Quantum Chromo-Dynamics (QCD), the current theory for strong interactions, has
been very successful at describing and predicting many areas of particle
physics. Its successes are limited, however, to the perturbative regime
where the strong coupling constant is small. About 40% of the total
cross section at the Tevatron is elastic and diffractive scattering which
are non-perturbative and cannot currently be calculated in QCD.
Figure 1(a) shows the diagram for elastic scattering
in which a strongly interacting color singlet (pomeron) is
exchanged resulting in the scattering of the proton and anti-proton.
The right-hand side of the figure shows how a scattering would
look in an ideal detector. The proton and anti-proton would be
detected at extreme pseudorapidities
with a separation of 
in azimuthal angle 
.
This figure also demonstrates the absence of associated particle production,
or the rapidity gap, expected in elastic scattering due to the lack of color
exchanged in the interaction.
Figure 1(b) shows the diagram for diffractive dissociation,
or single diffractive scattering, in which one of the beam particles
(the proton in this case) has broken up,
producing particles in the hemisphere
of the detector opposite the detected 
.
Figure 1: (a) The diagram for elastic scattering, in which a pomeron
is exchanged resulting in the scattering of the proton and anti-proton.
The 
-
plot shows the distribution of particles in this event--no particles
are produced between the scattered proton and
.
(b) The diagram for single diffractive scattering, which is similar to elastic
scattering except that the proton breaks up,
producing particles in a limited region of rapidity.
The properties of elastic and diffractive scattering are well-described
by the phenomenology of pomeron exchange (Regge theory), where the pomeron
is a color singlet with quantum numbers of the vacuum.
The literature on diffractive dissociation is extensive and
a few review articles are given in Ref. [1].
Regge theory predates the quark-gluon model, and it is not clear
how to combine it with QCD. Definitions of the pomeron
vary from a theoretical definition:
``the highest Regge trajectory with quantum numbers of
the vacuum, responsible for the growth in the hadronic cross section
with 
'' to an experimental one: ``the thing that causes
rapidity gaps'' [2].
Many experiments have studied diffractive and elastic scattering
at different center-of-mass energies,
but due to the non-perturbative nature of the interactions,
insight into the underlying process has been limited.
The exact nature of the pomeron (Is it composed of quarks and gluons?
hard or soft? the same object as a function of momentum transfer?)
remains elusive,
although recent theoretical ideas and experimental results
are beginning to yield some answers.
This brings us to the rather new field of hard diffraction.