Subatomic Physics

10.9. Electron–Positron Collisions and Quarks 315
r
w
f
r’
J�y
y(2 ) s
Figure 10.22: The ratio R of the total cross section for e + e − annihilation into hadrons to the
muon pair production cross section. [From PDG.]
It is therefore convenient to refer all other cross sections to that of muon pair
production by introducing the ratio R, defined by
U
R = σ(e+ e− −→ hadrons)
σ(e + e− −→ µ + µ − . (10.91)
)
This ratio is shown as a function of W in Fig. 10.22. A number of resonances
stand out like beanpoles above a flat landscape. The resonances and the flat background
can be described in terms of simple diagrams, as in Fig. 10.23. The resonances
(particles) have an energy dependence that is given by a Breit–Wigner
shape, Eq. (5.45), and they have large total cross sections. The photon’s quantum
numbers imply that the resonances have spin and parity J π =1 − . As will be
discussed later the resonances are “bound” (confined) quark–antiquark pairs that
appear as vector mesons. The flat “background” between resonances is ascribed to
nonresonant quark–antiquark pair production. Since quarks are confined, the nonresonant
quark–antiquark pair produced by the photon must encounter at least one
other quark–antiquark pair and combine with it before emerging as free particles.
This process is shown in Fig. 10.23(b).
If quarks are indeed spin- 1
2
point particles, as postulated in Section 5.11, the
cross section for the production of a qq pair should also be given by Eq. 10.89
multiplied by the square of the ratio of the quark-to-electron charge. If we denote
the electric charge of quark i as a multiple of e by qi, the assumption of point
charges immediately gives for the ratio R,
Z