146 The very early universe
quantum chromodynamics is known asasymptotic freedom. The decrease in the
coupling constant is due to the gluon loops, which dominate over the fermion loop
contribution and thus lead to antiscreening of the colors. Quark colors are mainly
due to the polarized halo of gluons.
The normalization pointμ^2 in (4.29) is arbitrary, and the value ofαs(q^2 ) does
not depend on it. Introducing the physical scaleQCD,defined by
ln^2 QCD
μ^2=−
12 π
(11n− 2 f)αs(μ^2 ),
we can rewrite (4.29) for the running strong fine structure constant in terms of a
single parameter:
αs(q^2 )=12 π
(11n− 2 f)ln(
q^2 /^2 QCD). (4.31)
Experimental data suggest thatQCDis about 220 MeV (to 10% accuracy). The
strong coupling constantαsis 0.13 atq100 GeV and increases to 0.21 when
the energy decreases to 10 GeV (in this energy rangef=5).According to (4.31),
the strength of strong interactions should become infinite atq^2 =^2 QCD. However,
this is not more than an informed estimate consistent with the confinement hypoth-
esis. We should not forget that (4.31) was derived in the one-loop approximation
and is applicable only ifαs(q^2 ) 1 ,that is, atq^2 ^2 QCD.Atq^2 ∼^2 QCD,all
loops give comparable contributions to theβ-function and whenαsbecomes the
order of unity, (4.31) fails. To go further we have to apply nonperturbative methods,
for instance, numerical lattice calculations. These methods also strongly support
the idea of confinement.
Quantum chromodynamics is a quantitative theory only when we consider highly
energetic processes withqO(1) GeV.The strong force binding baryons in the
nuclei is a low-energy process and cannot be calculated perturbatively. It can only
bequalitativelyexplained as the result of collective multi-gluon and pion exchange.
4.2.2 Cosmological quark–gluon phase transition
At high temperature and/or baryon density we can expect a transition from hadronic
matter to a quark–gluon plasma. In the very early universe at temperatures exceeding
QCD220 MeV,the strong couplingαs(T^2 ) is small and most quarks and gluons
only interact with each other weakly. They are no longer confined within particular
hadrons and their degrees of freedom are liberated. In this limit the quark–gluon
plasma consists of free noninteracting quarks and gluons, which can be described
in the ideal gas approximation. Of course, there always exist soft modes with
momentaq^2 ≤^2 QCD, which can by no means be treated as noninteracting particles;