Cancellation of Infrared Divergences in Hadronic Annihilation Decays of Heavy Quarkonia

Abstract

In the framework of a newly developed factorization formalism which is based on NRQCD, explicit cancellations are shown for the infrared divergences that appeared in the previously calculated hadronic annihilation decay rates of P-wave and D-wave heavy quarkonia. We extend them to a more general case that to leading order in $v^2$ and next-to-leading order in ${\alpha }_s$, the infrared divergences in the annihilation amplitudes of color-singlet $Q\bar{Q}{(}^{2S+1}{L}_J)$ pair can be removed by including the contributions of color-octet operators $Q\bar{Q}{(}^{2S+1}(L-1{)}_{J^{\prime }})$, $Q\bar{Q}{(}^{2S+1}(L-3{)}_{J^{\prime \prime }})$, ... in NRQCD. We also give the decay widths of ${}^3{D}_J\to LH$ at leading order in ${\alpha }_s$.

Comments: 8 pages, LaTex(3 figures included), to be published