The FEE Server Control Engine of the ALICE-TRD - Westfälische ...

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2 Theoretical background first generation second generation third generation Quarks up (u) charm (c) top (t) down (d) strange (s) bottom (b) Leptons electron neutrino νe muon neutrino νµ tau neutrino ντ electron (e) muon (µ) tau (τ) Table 2.1: Overview of the fundermental particles. Each of the particles have an anti-particle, too (not shown). Interaction Rel. Strength Range Mediators Electromagnetic Interaction Strong Interaction Weak Interaction α = 1 137 ∞ Photon γ, spin: 1, mass mγ = 0, interacts with electrically charged particles αs = O(1) (depends on momentum transfer) q ≈ α · 2 m2 Wc2 (depends on momentum transfer q) ≈ 1 fm 8 gluons gi, spin: 1, mass mg=0; interact with the color charge of quarks; gluons are color charged, too → self interaction between the gluons ≪ 1 fm 2 charged bosons (W − ; W + ) and one neutral boson (Z 0 ); spin: 1, mW = 80 GeV/c 2 ; mZ = 91 GeV/c 2 ; interact with all (anti-)leptons (e − , µ − , τ − , νe, νµ, ντ) and all (anti-)quarks (u, d, c, s, t, b) Gravitation α · 10 −36 ∞ interacts with all particles 10 Table 2.2: Overview of the four fundamental interactions.
2 Theoretical background The potential between two quarks reflects the confinement. It can be approximated by [Sat90] Vs(r) = − 4 αs + kr. (2.1) 3 r The potential increases proportional to the distance between two quarks. If one tries to separate a quark from a hadron, at some point the potential energy is high enough to form a new quark / anti-quark pair out of the vacuum. Instead of separating the quarks one creates two hadrons which both have no net-color charge. The factor αs in formula (2.1) is the running coupling constant. It can be written as αs(Q 2 ) = 12π (33 − 2n f ) ln(Q2 /Λ2 . (2.2) ) In this equation n f is the number of involved quark types, Λ a scale factor and Q the momentum transfer. In case of high momentum transfer which is equivalent to small distances the coupling constant becomes weak and the quarks can move freely. This property of the QCD is called asymptotic freedom. 2.2 The Quark-Gluon Plasma In case of low densities and low temperatures, quarks and gluons are confined to the size of hadrons and build the normal hadronic matter. When density and temperature become very high there is a phase transition to a new state, the quark-gluon plasma (QGP). In a QGP quarks and gluons are not longer confined to hadrons but can move freely. Figure 2.1 shows the corresponding phase diagram. Nowadays the only place where a QGP may exists is the core of neutron stars. But some 10 picoseconds after the Big Bang lasting for 10 microseconds the complete universe was filled with a QGP [BMS07]. To investigate this phase and to understand the properties of a QGP it has to be created in laboratory. The only possibility to get the necessary energy density is to collide heavy ions at highest available energies. A sketch of such a collision is shown in figure 2.2. Two nuclei, Lorentz contracted because of their speed, collide with each other. In the moment of collision scattering between the partons takes place. In case of a large momentum transfer during a scattering the scattered partons will form jets later (see section 2.3.2). The nuclei pass each other and in the collision zone an extremely high energy density is reached. Thousands or even tens of thousands of quarks and gluons are created. The created particles collide and after a time of about 1 fm c −1 thermal equilibrium is reached. Since a QGP is a collective state thermal equilibrium is a necessary condition to define variables like temperature or pressure. The QGP expands and cools down. The temperature drops below the critical temperature where a QGP can exists and the re-hadronisation takes place. The quarks and gluons are bound to hadrons again and the QGP vanishes. This moment is called chemical freeze-out. After the chemical freeze-out the number and the type of created hadrons are fixed. The cloud of particles expands further and at some point the mean free path of the particles becomes larger then the size of the cloud. This point in time is the kinetic freeze-out. Afterwards the energy distribution of the particles is fixed, too. The particles leave the collision zone and can be detected by particle detectors. There is no possibility to directly investigate a QGP because of its small size and short 11
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Bibliography [A + 05] V. Angelov et
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