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an increase at the deconfinement temperature, albeit
a much more gradual one, which is related to residual
interactions between the constituents.
However, confinement is not the only phenomenon
responsible for rapid changes in the thermodynamic
state variables. The transition related to the breaking
of chiral symmetry resulting in the dynamical generation
of hadron masses and the appearance of pions as
Goldstone bosons plays an essential role. The chiral
transition is characterised by a rapid decrease of the
quark-antiquark condensate with T and µ B , which in fact
serves as an order parameter of strongly interacting matter.
However, the key manifestations of chiral symmetry
restoration are its observable consequences for the
hadron spectrum. Chiral partners must be degenerate,
implying significant modifications of hadronic spectral
functions by the medium as the transition is approached.
Schematic models and numerical studies with LQCD
have been developed to quantify in-medium modification
of physical observables due to the restoration of
chiral symmetry.
The chiral condensate has been shown in LQCD to
drop rapidly over the same temperature interval where
the energy density drops. This suggests that deconfinement
and the restoration of approximate chiral symmetry
in QCD may be coincidental. However, the exact relation
between the deconfinement and chiral phase transition
is quantitatively far from established in LQCD.
Recent LQCD calculations constrain the temperature
of the chiral and deconfinement transitions at µ B = 0 to
T c ≈ 150 – 170 MeV. Methods have been developed in
LQCD to explore the shift of T c with µ B for µ B < 3T. Studies
also indicate the possible existence of a critical point
(CP) in the phase diagram at finite µ B . They have further
led to a quantification of the EoS of nuclear matter at
Box 2. Broken chiral symmetry and
the origin of hadron masses
The origin of the masses of particles is one of the most
fundamental questions that we may ask about nature.
The visible matter in our universe mainly consists of
protons and neutrons, which have a mass of about
1 GeV/c 2 each. However, within the ‘Standard Model’,
the elementary building blocks of protons and neutrons,
the quarks and gluons, are massless. Gluons mediate
the interaction between the quarks and have, like the
photons, no restmass. The quarks, on the other hand,
should be massless due to a fundamental property of
the strong force, chiral symmetry. In laboratory experiments
on Earth, however, we observe non-zero (and
very different) quark masses (as shown in the figure
below). In the ‘Standard Model’, quarks acquire mass
through their interaction with an elementary field filling
all space, the so-called Higgs field. The Higgs field
breaks chiral symmetry explicitly, generating quark
masses. The search for the Higgs particle is one of
the main goals of the LHC experiments.
The Higgs mechanism is able to explain the masses
of the heavy quarks (green bars in the figure). For the
light quarks, which account for the mass of the matter
surrounding us, the explicit symmetry breaking
is very small, and the resulting small quark masses
(5 – 10 MeV/c 2 ) are by far insufficient to explain the
observed mass of hadrons (for example, the proton
mass of ≈ 1 GeV/c 2 ). In order to explain the mass of a
hadron, the vacuum surrounding a quark or gluon inside
the hadron must be filled with a strong field of quarkantiquark
pairs, called the ‘chiral condensate’.
The interaction of the light quarks with this condensate
breaks chiral symmetry spontaneously, and
generates the large quark masses. Increasing the temperature
or baryon density of a system, for example
through a high-energy nuclear collision, modifies the
vacuum. The chiral condensate is diluted and chiral
symmetry is partly restored, causing a modification
(reduction) of the masses of hadrons. At very high
density or temperature the spontaneous breaking of
the symmetry should completely disappear and the
condensate should vanish. This transition may in fact
coincide with the deconfinement transition. The search
for signatures of chiral symmetry restoration is of fundamental
importance in physics and one central objective
of high-energy heavy ion collision experiments.
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