$O({\alpha }_s{v}^2)$ Corrections to Hadronic and Electromagnetic Decays of ${}^1{S}_0$ Heavy Quarkonium

Abstract

We study $O({\alpha }_s{v}^2)$ corrections to decays of ${}^1{S}_0$ heavy quarkonium into light hadrons and two photons within the framework of nonrelativistic QCD, and find these $O({\alpha }_s{v}^2)$ corrections to have significant contributions especially for the decay into light hadrons. With these new results, experimental measurements of the hadronic width and the $\gamma \gamma$ width of ${\eta }_c$ can be described more consistently. By fitting experimental data, we find the long-distance matrix elements of ${\eta }_c$ to be $|{\mathcal{R}}_{{\eta }_c}(0){|}^2=0.834_{-0.197}^{+0.281}{\text{GeV}}^3$ and $<{\mathbf{v}}^2{>}_{{\eta }_c}=0.232_{-0.098}^{+0.121}$. Moreover, ${\eta }_c(2S)$ is also discussed and the $\gamma \gamma$ decay width is predicted to be $3.34_{-2.10}^{+2.06}\text{KeV}$.

Comments: Version published in PRD, 22 pages, 7 figures, references added