Inclusive decays of ηc and ηb at NNLO with large nf resummation

Based on the nonrelativistic QCD factorization theorem, we resum QCD corrections to the inclusive decay rate of η_c and η_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 η_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.