specific transitions considered in this paper are the following: Υ(1S) →ηb(1S)γ, J/ψ(1S)→ηc(1S) γ, hb(1P)→χb0,1(1P)γ, χb2(1P)→hb(1P)γ, Υ(2S) →ηb(2S)γ, Υ(2S)→ηb(1S)γ and ηb(2S)→Υ(1S)γ. The effect of the new power counting is found to be large, and the exact treatment of the soft logarithms of the static potential makes the factorization scale dependence much smaller. The convergence for the bb̄ ground state is quite good, and also quite reasonable for the cc̄ ground state and the bb̄ 1P state. For all of them we give solid predictions. For the 2S decays the situation is less conclusive, yet our results are perfectly consistent with existing data, as the previous disagreement with experiment for the Υ(2S) →ηb(1S)γ decay fades away. We also compute some expectation values like the electromagnetic radius, or. We find to be nicely convergent in all cases, whereas the convergence of is typically worse. © 2013 American Physical Society.
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|Publication status||Published - 22 Apr 2013|