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

Abstract

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 t t ¯ , b b ¯ and c c ¯ 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 ( η b ( 1 S ) → γ γ ) = 0.659 ± 0.089 ( th. ) − 0.018 + 0.019 ( δ α s ) ± 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 α 4 ln 2 α and α 5 ln 3 α .