QCD radiative correction to the hadronic annihilation rate of 1$^{\pm}$ heavy quarkonium

Hadronic annihilation rate of 1^{+-} heavy quarkonium is given to next-to-leading order in \alpha_s using a recently developed factorization formalism which base on NRQCD. The result includes two parts at leading order in v^2, one comes from the annihilation of P-wave state of color-singlet Q\bar{Q} component, another comes from the annihilation of S-wave state of color-octet Q\bar{Q} component. Logarithms of the binding energy encountered in previous perturbative calculations of 1^{+-} quarkonium decays is treated correctly in this factorization approach