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104 Chapter 9. Nuclear Transparency
Requirement 1 : Small objects are produced at high Q 2 collisions.
Consider a highly energetic virtual photon impinging upon a bound nucleon in the
nucleus. On the basis of the qualitative features of the nucleon-nucleon cross sections
at high energies (see Fig. 5.5) one would expect the struck proton to be scattered
into the inelastic channels. However, as high momentum transfer is associated with
small wavelenghts, the virtual photon can probe the subnucleonic degrees of freedom.
Suppose now that the incoming photon hits one of the confined color quarks.
As the quark is now in a highly excited state, it will move very rapidly in some
direction. According to the uncertainty principle, the excited quark which now has
an energy surplus of δE ∼ ω, will decay by emitting gluons in a time τ ∼ 1/ω. A
single quark is colored, and colored objects are not allowed to exist freely according
to the confinement principle. Hence, the struck quark will hadronize unless it is
followed by its two companion quarks. In order now for these two quarks to be
able to follow the escaping quark, they must have been close together initially. On
average the radiated gluons must be absorbed by quarks which are a distance less
than r = τ ∼ 1/ω away. This means that the struck proton must have been in a
small-sized fluctuation. Note that one has to make a distinction between the initially
bound nucleon and the “object” which moves through the nucleus which should not
really be looked upon as a nucleon.
QCD lattice calculations indicate that hadrons are bound states of strongly interacting
quarks and gluons. The hadron can be described in terms of an infinite
number of configurations, and different configurations are expected to have different
sizes :
|N >= |qqq > +|qqq + π > +... (9.1)
For example, a configuration containing a π meson cloud will have a maximal radius
due to the light mass of the pion. As in ordinary quantum mechanics, this system
fluctuates between its different configurations. Consequently, images of a hadron
taken at different times would reveal both small and large-sized configurations. One
refers to this phenomenon as color fluctuations. The average time it takes to fluctuate
between two configurations can be estimated on the basis of the uncertainty
principle. As the time scale is inversely proportional to the energy (or mass) difference
between the two configurations one can write that τ ∼ 1/(m − M). As the
mass differences are of the order of a few hundreds of MeV, the fluctuation time is
very small, and of the order of 1 fm. Some hadronic models predict that these small,
point-like configurations (PLC) could already be produced for momentum transfers
as low as 1-2 GeV/c.