Two-loop QCD-corrections to $e^{+} e^{-} \rightarrow Z^{\ast} \rightarrow \boldsymbol{J /ψ}+\boldsymbol{J/ ψ}$

TL;DR

This paper delivers the first complete NNLO QCD calculation for $e^{+}e^{-} \rightarrow Z^{\ast} \rightarrow J/\psi+J/\psi$ within NRQCD. By computing the two-loop amplitudes through rigorous IBP reduction, differential-equation master integrals, and asymptotic expansions, the authors show that NNLO corrections greatly enhance the NLO result (by factors of ~2–3) and provide detailed renormalization/IR subtraction including $\

Abstract

We present a next-to-next-to-leading-order calculation within the nonrelativistic QCD framework for the process of $e^{+}e^{-} \rightarrow Z^{\ast} \rightarrow J/ψ+J/ψ$ . 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 $Z^{\ast} \rightarrow Υ+Υ$. Using the obtained hadronic amplitudes, we predict the decay width of the $Z$ boson into these rare di-charmonium and di-bottomonium final states.

Figures (16)

• Figure 1:
• Figure 2:
• Figure 3:
• Figure 4:
• Figure 6: