Radiative Upsilon Decay at the Endpoint

The standard NRQCD power counting breaks down and the OPE gives rise to color-octet shape functions at the upper endpoint of the photon energy spectrum in radiative Upsilon decay. Also in this kinematic regime, large Sudakov logarithms appear in the octet Wilson coefficients, ruining the perturbative expansion. Using SCET, the octet shape functions arise naturally and the Sudakov logarithms can be summed using the renormalization group equations. We derive an expression for the resummed octet energy spectrum.