Rigorous QCD predictions for the decay rates of the $P$-wave states of heavy quarkonia are presented. They are based on a new factorization theorem which is valid to leading order in the heavy-quark velocity and to all orders in the running coupling constant of QCD. The decay rates for all four $P$ states into light-hadronic or electromagnetic final states are expressed in terms of two phenomenological parameters, whose coefficients are perturbatively calculable. Logarithms of the binding energy encountered in previous perturbative calculations of $P$-wave decays are factored into a phenomenological parameter that is related to the probability for the heavy-quark-antiquark pair to be in a color-octet $S$-wave state. Applying these predictions to charmonium, we use measured decay rates for the ${\chi }_{c1\mathrm{}}$ and ${\chi }_{c2\mathrm{}}$ to predict the decay rates of the ${\chi }_{c0\mathrm{}}$ and $h_c$.

• Received 24 April 1992

DOI:https://doi.org/10.1103/PhysRevD.46.R1914