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

TL;DR

This paper calculates $O( ext{alpha}_s v^2)$ corrections to $ ext{S}$-wave heavy quarkonium decays, improving theoretical predictions for decay widths and aligning them more closely with experimental data.

Contribution

It provides the first detailed calculation of $O( ext{alpha}_s v^2)$ corrections to $^1S_0$ heavy quarkonium decays within NRQCD, enhancing the understanding of decay processes.

Findings

Significant $O( ext{alpha}_s v^2)$ corrections for light hadron decay.

More consistent description of $ ext{eta}_c$ decay widths with experimental data.

Predicted $ ext{eta}_c(2S)$ $ ext{gamma} ext{gamma}$ decay width as 3.34 KeV.

Abstract

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