Cancellation of Sudakov Logarithms in Radiative Decays of Quarkonia

Abstract

We study infrared QCD effects in radiative quarkonia decays. We examine the endpoint region z -> 1 of the photon spectrum. We point out a cancellation mechanism for the corrections in $\alpha_s^n \ln^{m} (1-z)$, $m \leq 2 n$, in the short-distance coefficient for the color-singlet Fock state in the quarkonium. The cancellation is due to the coherence of the color radiation, and applies even though logarithmic contributions are present in the jet distributions associated with the decay. We comment on the implications of our results for the modeling of hadronization in the endpoint region and for the role of color-octet states in the quarkonium.