4.5. STRONG INTERACTION POTENTIALS 227
4.5.4 Asymptotic freedom
The strong interaction potentials provide also a natural explanation for the asymptotic free-
dom phenomena. To this end, we need to introduce the asymptotic freedom in two persptives:
the deep inelastic scattering experiments, and the QCD theory for the coupling constant of
quark potentials.
1.Deep inelastic scattering experiments.In physical experiments, the interior of a proton
is probed by using the accelerating electrons to hit this proton. The collision is called the
elastic scattering if there is no momentum exchange as in thee-pelastic scattering:
(4.5.49) e−+p→e−+p.
The collision is an inelastic scattering if the particles are changed after the collision. For
example the usuale-pinelastic scatterings are as follows
(4.5.50)
e−+p→e−+π++n,
e−+p→e−+π^0 +p.
In 1967, three physicists J. L. Friedman, H. W. Kendall and R.E. Taylor performed a
series of deep inelastic experiments, which not only provided sufficient evidence for the exis-
tence of quarks, but also exhibited the asymptotic freedom phenomena. Due to their pioneer-
ing investigations concerning deep inelastic scattering,the three physicists were awarded the
Nobel Prize in 1990.
In thee-pscattering experiments, if an electron at lower energy collides with a proton,
then the proton looks as a point particle, and the collision is an elastic scattering. However, if
the accelerating electron is at higher energy, this electron will hit deeply into the interior of
a proton, and collides with a quark in the proton, as shown in Figure4.1. The experiments
show that the the collided quark acts as if it is a free particle.
e
p
Figure 4.1: Black dots represent three quarks in a proton.- QCD theory for asymptotic freedom. The notion of asymptotic freedom was first
introduced by (Gross and Wilczek, 1973 ;Politzer, 1973 ), who were awarded the Nobel Prize
in 2004. By using the renormalization group, they derived the strong interaction coupling
constant of quarks as follows
(4.5.51) αs=
4 π
( 11 −^23 nf)ln(q^2 /λ^2 )