Jeffrey R. Forshaw ( jeff.forshaw-at-manchester.ac.uk )

and

Douglas A. Ross ( dar-at-phys.soton.ac.uk )

Published by Cambridge University Press in the Lecture Note series.

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The BFKL equation is derived from the Feynman rules of perturbative QCD and its solution obtained. The physical properties of the "pomeron" that emerges are discussed and a variety of important applications presented. In particular, we study deep inelastic scattering at small Bjorken-x and rapidity gap (diffractive) processes. The book is aimed at anyone with an interest in scattering processes at high centre-of-mass energies and the nature of diffraction. It is only assumed that the reader has completed an introductory course in quantum field theory.

- What is a Pomeron?:A basic introduction to Regge theory is provided.
- A simple example: A simplified model of scalar gluons and quarks is used to illustrate many of the essential features of scattering at high energies.
- The reggeized gluon: Turning to QCD, we first consider quark-quark scattering with colour octet exchange. The gluon is seen to reggeize.
- The QCD Pomeron: We move on to study elastic scattering amplitudes (i.e. with colour singlet exchange) within QCD. We derive the BFKL equation and its solution.
- From cuts to poles: The effect of including asymptotic freedom is studied along with some general methods designed to account for the non-perturbative effects in the theory.
- Applications in deep inelastic scattering: The deep inelastic structure functions in the region of small Bjorken-x are examined. A more direct probe of the BFKL pomeron is provided by the more exclusive process, whereby an additional forward jet is required. This process is computed. Connection with the usual DGLAP formalism is illustrated. The role of coherence is also examined.
- Diffraction: Rapidity gap processes are discussed. Large-t scattering is shown to provide an excellent test of the BFKL physics. Photon dissociation is discussed as a classic example of a diffractive process and the concept of a pomeron structure function introduced.
- Taming the growth: The colour dipole approach to high energy scattering is discussed and shown to produce equivalent results to those previously derived for elastic scattering processes. Dipole re-scattering corrections are computed and shown to lead to a unitary amplitude.

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