Two-loop QCD-corrections to $e^{+}{e}^{-}\to Z^{\ast }\to \mathbf{J}/\ddot{\mathbf{I}}ˆ+\mathbf{J}/\ddot{\mathbf{I}}ˆ$

Abstract

We present a next-to-next-to-leading-order calculation within the nonrelativistic QCD framework for the process of $e^{+}{e}^{-}\to Z^{\ast }\to J/\ddot{I}ˆ+J/\ddot{I}ˆ$ . We find that the NNLO contribution is 2-3 times larger than the next-to-leading-order contribution, which itself is already 3-5 times larger than the leading-order result. In the high-energy limit, we provide analytic expressions for the leading-power coefficients in the asymptotic expansion of the two-loop amplitudes. Our results are directly applicable to the bottomonium process $Z^{\ast }\to \hat{I}\yen +\hat{I}\yen$. Using the obtained hadronic amplitudes, we predict the decay width of the $Z$ boson into these rare di-charmonium and di-bottomonium final states.

10 pages, 5 figures