Abstract
The strong interaction between the elementary constituents of matter (quarks and gluons) is described by the theory of Quantum Chromodynamics (QCD). The basic ingredients of this quantum field theory will be explained in Sect. 1.1 and its peculiar properties driven by the running of the strong coupling constant will be addressed in Sect. 1.2. These properties lead to the prediction that strongly-interacting matter can exist in different phases depending on the temperature and the density of the system. Nuclear matter at extremely high temperatures and energy densities is obtained with ultra-relativistic heavy-ion collisions, which allow to create a state of matter where quarks and gluons are interacting without being confined into hadrons. According to the hot Big Bang model, this state of matter should have appeared after the electro-weak phase transition, a few microseconds after the Big Bang. The Lattice QCD approach, which is introduced in Sect. 1.3, allows to obtain quantitative predictions on the basic properties of the QCD phase diagram and on the phase transition, which are described in Sect. 1.4. The second part of the chapter (Sect. 1.5) is devoted to a review of the first results obtained by the experiments at the CERN Large Hadron Collider (LHC) in Pb–Pb collisions at the energy of \(\sqrt{s_\mathrm{NN}}=2.76\) TeV per nucleon–nucleon (NN) collision, also compared with the measurements performed at lower energies at the Relativistic Heavy-Ion Collider (RHIC) at the Brookhaven National Laboratory (BNL).
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Notes
- 1.
In the Standard Model of particles flavour is the property that distinguishes different particles in the two groups of building blocks of matter, the quarks and the leptons. There are six flavours of subatomic particle within each of these two groups: six leptons (the electron, the muon, the tau and the three associated neutrinos) and six quarks (up, down, charm, strange, top and bottom). In QCD flavour is a global symmetry, this means that flavour changing processes are mediated only by electroweak interaction.
- 2.
In a pion gas the degrees of freedom are the 3 values of the isospin for \(\pi ^+\), \(\pi ^0\) and \(\pi ^-\). In a QGP with \(n_f\) quark flavours the degrees of freedom are \(n_g+\frac{7}{8}(n_q+n_{\bar{q}})=(8\times 2)+\frac{7}{8} \) \((2\times 3\times 2 \times n_f)=(16+\frac{21}{2}n_f)\). The factor 7/8 takes into account the difference between Bose–Einstein (gluons) and Fermi–Dirac (quarks) statistics.
- 3.
During LHC Run 2 the energy will reach \(\sqrt{s_\mathrm{NN}}=5.1\) TeV per nucleon pair, and during Run 3 its design value of \(\sqrt{s_\mathrm{NN}}=5.5\) TeV per nucleon pair.
- 4.
Alternatively the number of nucleon–nucleon collisions is expressed as \(N_\mathrm{coll}(b)=T_\mathrm{AB}(b)\sigma _\mathrm{inel}^\mathrm{NN}\) if \(\rho _A(\mathbf {s}-z_A)\) is normalized to A. This convention is used, for example, in [21].
- 5.
The pseudorapidity is defined as \(\eta = -\ln [\tan (\theta /2)]\), where \(\theta \) is the polar angle with respect to the beam direction. For a particle with velocity \(v\rightarrow c\), \(\eta \approx y\), being y the longitudinal rapidity. The longitudinal rapidity of a particle with four-momentum \((E, \vec {p})\) is defined as \(y=\frac{1}{2}\ln \left( \frac{E+p_z}{E-p_z}\right) \), being z the direction of the beam.
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Festanti, A. (2016). Introduction to the Physics of Ultra-Relativistic Heavy-Ion Collisions. In: Measurement of the D0 Meson Production in Pb–Pb and p–Pb Collisions. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-43455-1_1
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