Resumming the color-octet contribution to radiative Upsilon decay

Abstract

At the upper endpoint of the photon energy spectrum in Upsilon -> X gamma, the standard NRQCD power counting breaks down and the OPE gives rise to color-octet structure functions. Furthermore, in this kinematic regime large Sudakov logarithms appear in the octet Wilson coefficients. The endpoint spectrum can be treated consistently within the framework of a recently developed effective field theory of collinear and soft particles. Here we show that within this approach the octet structure functions arise naturally and that Sudakov logarithms can be summed using the renormalization group equations. We derive an expression for the resummed energy spectrum and, using a model lightcone structure function, investigate the phenomenological importance of the resummation.