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

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 $\mathrm{\mid }{\mathcal{R}}_{{\eta }_c}(0){\mathrm{\mid }}^2=0.834_{-0.197}^{+0.281}{\text{GeV}}^3$ and $< \bm{v}^2 >{\eta_c}=0.232^{+0.121}{-0.098}$\mathrm{.}Moreover,$\eta_c(2S)$ is also discussed and the $\gamma \gamma$ decay width is predicted to be $3.34_{-2.10}^{+2.06}\text{ KeV}$.