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4.1.2 Basic Properties
of Quantum Chromodynamics
Quantum Chromodynamics (QCD) is a non-abelian
gauge theory based on local SU(3) colour invariance. The
basic matter fields are spin-1/2 fermions with fractional
electric charges that come in six flavours, the up, down,
strange, charm, bottom and top. The interactions are
mediated by eight massless gauge bosons, the gluons,
which are also subject to self-interactions. This makes
the field equations of QCD highly non-linear, leading
to many fascinating properties. First, the running of
the gauge coupling is driven by an intricate interplay of
gluon and fermion loop effects, leading to asymptotic
freedom at large energies and infrared slavery in the
low-energy regime. In fact, quarks and gluons cannot
be observed in isolation but only appear as colour neutral
compounds, the strongly interacting particles – the
hadrons. It is one of the most fascinating aspects of
modern physics that the properties of the basic constituents
of the underlying theory can only be indirectly
inferred by studying the rich manifestations of the strong
force in the structure, the decays, the production, the
spectrum, and the interactions of the hadrons. Indeed
one of the most challenging questions is to understand
the emergence of the hadronic world in terms of the
point-like and unobservable constituents.
The six flavours of quarks have masses that range
from a few MeV to about 175 GeV. The masses of the
lightest (up and down) are much smaller than the typical
hadronic scale of ~1 GeV, whereas the mass of the
bottom quark is much larger than that scale. (The top
quark has too short a lifetime to appear as a constituent
of hadrons.) Consequently, hadrons made of light quarks
require a relativistic description, whereas the hadrons
made of heavy quarks alone can effectively be described
in non-relativistic schemes. In between lie the strange
quark with a current mass of about 100 MeV and the
charm quark with a mass of 1.3 GeV. Important open
questions are the extent to which these can be treated
using methods appropriate to light and heavy quarks,
respectively.
In the description of hadron properties and their
dynamics, symmetries play central roles. In the lightquark
sector, one can decompose the quark fields into
left- and right-handed components, which are mixed
only by the small quark masses. This leads to a chiral
symmetry, which, however, is not explicit in the hadron
spectrum. Rather it is hidden (spontaneously broken) by
the condensation of quark-antiquark pairs in the QCD
vacuum. This breaking has important consequences,
since for each broken generator appear massless gauge
bosons. This explains the peculiar property of the hadron
spectrum that the pions, the kaons and the eta have
much smaller masses than all the other hadrons made
of u, d, and s quarks. The non-vanishing mass of the π,
K, η is due to the finiteness of the light quark masses.
Another intriguing property of light quark QCD is the
role played by anomalies – symmetries of the classical
theory that are broken by the quantization. Important
are the breaking of the axial U(1) anomaly that lifts the
mass of the η’ to the typical hadronic mass, the trace
anomaly that governs the balance of field versus matter
energy in the mass budget of the hadrons and chiral
anomalies that lead to parameter-free predictions for
certain meson interactions.
In contrast, the heavy quark sector displays a quite
different pattern of symmetry breaking. Since all fine and
hyperfine structure effects are suppressed by inverse
powers of the heavy-quark mass, this possesses an
exact spin and flavour symmetry in the limit of infinitely
heavy quarks. This leads to a variety of relations between
various heavy meson decay form factors that are of major
importance in the extraction of certain CKM matrix elements
from heavy meson decays.
Finally there are so-called heavy-light systems, containing
a single heavy quark. These can be best treated
as an almost static source surrounded by a cloud of
light particles. Here both heavy-quark and chiral symmetries
provide constraints that must be respected by
any systematic analysis of their properties.
For most aspects of hadron physics, the gauge coupling
is so large that it requires non-perturbative methods
to analyse the structure and dynamics of hadrons. The
two most powerful tools are lattice QCD (see Box 1)
and effective field theories (EFTs) (see Box 2), supplemented
by renormalization group methods, dispersion
relations and models, like e.g. the constituent quark
model or meson-exchange models. While lattice QCD
operates with the underlying degrees of freedom, the
quarks and the gluons, EFTs are formulated in terms
of the appropriate hadronic degrees of freedom and
provide a crucial tool for analysing the properties and
interactions of hadrons and nuclei.
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