Opening the door to the quark-gluon plasma

30 May 2000

Recent experiments at CERN (April, p13) using high-energy
beams of nuclei reported evidence for a quark-gluon plasma.
Interpreting such evidence is not straightforward, and this
article underlines the physics message.

A nucleus is like oranges stacked in a bag – with discernable
“fruit” or nucleons (protons and neutrons) and spaces in
between. Crush the bag and the oranges dissolve into juice,
which fills the reduced space. A pip that once belonged to a
particular orange is now free to move anywhere. In the same
way, when a nucleus is crushed, it dissolves into a plasma of
quarks and gluons. These, once imprisoned inside a particular
nucleon, are free to move inside a much larger

In ordinary nuclear matter a nucleus consists of
nucleons with a vacuum between them. Each nucleon has a
volume of about 2 fm3and contains three
valence quarks together with a cloud of gluons – the carriers
of the strong nuclear force that binds the quarks in the
nucleon and the nucleons in the nucleus.

In physics a
phase diagram shows the boundaries between different types
of the same substance, such as steam, water and ice, depicting
where boiling and freezing occur. Boiling and freezing are
very dependent on external conditions, such as pressure and
temperature. For nuclear matter the phase diagram shows the
boundary between normal nuclear matter, composed of
nucleons, and the quark-gluon plasma (QGP).

nuclear matter is situated at temperature zero and a
baryochemical potential (a measure of the nucleon density) of
about 765 MeV. The nucleon density is about 0.145
fm-3 and the energy density is about 0.135 GeV

Compressing nuclear matter, so that
the nucleons start to interpenetrate and overlap (by at least
3%), makes the intervening vacuum disappear. Each nucleon
dissolves and its constituent quarks and gluons are free to
move inside a larger volume, which has become very dense
by compression. A new state of matter is now formed – the
deconfined QGP – with a critical nucleon density and an
energy density of greater than 0.72 fm-3 and 0.7
GeV fm-3 respectively. Liberating quarks at zero
temperature therefore requires matter and energy densities at
least five times as large as those of normal nuclear

How can this be achieved? The only known
way is by compressing and heating nuclear matter, by
slamming a very-high-energy beam of nuclei onto fixed-target
nuclei, or by bringing two counter-rotating nuclear beams into
collision. This was the objective of the heavy-ion fixed-target
programme at CERN’s SPS and Brookhaven’s AGS
accelerators, and it will also be the aim of the upcoming RHIC
and LHC colliders at Brookhaven and CERN

Theoretical statistical models have been
used to analyse and evaluate the data from nucleus-nucleus
interactions. Such models produce very satisfactory
representation of the experimental data, verifying that the
statistical model is applicable. However, little fundamental
insight is gained into the actual dynamics of the

The important objective is to ascertain where
on the phase diagram the original thermal source (fireball) is
situated – in the domain corresponding to a gas of nucleons or
in that of the QGP. For this a simple statistical analysis is
inadequate. Only if interactions among the multitude of
emitted particles are taken into consideration can the
description of a possible change of phase into the QGP be

Statistical approach

Statistical Bootstrap Model (SBM), introduced by Rolf
Hagedorn at CERN some 35 years ago, is a statistical
approach, incorporating at the same time the effects of
interactions in a self-consistent way. Recent development and
extension of this model, the so-called S (for strangeness) SBM,
can define the phase diagram and the limits of nuclear matter,
as shown in the diagram (Kapoyannis, Ktorides and
Panagiotou, in press). This boundary incorporates the largest
possible and physically meaningful value of the critical
temperature at zero baryochemical potential
(To= 183 MeV) so as to have the largest possible
nucleon domain and avoid over-optimistic

SSBM-based analysis of data from the
NA35 experiment at CERN’s SPS has shown compelling
evidence that head-on collisions of even light-nuclei, such as
sulphur-32, at 200 GeV/nucleon have attained the critical
conditions, thereby allowing us to probe the deconfined quark

The overall situation resulting from the data
analysis is depicted in the diagram. It is found that the
sulphur-sulphur interaction is situated 76% inside the QGP
domain, beyond the nucleon phase, while the
proton-antiproton collision, measured in the UA5 experiment
at CERN, is well within the nucleon region, as

A second indication that the QGP phase has
been reached in the sulphur-sulphur collisions is the substantial
excess of pion (entropy) production, the explanation for which
calls for a contribution of at least 30% from a high-entropy
phase, such as that of the QGP.

A third important sign
is the achievement of thermal and chemical equilibrium
conditions (equilibrium between the different quark species
produced) in the initial stage of the nuclear interaction,
materializing at a temperature of at least 177 MeV, a
baryochemical potential of more than 252 MeV and a
strangeness saturation (specifying the relative strange-quark
production in chemical equilibrium) of close to unity. Thermal
and chemical equilibrium conditions are expected and required
for the transition to QGP. Finally, the energy density created
in these interactions is at least 2 GeV fm-3– well
above the critical value for deconfinement of about 1 GeV

These observations, together with
several other intriguing clues (CERN
November 1999 p8), give rather definitive
indications that the door to the quark-gluon plasma has been
opened by the SPS heavy-ion programme at

Further reading
Kapoyannis, C N Ktorides and A D Panagiotou, in press
European Physical Journal C(hep-ph/9911306).

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