Inclusive decays of ${\eta }_c$ and ${\eta }_b$ at NNLO with large $n_f$ resummation

Abstract

Based on the nonrelativistic QCD factorization theorem, we resum QCD corrections to the inclusive decay rate of ${\eta }_c$ and ${\eta }_b$ in the large-$n_f$ limit using bubble chain resummation. By employing dimensional regularization, we show explicitly the cancellation of the infrared renormalon ambiguity in the factorization formula at leading order in $v$ in the large-$n_f$ limit, where $v$ is the typical heavy quark velocity inside the meson. We also make predictions of the ratio of the inclusive decay rate to the decay rate into two photons. By comparing our results with a fixed-order calculation we conclude that resummation of QCD corrections is crucial in making an unambiguous prediction. We also find significant corrections beyond the large-$n_f$ limit for the decay of ${\eta }_c$, which may imply that QCD corrections need to be resummed beyond the large-$n_f$ limit to make an accurate prediction of the decay rate.

41 pages, 6 figures, minor corrections, reference added, version published in Phys. Rev. D

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Cited by in corpus (11)

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• The Glueball content of ${\eta }_c$
• New puzzle in charmonium decays
• The heavy quarkonium inclusive decays using the principle of maximum conformality
• Bottomonium spectroscopy motivated by general features of pNRQCD
• Renormalons beyond the Borel plane
• Observation of the charmonium decay ${\eta }_c\to \gamma \gamma$ in $J/\psi \to \gamma {\eta }_c$
• Self-consistent analysis for the ${\eta }_c\to \gamma \gamma$ process
• Color-octet nonrelativistic QCD matrix elements for heavy quarkonium decays in the refined Gribov-Zwanziger theory
• Study of the Magnetic Dipole Transition of $J/\psi \to \gamma {\eta }_c$ via ${\eta }_c\to p\bar{p}$