Analytic resummation for the quark form factor in QCD

Abstract

The quark form factor is known to exponentiate within the framework of dimensionally regularized perturbative QCD. The logarithm of the form factor is expressed in terms of integrals over the scale of the running coupling. I show that these integrals can be evaluated explicitly and expressed in terms of renormalization group invariant analytic functions of the coupling and of the space--time dimension, to any order in renormalized perturbation theory. Explicit expressions are given up two loops. To this order, all the infrared and collinear singularities in the logarithm of the form factor resum to a single pole in epsilon, whose residue is determined at one loop, plus powers of logarithms of epsilon. This behavior is conjectured to extend to all loops.