8 - Taming the growth

Summary

So far, this book has been concerned with the behaviour of QCD in the leading logarithmic approximation, which should be appropriate for large enough centre-of-mass energies and for those processes which satisfy the criteria relevant for the use of perturbative QCD. In Chapters 2–4, we derived and solved the BFKL equation. We were led to think of the Pomeron as the t-channel exchange of a pair of (interacting) reggeized gluons. In this chapter, we start off by reformulating the results already obtained for the elastic-scattering amplitude of two colourless states in a way which suggests that we view the scattering as the incoherent scattering of individual colour dipoles whose locations in configuration space are frozen over the time of interaction. This approach will lead us to a very tangible physical picture of high energy scattering in configuration space.

In Section 8.2 we turn our attention to the undesirable feature which afflicts the scattering amplitudes calculated in the leading logarithm approximation. This is the violation of unitarity which results from the strong growth of the total cross-section with increasing energy. The dipole formalism discussed in Section 8.1 provides a very elegant framework in which to investigate the dominant corrections to the leading logarithm approximation which ensure that the theory remains unitary. We begin Section 8.2 by setting up an operator formalism (due to Mueller (1995)) to describe the dipole evolution and interaction.