Spin dependence of heavy quarkonium production and annihilation rates: complete next-to-next-to-leading logarithmic result

The ratio of the photon mediated production or annihilation rates of spin triplet and spin singlet heavy quarkonium states is computed to the next-to-next-to-leading logarithmic accuracy within the nonrelativistic renormalization group approach. The result is presented in analytical form and applied to the phenomenology of tt-bar, bb-bar and cc-bar systems. The use of the nonrelativistic renormalization group considerably improves the behaviour of the perturbative expansion and is crucial for accurate theoretical analysis. For bottomonium decays we predict Γ(ηb(1S)->γγ)=0.659+/-0.089(th.)-0.018+0.019(δαs)+/-0.015(exp.) keV. Our results question the accuracy of the existing extractions of the strong coupling constant from the bottomonium annihilation. As a by-product we obtain a novel result for the ratio of the ortho- and parapositronium decay rates: the corrections of order α4ln2α and α5ln3α