Resummation for QCD Hard Scattering

Abstract

We resum distributions that are singular at partonic threshold (the elastic limit) in heavy quark production, in terms of logarithmic behavior in moment space. The method may be applied to a variety of cross sections sensitive to the edge of phase space, including transverse momentum distributions. Beyond leading logarithm, dependence on the moment variable is controlled by a matrix renormalization group equation, reflecting the evolution of composite operators that represent the color structure of the underlying hard scattering. At next-to-leading logarithmic accuracy, these evolution equations may be diagonalized, and moment dependence in the cross section is a sum of exponentials. Beyond next-to-leading logarithm, resummation involves matrix-ordering. We give a detailed analysis for the case of heavy quark production by light quark annihilation and gluon fusion.