  We study the evolution of flavor-singlet, light-cone amplitudes in the
soft-collinear effective theory (SCET), 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 radiative Upsilon
decay.
