QCD predictions for annihilation decays of P-wave quarkonia to next-to-leading order in ${\alpha }_s$

Abstract

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.

Comments: 10 pages Latex(5 figures included). We have corrected a numerical error in Eq.(5) and Eq.(11)