Flavor-singlet light-cone amplitudes and radiative Υ decays in the soft-collinear effective theory

We study the evolution of flavor-singlet, light-cone amplitudes in the soft-collinear effective theory, and reproduce results previously obtained by a different approach. We apply our calculation to the color-singlet contribution to the photon endpoint in radiative {upsilon} decay. In a previous paper, we studied the color-singlet contributions to the endpoint, but neglected operator mixing, arguing that it should be a numerically small effect. Nevertheless the mixing needs to be included in a consistent calculation, and we do just that in this work. We find that the effects of mixing are indeed numerically small. This result combined with previous work on the color-octet contribution and the photon fragmentation contribution provides a consistent theoretical treatment of the photon spectrum in {upsilon}{yields}{gamma}X.