QCD Radiative Correction to the Hadronic Annihilation Rate of 1⁺⁻ Heavy Quarkonium

Hadronic annihilation rate of $1^{+-}$ heavy quarkonium is given to next-to-leading order in $\alpha_s$ and leading order in $v^2$ using a recently developed factorization formalism which is based on NRQCD. The result includes both the annihilation of P-wave color-singlet $Q\bar{Q}$ component, and the annihilation of S-wave color-octet $Q\bar{Q}$ component of the quarkonium. The notorious infrared divergences due to soft gluons, i.e., the Logarithms associated with the binding energy, encountered in previous perturbative calculations of $1^{+-}$ quarkonium decays are found to be explicitly cancelled, and a finite result for the decay width to order $\alpha_s^3$ is then obtained.