Inclusive decays of $\eta_c$ and $\eta_b$ at NNLO with large $n_f$ resummation

TL;DR

This paper performs NNLO resummation of QCD corrections for inclusive $ ext{eta}_c$ and $ ext{eta}_b$ decays, demonstrating renormalon cancellation and emphasizing the importance of resummation for precise predictions.

Contribution

It introduces a large-$n_f$ resummation approach for inclusive heavy quarkonium decays within nonrelativistic QCD, highlighting the significance of beyond fixed-order corrections.

Findings

Renormalon ambiguity cancels at leading order in $v$.

Resummation is essential for unambiguous decay rate predictions.

Significant corrections beyond large-$n_f$ limit for $ ext{eta}_c$ decay.

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.