$O(α_s v^2)$ Corrections to Hadronic and Electromagnetic Decays of $^1S_0$ Heavy Quarkonium

Abstract

We study $O(α_sv^2)$ corrections to decays of $^1S_0$ heavy quarkonium into light hadrons and two photons within the framework of nonrelativistic QCD, and find these $O(α_sv^2)$ corrections to have significant contributions especially for the decay into light hadrons. With these new results, experimental measurements of the hadronic width and the $γγ$ width of $η_c$ can be described more consistently. By fitting experimental data, we find the long-distance matrix elements of $η_c$ to be $|\mathcal{R}_{η_c}(0)|^2=0.834^{+0.281}_{-0.197}\ \textrm{GeV}^3$ and $< \bm{v}^2 >_{η_c}=0.232^{+0.121}_{-0.098}$. Moreover, $η_c(2S)$ is also discussed and the $γγ$ decay width is predicted to be $3.34^{+2.06}_{-2.10}\ \textrm{KeV}$.