QCD and the Pomeron
Jeffrey R. Forshaw (
( 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
- 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.
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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