Subatomic Physics

14.7. Strong Processes at High Energies 447
experimentally γ is considerably smaller, γ =0.127 ± 0.009. (33)
The slower logarithmic increase predicted by QCD indicates that not all the
energy is distributed statistically, but that a disproportionate amount goes to a few
“leading” particles. (35)
Figure 14.18: Normalized distributions in charged multiplicity
in the range of c.m. energies of 11.3–62.2 GeV (ISR,
FNAL and Serpukhov) and at 546 GeV (UA5). [From
J. G. Alner et al., (UA5 Collaboration), Phys. Lett. 138B,
304 (1984).]
(iii) Poisson-like distributions.
The cross sections for the
production of events with n
prongs are shown for two energies
in Fig. 14.18. (33,36) The
distributions are plotted as
a function of z = n/〈n〉.
Fig. 14.18 shows that the
normalized distributions resemble
a Poisson distribution,
Eq. (4.3), but are somewhat
broader. On the basis of scaling,
it was predicted by Koba,
Nielsen, and Olesen (37) that
the normalized charged particle
multiplicity should become
independent of energy
for asymptotically large energies;
this is often referred to
as KNO scaling. This scaling
behavior appears to hold over
a region of c.m. energies of
about 10–70 GeV.
However, at higher energies we observe in Fig. 14.18 that the tail of the distribution
function broadens, so that “asymptotia” has not yet been reached.
High-Energy Theorems (Asymptotia) Processes at ultrahigh energies can be
extremely complex. It is nevertheless possible to extrapolate lower-energy data to
predict features of cross sections that should emerge as the total energy in the c.m.,
33 C. Geich–Gimbel, Int. J. Mod. Phys. A4, 1527 (1989).
34 E. Fermi, Phys. Rev. 81, 683 (1951); L. D. Landau, Izv. Akad. Nauk SSSR 17, 51 (1953)
[transl. Collected Papers of L. D. Landau, (D. ter Haar, ed.)] Pergamon Press and Gordon and
Breach, New York, 1965; M. Kretzschmar, Annu. Rev. Nucl. Sci. 10, 765 (1958); D. Kharzeev,
E. Levin and M. Nardi, Nucl. Phys. A 747, 609(2005); .
35 E. M. Friedlander and R. M. Weiner, Phys. Rev. D28, 2903 (1983).
36 G. J. Alner et al., (UA5 Collaboration), Phys. Lett. B138, 304 (1984).
37 Z. Koba, H. B. Nielsen, and P. Olesen, Nucl. Phys. B40, 317 (1972); T. Renk, S.A. Bass and
D.K. Srivastava, Phys. Lett. B 632, 632 (2006).