Spin Dependence of Heavy Quarkonium Production and Annihilation Rates: Complete Next-to-Next-to-Leading Logarithmic result

Details Spin Dependence of Heavy Quarkonium Production and Annihilation Rates: Complete Next-to-Next-to-Leading Logarithmic result Spin Dependence of Heavy Quarkonium Production and Annihilation Rates: Complete Next-to-Next-to-Leading Logarithmic result

2004-06-16

arxiv.org/abs/hep-ph/0406175v2

Nucl.Phys.B699:183-206,2004; Erratum-ibid.829:398-399,2010

Physics

High Energy Physics

High Energy Physics - Phenomenology

Appendices A.4, A.5 and B corrected

Scientific paper

10.1016/j.nuclphysb.2004.08.026

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 $t\bar{t}$, $b\bar{b}$ and $c\bar{c}$ 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 $\Gamma(\eta_b(1S) \to \gamma\gamma)=0.659\pm 0.089 ({\rm th.}) {}^{+0.019}_{-0.018} (\delta \alpha_{\rm s})\pm 0.015 ({\rm exp.}) {\rm keV}$. Our results question the accuracy of the existing extractions of the strong coupling constant from the bottomonium annihilation. As a by-product we obtain novel corrections to the ratio of the ortho- and parapositronium decay rates: the corrections of order $\alpha^4\ln^2\alpha$ and $\alpha^5\ln^3\alpha$.

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