The photon spectrum in [Formula Presented] decays

We present a theoretical prediction for the photon spectrum in radiative [Formula Presented] decay. Parts of the spectrum have already been understood, but an understanding of the end point region has remained elusive. In this paper we provide the missing piece, and resolve a controversy in the literature. We treat the end point region of [Formula Presented] decay within the framework of the soft-collinear effective theory (SCET). Within this approach the [Formula Presented] structure function arises naturally, and kinematic logarithms are summed by running operators using renormalization group equations. In a previous paper we studied the color-octet contribution to the decay. Here we treat the color-singlet contribution. We combine our result with previous results to obtain the [Formula Presented] spectrum. We find that resumming the color-singlet contribution in the end point gives a result that is in much better agreement with the data than the leading order prediction.