QCD predictions for annihilation decays of P-wave quarkonia to next-to-leading order in $\alpha_s$

The decay rates of P-wave heavy quarkonia to light hadrons are presented to leading order in $v^2$ and next-to-leading order in $\alpha_s$. They include contributions from both the color-singlet component and the color-octet component of quarkonia. Applying these results to charmonium and using measured decay rates for the $\chi_{c1}$ and $\chi_{c2}$ by E760, we determine the two nonperturbative decay matrix elements, and then predict the hadronic decay rates of $\chi_{c0}$ and $h_c$, and the electromagnetic decay rates of $\chi_{c0}$ and $\chi_{c2}$. The obtained decay rates of $\chi_{c0}\to LH$ and $\chi_{c0}\to\gamma\gamma$ are in agreement with the Crystal Ball result, and also with the new measurement by BES. However, the results for $\Gamma(\chi_{c0}\to LH)$ are dependent on the choice of renormalization scale.