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.
Highlights
Nowadays there is much experimental effort devoted to investigating the nature of heavy quarkonium states
By computing the perturbative corrections in nonrelativistic QCD (NRQCD), that perturbative NRQCD reproduces exactly the large nf leading renormalon ambiguity in perturbative QCD, and the NRQCD factorization formula is free of this kind of renormalon ambiguities
Due to the limited knowledge on NRQCD longdistance matrix elements (LDMEs) of higher orders in v, using a hard cutoff instead of dimensional regularization to regularize the ultraviolet divergences in NRQCD leads to an expression for the decay rate of ηQ that is more useful for phenomenological applications
Summary
Nowadays there is much experimental effort devoted to investigating the nature of heavy quarkonium states. The nonconvergence of the perturbation series may correspond to renormalon ambiguities that arise when computing diagrams in dimensional regularization and resumming the perturbation series by using the Borel transform These difficulties can be partially overcome by considering R, the ratio of the inclusive decay rate to the electromagnetic decay rate to two photons. The renormalon ambiguities associated with the loop corrections to the initial heavy quark-antiquark states cancel in the ratio up to relative order v2. We consider the resummation of perturbative corrections to the ratio R that are associated with the chain of vacuum-polarization bubbles in the final-state gluons in the inclusive decay rate of ηQ, where Q 1⁄4 c or b.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
