Subatomic Physics

454 Strong Interactions
Figure 14.24: Shielding and antishielding. (a) An external charge −e is shown surrounded by
electron–positron pairs; (b) Feynman diagram corresponding to Fig. (a); (c) and (d) + (e) are
diagrams similar to (a) and (b), respectively, but for QCD and a quark q.
is the mass of the electron. A Feynman diagram corresponding to Fig. 14.24(a) is
shown in Fig. 14.24(b). Since the external electron attracts positive charges, the
positron of the virtual pair will be closer to the test electron than the electron of the
pair. Consequently the effective charge (strength of interaction) of the real electron
seen by a very small test charge is reduced when the test charge is some distance
away. But this effective charge increases in magnitude as the test charge approaches
the electron, since its screening by the positron of the e − e + pair is reduced. The
effective interaction strength, α = e 2 /�c, increases slightly at small distances or
high momentum transfers. The situation is different in QCD, because in addition
to the effect of screening from quark–antiquark pairs (Fig. 14.24(d)), the gluons can
interact with themselves (Fig. 14.24(e)). These gluons carry away color so that, if
not too many types of quark–antiquarks pairs can be created, there is antishielding
and the color charge decreases as we approach the colored quark, as shown in
Fig. 14.24(e). Eq. (14.58) implies that this decrease holds for nf < 33/2. Thus
αs, which measures the strength of the interaction, is reduced at short distances
or large momentum transfers, quite the opposite from QED. At these momentum
transfers, which require very high energies, QCD can be and has been tested. If the
effective strength, as measured by αs, is sufficiently weak, then perturbation theory
can be used.
As an example, consider the production of quark pairs in e + e − collisions at very
high energies, as shown in Fig. 10.23(b). By analogy to Eq. 10.89, e + e − → µ + µ − ,
the production of qq, Fig. 10.23(b), should show the same angular distribution,
namely (1 + cos 2 θ). In the colliding frame, which is the c.m. frame, the µ + µ − or