Resummation of large logarithms in e +e − event shape distributions

Abstract

We describe a method for the resummation of leading and next-to-leading large logarithms to all orders in QCD perturbation theory, applicable to e +e − event shape distributions that have the property of exponentiation near the two-jet region. After a general discussion of the conditions for exponentiation and the evaluation of matrix elements and phase space to next-to-leading logarithmic accuracy, we give details of the application of the method to the thrust and heavy jet mass distributions. We show how the resummed expressions can be matched with known second-order results to obtain improved predictions throughout the whole of phase space, and how to suppress spurious higher-order terms generated by resummation outside the physical region. We also give the necessary ingredients for the improvement of third-order predictions by resummation when they become available.