Excerpt
Contents
1. Introduction
1.1. Hadronic Matter
1.1.1. Quark Combinations
1.1.2. Color Charge
1.2. The Strong Interaction: Confinement
1.2.1. Chiral Symmetry Restoration
1.3. The Phase Diagram of Strongly Interacting Matter
1.4. Relativistic Heavy Ion Collisions
1.5. Strangeness
1.5.1. Strangeness Production in a Hadronic Gas
1.5.2. Strangeness Production in a Quark Gluon Plasma
2. The NA49 Experiment at CERN SPS
2.1. The NA49 Detector Layout
2.2. Time Projection Chambers
2.2.1. The NA49 TPCs
2.3. Event Reconstruction
2.3.1. V0 Reconstruction
2.3.2. V0 Finding
2.3.3. V0 Fitting
2.3.4. Multi-Strange Hyperon Reconstruction . .
2.3.5. Ξ Finding
3. Data Analysis
3.1. Data sets
3.2. Event Cuts
3.2.1. Central Pb+Pb
3.2.2. Minimum Bias Pb+Pb
3.2.3. Semi-Central Si+Si
3.3. Analysis Cuts
3.3.1. Cuts on the Ξ Candidate
3.3.2. Cuts on the Daughter π of the Ξ Candidate
3.3.3. Cuts on the Daughter Λ Candidate
3.4. Invariant mass method
3.5. Correction
3.5.1. Geometrical Acceptance
3.5.2. Reconstruction Efficiency
3.5.3. Centrality Bin Size Effect
3.5.4. Influence of δ Electrons
4. Extraction of Spectra, Yields and Systematic Error
4.1. Transverse Momentum and Transverse Mass Spectra
4.1.1. Extrapolation of the Transverse Momentum Spectra
4.2. Rapidity Spectra and 4π Yields
4.3. Stability Checks of the Results and the Systematic Error . .
4.4. Lifetime
4.5. Comparision with another Ξ Analysis at 158 AGeV . .
5. Discussion
5.1. Comparison with Other Experiments
5.2. Energy Dependence
5.2.1. Inverse Slope Parameter and Mean Transverse Mass of the Ξ Hyperon
5.2.2. Strange Hadron Yield Enhancement
5.2.3. Excitation Function of Ξ production
5.2.4. Antibaryon/Baryon Ratio
5.3. Theoretical Models
5.3.1. Spectator-Participant Model
5.3.2. RQMD v2.
5.3.3. UrQMD v1.3
5.3.4. Statistical Hadron Gas Models
5.3.5. Comparison to Models
6. Summary and Conclusion
A. Relativistic Kinematics and Lorentz-Transformation
A.1. Four Vector and Lorentz Transformation
A.2. Rapidity and Transverse Momentum
A.3. Pseudorapidity
A.4. Center of Mass Energy
B. Eventcuts
B.1. Central Pb+Pb
B.2. Minimum Bias Pb+Pb
C. Invariant Mass Distribution and Efficiency
D. Invariant Mass Distribution for pt and mt - m0 Spectra and Numerical Values
D.1. Central Pb+Pb
D.2. Minimum Bias Pb+Pb
D.3. Semi-Central Si+Si
E. Invariant Mass Distribution for y Spectra and Numerical Values
E.1. Central Pb+Pb
F. Systematic Errors
G. Inverse Slope Parameter versus Particle Mass
1. Introduction
The goal of relativistic heavy ion collisions is to explore strongly interacting matter under extreme conditions. At high temperature and baryon density, nuclear matter is expected to melt into a state of free quarks and gluons, known as the Quark Gluon Plasma (QGP)
The study of deconfined matter is of interest not only in nuclear physics, but also in cosmology and astrophysics. The Universe (see Figure 1.1) itself existed in a similar state approximately 10−6 seconds after the big bang1 before it expanded and cooled sufficiently for quarks and gluons to hadronize into nucleons and other hadrons. Even today, large volumes of deconfined quark matter might exist in the dense cores of neutron stars2 and exploding black holes.
Figure 1.1.: The history of the Universe.
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1.1. Hadronic Matter
Until the early 1960s, baryons and mesons were considered to be the build- ing blocks for hadronic matter. Together with leptons, they were thought to constitute all the material in the known Universe. However, through deep in- elastic electron-nucleon scattering experiments3, it was eventually discovered that baryons and mesons must have substructure. A model based around such sub-particles, named quarks (q), was introduced independently by Zweig and Gell-Mann and developed by Gell-Mann in the 1960s4. It is believed that six types of flavors of quark named up (u), down (d), strange (s), charm (c), bot- tom (b) and top (t), and their corresponding anti-quarks (u d, s, c,b, t), grouped into three generations, constitute the total number of quarks.
Flavor Symbol Mass (MeV) Charge (e) Quantum Number
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Table 1.1.: The properties of the 6 known quarks.
Table 1.1 shows properties of quarks5 which all have spin12 h,includingthe approximate mass, fractional charge and relevant quantum number. In addition to the quantum numbers associated with quark flavour (isospin, strangeness, charm, bottom and top), each quark has the baryon number, B =13.Anti- quarks, which are the antiparticle equivalent of quarks, have the same mass as their quark counterparts but opposite charge and quantum numbers.
1.1.1. Quark Combinations
Quarks themselves are never seen in isolation, but always form strongly inter- acting particles, referred to as hadrons. The simplest combinations allowed are integer spin (0 h, 1 h) mesons or half integer spin (1
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Figure 1.2.: a) The octet of spin 1/2 even parity baryons, b) The nonet of spin 0 odd parity mesons, c) The decuplet of spin 3/2 even parity baryons.
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Table 1.2.: The mass and strangeness of some of the predominant decay strange hadrons, where the branching ratios and lifetimes are given.
1.1.2. Color Charge
Quarks are assigned a color charge, either red, green or blue, and antiquarks either antired, antigreen or antiblue. However, as individual quarks have never been observed in nature, it is postulated that the color charge itself is confined, and hence all baryons and mesons must be colorless objects. Mesons are formed by a color-anticolor q q pairs, for example sblue santiblue, with baryons formed from three quarks with one of each color, for example sredsbluedgreen.
The introduction of color is necessary in order not to contravene the Pauli exclusion principle, which forbids two fermions from occupying the same quantum state. The need for this is seen when examining particles such as the Δ− (ddd), Δ++ (uuu) and Ω− (sss). Each particle consists of three identical quarks leading to a symmetric spatial wavefunction, Ψtotal. The spin part of the wavefunction, ψspin must also be symmetric because the total spin is32 h which means that all three quarks must have parallel spin. In order to satisfy the Pauli exclusion principle in the cases of the Δ−, Δ++ and Ω−, each quark in the baryon must carry a different color charge.
1.2. The Strong Interaction: Confinement
The strong nuclear force is described by Quantum Chromodynamics (QCD), the parallel field theory to Quantum Electrodynamics (QED) that describes the electromagnetic force. It is propagated by gluons analogously to photons in the electromagnetic force, but unlike photons, which do not carry electric charge, gluons carry color, and they can self-interact. The fact that gluons are not color neutral is an important difference between the strong and electromag- netic forces, which is manifested in the behaviour of the strong force potential. The potential between a quark and antiquark with a distance r apart is of the form
V (r) ∼ −4 αs(r) 3 r
where αs(r) is the strong coupling constant, k is a constant of the order of 1 GeV/fm and r is the separation of the quarks. The1 r termdeterminesthe potential at short distances, where the gluon distribution from a quark is radial, as shown in Figure1.3 a. Between any two separating (q or q) quarks, for r ≥
1 fm, the second term in equation 1.1 dominates and V (r) → ∞. Here, the constant k can be thought of as a spring constant providing the tension in the string. The self coupling of gluons causes the color field lines between the quarks to form a tube (Figure 1.3b). Therefore, the potential at large distances increases linearly with the separation of the quarks as the density of field lines remains constant. One implication of equation 1.1 is that an infinite amount of energy is required to separate two color charges. However, in practice, if the color flux tube is stretched enough, it becomes energetically favorable to rupture the tube and terminate the field lines with a qq pair created out of the QCD vacuum. Therefore it is not possible to separate two quarks on a large distance scale.
Equation 1.1 also implies, that on the small distance scale which is governed by the term proportional to1 r,deconfinementispossibleifαs tendsto0 faster than r.
1.2. The Strong Interaction: Confinement
Figure 1.3.: The gluon distribution of a quark. a) Near the quark, they form a radial distribution, b) Further from the quark, they form a flux tube.
There are two phenomena which can lead to quark deconfinement at short distance scales. At very high energies, the bare quark itself can be probed and it is found that its effective color charge tends to zero as the energy with which it is probed increases. This process is called asymptotic freedom. At high hadronic density, quarks can interact with quarks from other hadrons. In this process, they lose their memory as to which hadron they are associated with. This is known as Debye screening.
Gluons carry both color and anticolor. Quarks are constantly emitting and reabsorbing virtual gluons according to the Heisenberg uncertainty principle. Consequently the net color of the system is not on the quark but rather sur- rounds it in the cloud of gluons. This has the effect of shielding the amount of original quark color seen by an approaching parton. In other words, the poten- tial felt by a parton will decrease as the parton and quark separation decreases. From the first term in equation 1.1 it may be expected that V (r) → -∞ as r →
0 [6, 7]. However at short distances, the strong coupling constant αs(r) has a large dependence on Q2 (and also r). The dependence is shown in equation 1.2
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where nf is the number of quark flavors and Q2 is the Lorentz invariant squared momentum transfer, and is only valid for Q2 ≫ Λ2 QCD.ThevariableΛQCD can be thought of as the energy scale at which the strong force becomes strong. At distance of the order of the size of a nucleon (about1 fm), over which confinement occurs, ΛQCD ≈ 213 MeV. At small distances, αs(r) → 0, quicker than r → 0 and so consequently V (r) → 0. Quarks are then said to be free within the proximity of a nucleon, an effect which is known as asymptotic freedom.
An alternative consideration, which is applicable to bulk matter and also results in deconfinement of quarks and gluons, is that of Debye screening, analogous to the same effect in QED. In dense matter, the Coulomb potential felt by an orbiting electron is modified according to the formula
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where the electron binding radius is r, and the Debye screening radius, rD is related to the number density of atoms, nD by
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As the number density is increasing, rD becomes smaller than the electron binding radius, and the exponential term in equation 1.1 tends to zero. As a result of Debye screening, the outermost electrons are freed from their host atom and the material becomes an electrical conductor. For the strong force equivalent, compression of quark matter is expected to give rise to a color conducting system of deconfined quarks and gluons.
1.2.1. Chiral Symmetry Restoration
At usual temperature and pressure, our world implies broken chiral symmetry. A transition into a chirally symmetric phase can occur at temperatures ap- proximately the same as those required for a deconfined transition8. Chiral symmetry is related to the helicity of quarks. Particles whose spin vectors are aligned to their momentum vector are said to be right handed, while particles whose spin vectors are anti-parallel to the momentum vectors are referred to as being left handed. In any interaction with massless particles, the helicity of the particles is conserved.
At temperatures below this transition, quarks are massive particles. As αs is greater than zero, quarks can interact and these interactions have the effect of increasing their mass so that it is greater than the current masses listed in Table 1.1. This is known as their dynamical mass and can be calculated from the hadronic masses using phenomenological models. This leads to light quark (u and d) masses of approximately 300 MeV, and a strange quark (s) mass of approximately 500 MeV. It is the easy to see why chiral symmetry is broken at these lower temperatures. As a quark with mass cannot travel at the speed of light, it is always possible to transform to a frame of reference where, in the case of a right handed particle, the momentum vector is no longer aligned to the spin vector, but anti-parallel to it. This situation, where quarks may appear to be either left handed or right handed depending on the frame of reference, clearly breaks chiral symmetry.
At temperatures above the chiral transition, αs tends to zero and the interac- tions between quarks are reduced. Therefore, their effective mass is no longer given by their dynamical mass, but by their current value. As these values are still greater than zero, chiral symmetry can not be restored completely, only partially.
1.3. The Phase Diagram of Strongly Interacting Matter
The manifestation of a restoration of chiral symmetry in relativistic heavy ion collisions, where quark masses are given by their current value, rather than their dynamical value, may be two-fold. Firstly, the hadronic masses may be lower than expected, which could be visible in the lowering and broadering of resonance masses. Secondly, an increase in production rates of the heavier quarks may be seen. This should be most notable for the strange quark as the temperature of the system becomes comparable to the mass of the ss.
The sketch of the phase diagram of strongly interacting matter as a function of the temperature, T , and of the baryonic chemical potential (related to the net baryon density), μB as suggested by QCD-based considerations [9, 10] is shown in Figure 1.4. To a large extent these predictions are qualitative, as QCD at finite temperature and baryon number is one of the least explored domains of the theory. Three different states of matter are indicated: hadronic matter, QGP and color superconductor.
More quantitative results come from lattice QCD calculations which can be performed at μB = 0. They strongly suggest a rapid crossover from the hadron gas to the QGP at the temperature Tc = 170 − 190 MeV [8, 11], which seems to be somewhat higher than the chemical freeze-out temperatures of central Pb+Pb/Au+Au collisions (T = 150 − 170 MeV)12 at the top SPS and RHIC energies.
The nature of the transition to a QGP is expected to change with the increasing baryonic chemical potential. At high potential the transition may be of first order, with the end point of the first order transition domain, marked E in Figure 1.4 and calculated from11 (2 + 1 flavors with physical quark masses), being the critical point of the second order.
Relativistic heavy ion collisions are a useful tool to explore the phase diagram of strongly interacting matter experimentally.
1.4. Relativistic Heavy Ion Collisions
To study nuclear matter under extreme conditions, it is necessary to create hot and dense nuclear matter in the laboratory. This can be achieved by colliding nuclei, either by shooting accelerated ions at a stationary target, or by head-on collisions of two ion beams. In order to achieve the biggest volume of excited nuclear matter, very heavy nuclei such as lead (Pb) or gold (Au) are used.
Therefore experiments beginning at Bevalac in Berkeley and continuing at the Joint Institute for Nuclear Research (JINR), at CERN SPS, the Schwerionen- Synchrotron (SIS) at the Gesselschaft für Schwerionenforschung (GSI), Alter- nating Gradient Synchrotron (AGS) and the Relativistic Heavy Ion Collider
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Figure 1.4.: The phase diagram of strongly interacting matter as a function of the temperature T and of the baryonic chemical potential μB . The chemical freeze-out points of hadrons produced in central Pb+Pb (Au+Au) collisions are taken from12 and the critical point and the crossover curves for 2 +1 flavors with physical quark masses from11.
(RHIC) at the Brookhaven National Laboratory (BNL) and CERN LHC (Large Hadron Collider) are done. Presently this is the only way to search and confirm the existence of the QGP. Many nucleons are participating in nucleus-nucleus collisions compared to elementary proton-proton collisions, which are making multiple collisions in the reaction zone. The number of collisions as well as deposed energy depends on the size of the nucleus. The yield of secondary par- ticles is much higher in Pb+Pb than in proton-proton collisions, so that there is a possibility of re-scattering between the produced hadrons.
There are different idealized pictures to describe heavy ion collisions. In the Landau picture13 the interacting Lorentz contracted nuclei are fully stopped creating a baryon rich region in the center of mass of the interaction which is shown in Figure 1.5a. At the end, a hydrodynamically expanding fireball is left, which expands faster longitudinally than transversal due to the higher pressure gradient in longitudinal direction. The non-participating nuclei are flying without decelerate forward. In the laboratory frame, the initial energy density of the target nucleus is ϵ0 = E/V , where E and V are the energy and volume respectively. This is also the energy density of the beam ion in its rest
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As the two ions are completely stopped, they occupy the same physical space, so the energy density is given by equation:
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In the Bjorken picture1, the initial baryon charge of the target and pro- jectile is so far apart in phase space that it cannot be slowed down completely during the heavy ion collision. In this so-called transparent energy regime the quanta carrying the baryon charge will essentially keep their initial velocities, i.e., the center of the reaction zone will be almost baryon free, which is shown in Figure 1.5b. However, much energy will be deposited in this baryon free region.
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Figure 1.5.: Illustration of the Landau a) and Bjorken b) picture of nu- cleus+nucleus collisions.
Bjorken1 has given a simple estimate of the initial energy density reached in central A+A collisions
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where A is the transverse area of the incident nuclei,dEtdy denotesthetransverse energy of the collision product per unit of rapidity and the hadron formation time (assumed to be τ = 1 fm/c). In both approaches the energy density increases with collision energy and thus at high enough energy a QGP should be formed.
The space-time evolution of a heavy ion collision in the center of mass frame with and without formation of a QGP is shown in Figure 1.6. The situation before the collision is shown in a). The nuclei are accelerated to relativistic speed, which is why they appear Lorentz contracted. In b) the initial conditions are illustrated.
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Figure 1.6.: Space-time evolution of the high-energy nuclear collisions with and without formation of a QGP.
The nuclei collide and interactions at small distances between quarks (partons) of the participating nucleons take place in a small volume. In both cases first a formation time is needed before either a hadron gas or a QGP is created. First the case QGP creation will be explained. In the follwowing stage c), the QGP fireball is expanding due to internal pressure and cools down rapidly. Particle interactions become much softer, and processes at low transverse momentum play a dominant role. With the end of the production of new quarks, the system approaches chemical equilibrium. In d), the hadronization phase is represented. In this stage a QGP is transformed into mesons and baryons. Inelastic processes are stopped at a given temperature Tch, this is known as chemical freeze out. The expansion and cooling continues until elastic collisions between particles stop at the thermal freeze out temperature Tfo, when momenta of the particles are fixed, which is shown in e). The freeze out times might be different for various particle species because of the different cross-section.
1.5. Strangeness
The emitted particles move freely towards the detectors, where they are finally measured.
On the right hand side of Figure 1.6 the evolution of a heavy ion collision is presented without quark gluon plasma phase transition. Characteristic for the hadron gas are frequent interactions (rescattering) which can change the kinetic properties via elastic and the particle composition of the system via inelastic interactions.
The strange (s) and anti-strange (s) quarks are not contained in the colliding nuclei, but are newly produced and show up in the strange hadrons in the final state. Rafelski and Müller suggested that strange particle production is enhanced in the QGP with respect to that in a hadron gas14 −16. This enhancement is relative to a collision where a transition to a QGP phase does not take place, such as p+p collisions where the system size is very small. The enhancement occurs because different channels are availible for the production of strange quarks, as well as a difference in threshold energies due to the fact that in a deconfined state, only the strange quarks have to be produced, rather than strange hadrons themselves.
1.5.1. Strangeness Production in a Hadronic Gas
The hadronic interactions which create strange hadrons have a high energy threshold, which is calculated from the difference in masses between the initial and final state particles. Two such typical reactions involving nucleons (N) are given in equations 1.7 and 1.8. As strangeness is conserved in the strong inter- action, a hadron containing a s quark must be produced in the same reaction as a hadron containing a s quark. An example of a production reaction for Λ hyperons in a Hadronic Gas is presented in equation 1.7 and 1.8, where the threshold energy of 700 MeV and 2200 MeV, respectively:
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These threshold energies are quite large to produce strangeness in an initial collision. More realistically, the production of strange quarks is dominated by the re-scattering of particles as the fireball is dominated by produced pions, except when the net baryon density is large. The principal channels for strangeness production are given by equations 1.9 − 1.16, which have lower energy thresholds than strangeness production in primary interactions:
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Although the threshold energy for production of the Λ andΛ are the same, (as given by equations 1.10 and 1.11), dependent upon the amount of stop- ping, strange baryons are produced more readily due to the absence of anti- nucleons N ). This is because there already are protons and neutrons present from the colliding ions while anti-nucleons have to be produced. Consequently, the Hadronic Gas phase has to be long lived to enable an equilibration of strangeness.
1.5.2. Strangeness Production in a Quark Gluon Plasma
For almost 25 years, it has been expected that the production of strange particles in a QGP phase would be enhanced with respect to a Hadron Gas [14, 16]. Strangeness is a good quantum number because it is conserved in strong interactions. Strange quarks (and therefore strange hadrons) decay via the weak interaction, where decay lifetimes of 10−10 s are typical and so these decays are not important on the time scale of a hadronizing QGP.
The production mechanisms for strange quarks in a QGP are different from a Hadronic Gas. They are produced due to gluon fusion (g + g → ss), as well as the annihilation of light q q pairs (q q → ss) which are shown in Figure 1.7. As the plasma is expected to be initially gluon rich, and the equilibration of quarks takes time compared to the gluon equilibration time, the gluonic chan- nels contribute more than 80 % to the total production rate of strange quarks.
The threshold energy required to create a pair of ss quarks in the QGP is just the bare mass of the two strange quarks (Ethresh ≈ 2ms ≈ 300 MeV). This means that due to the high temperatures involved in the QGP phase, the thermal production of ss pairs is possible. A further source of enhancement of ss pairs comes from the process of Pauli blocking of the light quarks. As all quarks are fermions, they obey the Pauli Exclusion Principle which states that no two fermions can be in the same quantum mechanical state. Therefore, as more and more light quarks are produced in the collision, they fill up the available energy levels and it becomes energetically favourable to create ss pairs. It is expected that the extra mechanisms for ss production in a QGP should lead to a production rate which is 10 to 30 times higher than in a Hadronic
1.5. Strangeness
Gas, and this should allow equlibration of strangeness even in the short lifetime of the fireball16.
It therefore follows that the production of anti-strange and multi-strange baryons at freeze-out will be enhanced if the system passes through a deconfined phase, than if it remains in the Hadronic Gas phase only.
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Figure 1.7.: Leading order QCD Feyman diagrams for ss production by gluon fusion and pairs of light quarks : a) gg → ss, b) qq → ss.
Even if an enhancement of strangeness occurs in a QGP, there are still dif- ficulties in quantifying the magnitude of this enhancement. As the lifetime of the QGP phase (or even the fireball in general) is unknown, it is impos- sible to compute the actual values of particle production in the two different scenarios. An enhancement is expected to occur ordinarily in A+A collisions compared to scaled p+p collisions, as strangeness will be produced in the sec- ondary collisions indicated in equations 1.9 − 1.12. Another useful way to study strangeness enhancement is by using the ratio of strange quark pairs with re- spect to the produced non-strange quark pairs before resonance decays, the so-called strangeness suppression factor17 defined as:
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This ratio is strongly dominated by the most abundant strange and non-strange particles, kaons and pions. Kaons carry most of the produced (anti-) strangeness,
the ratio K +K tion:
/〈π〉 is often used to quantify relative strangeness produc-
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An increase in the K +K
/〈π〉 ratio in A+A collisions compared to p+p or
p+A collisions could then indicate an increase in the production of strangeness. The K+/π+ ratio is often used as a measurement of strangeness enhancement rather than the K +K /〈π〉 ratio. The reason is that K+ carry about 50% of all s-quarks independent of the energy.
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Figure 1.8.: The dependence of the K/π ratio, defined as the sum of the total kaon multiplicity (K+, K−, 2K0 s)dividedbyallpions(π+,π+, π0 ), on the number of participant nucleons at 158 AGeV.
The first possibility to compare the above expectations with the data was in 1988 when the preliminary results from sulfur and silicon beams at SPS and AGS became available. The NA35 experiment reported [18, 19] that in central S+S collisions at 200 AGeV the kaon to pion ratio is approximately two times higher than in N+N interactions at the same energy per nucleon (see Figure 1.8). The results for 〈K +K〉/〈π〉 is obtained by using the pion multiplicities measured in the same data sample20 and are not just compared to S+S but also to S+Ag21, N+N and p+A data [22, 23].
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Figure 1.9.: The double ratio 〈K+〉/〈π+〉 from central Pb+Pb and Au+Au re- actions divided by 〈K+〉/〈π+〉 from p+p reactions as a function of the initially available energy. The errors include statistical and a 15% uncertainty in the parametrization of the 〈K+〉/〈π+ 〉 from p+p reactions.
A suppression with respect to p+p interactions is observed in p+A collisions. An enhancement is observed going to S+S collisions. No further enhance- ment is visible going from S+Ag to Pb+Pb collisions. An even larger en- hancement was measured by the E802 collaboration24. Recent data on central Pb+Pb/Au+Au collisions from low AGS to RHIC25 −31 ener- gies complete this picture. Figure 1.9 shows the 〈K+〉/〈π+〉 ratio measured in Pb+Pb/Au+Au collisions divided by the corresponding ratio in p+p inter- actions [32, 33]. It is visible that a strangeness enhancement is observed at all energies and the enhancement is even stronger at lower AGS energies than at RHIC energies. Thus an interpretation following the original concept that strangeness enhancement is a signature for the QGP14 −16 is questionable. At low AGS energies due to lower energy density formation of a QGP is not expected and therefore no strangeness enhancement should be observed. Quite contrary a larger strangeness enhancement is seen at AGS energies than at RHIC energies. Therefore one can conclude that the concept of strangeness en- hancement as a signal of QGP is incorrect34. It is argued that the strangeness production mechanism in p+p is different than in A+A. Thus it was suggested in35 to analyze the energy dependence of strangeness to pion ratio in A+A collisions. Furthermore the model predicts a transition to a QGP between AGS and SPS energies to be indicated by a ”horn” like structure in strangeness to entropy ratio (see Figure 1.10). The model predicts energy dependence of total strangeness and entropy production but gives no specific predictions concerning production of identified hadrons, e.g. Ξ hyperons considered in this thesis.
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Figure 1.10.: Energy dependence of full phase space 〈K+〉/〈π+〉 ratio in central Pb+Pb and Au+Au collisions from AGS to RHIC energies25 − 31. The data for p+p interactions are shown by open circles for comparison [32, 33].
This prediction motivated the energy scan program of NA49. The experiment registered central Pb+Pb collisions at 20, 30, 40, 80 and 158 AGeV, semi-central Si+Si collisions at 158 AGeV and minimum bias Pb+Pb collisions at 40 and 158 AGeV. In this work the energy and system size dependence of Ξ− andΞ+ production is studied.
2. The NA49 Experiment at CERN SPS
The measurements described in this thesis are part of the experimental program of the NA49 collaboration. The NA49 experiment is located in the North Area of the European Center for Nuclear Reasearch (CERN) at the H2-Beamline. Figure 2.1 illustrates the layout of the CERN accelerator complex. Since 1994 it has been possible to accelerate lead ions with a momentum of 158 GeV per nucleon. Ions are first produced by an Electron Cyclotron Resonance (ECR) source and separated with a spectrometer. Then Pb25 + ions are accelerated with a Radio Frequency Quadrupole (RFQ) and Linear Accelerator (LINAC). The ions are then stripped to the Pb53 + state and enter the Proton Synchrotron Booster ring (Booster). After being accelerated to 94 MeV per nucleon, the ions are injected into the Proton Synchrotron (PS). Following a further acceleration, the ions are injected into the Super Proton Synchrotron (SPS) via a second stripper foil. In the SPS, fully stripped Pb82 + ions are accelerated to their final energy37. With the current configuration it is just possible to accelerate (anti-)protons and lead ions. The study of silicon+silicon reactions is possible through the generation of a secondary fragmentation beam which is produced by a primary target (1 cm carbon) in the extracted lead-beam. With the proper setting of the beam line magnets a large fraction of all Z/A = 1/2 fragments at ≈ 158 AGeV are transported to the NA49 experiment.
For central lead+lead interactions at top SPS energies (158 GeV per nucleon) about 1600 charged particles have to be detected to study heavy ion collisions. It is desirable to measure as many as possible of the produced particles, and extract the maximum information of the collision. With this assumption, a dectector has to be designed with a large acceptance, good momentum reso- lution, good two-track resolution and particle identification. This condition is fullfield in NA49 with four Time Projection Chambers (see section 2.1) as pri- mary detectors for charged particles, Time of Flight walls and two Calorimeters. NA49 can be operated with different target configurations (lead-, carbon- and siliconfoil, liquid hydrogen) to analyze a multitude of diverse collisions, from elementary hadron-hadron colllisions over hadron-nucleus to collisions of light nuclei to lead-lead collisions.
2. The NA49 Experiment at CERN SPS
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Figure 2.1.: Layout of the CERN accelerator complex.
2.1. The NA49 Detector Layout
The NA49 experiment36 is a large acceptance spectrometer for charged hadrons. In a central lead-lead collision 1600 charged particles are produced. Because of the high track density, a detector is needed with good space- and two track res- olution and a minimum of material in the acceptance in order to minimize the rate of secondary interactions and multiple scattering. Therefore Time Projec- tion Chambers (TPC) were selected, which are the main components in NA49. Figure 2.2 shows a detailed layout of the NA49 experimental apparatus.
The first two Vertex TPCs (VTPC-1 and VTPC-2) are located each in one su- perconductive dipole magnet (VTX-1 and VTX-2). At 158 AGeV the magnetic field is 1.5 Tesla for VTX-1 and 1.1 Tesla for VTX-2. The total bending power
for the magnets is 7.8 Tm for a length of 7 m. It is possible to operate the magnet in two polarizations (std ±). The job of the magnets is to expand the reaction cone to measure particle tracks in high track density reagions. It is possible to determine the momentum p of charged particles from the deflection in the magnetic field B38:
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where q is the charge of the particle, R the radius of curvature of the particle and λ the track angle in y-direction. The exact knowledge of the magnetic field is needed to determine the momenta and therefore two methods independent of each other have been used. On the one hand the magnetic field is calculated with the program TOSCA and on the other hand it is measured in 4 cm3 steps with a Hall probe39. The deviation between both methods is 0.5%.
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Figure 2.2.: Set-up of the NA49 experiment at the CERN SPS.
Dependent on particle topology the track momenta can be determined up to
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Downstream of VTPC-2 are two large volume Main TPCs (MTPC-L and MTPC-
R) positioned on either side of the beam in a field-free area. In the Main TPCs the particle identification is done via the specific energy loss dE/dx. The resolu- tion of the specific energy loss is in the range of 3−4%. Beyond the Main TPCs are the Time-of -Flight (TOF) walls. The TOF acceptance is at midrapidity and it supports the particle identification in the TPCs. The flight time measure- ment starts as soon as the projectile passes the Quartz Cerenkov-counter S1. The time between the start time and the end time defines the flight time, where the height of the signal is the dimension of the particle charge. The particle identification with the Time-of-Flight measurement is based on the relativistic
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It is now possible to determine the mass m of the particle from the flight time and the momentum p, which is determined in the TPC.
Two downstream calorimeters complete the setup. The opening of the Colli- mator (COLL) is adjusted such that beam particles, projectile fragments and spectator neutrons and protons can reach the Veto-Calorimeter (VCAL)36. The Veto-Calorimeter is 20 meters behind the target and after the Collimator. The Veto-Calorimeter, constructed originally for the NA5 experiment40, con- sists of lead scintillators and iron scintillators. The energy resolution can be
parametrized by : √
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Central collisions can be selected by discriminating the analog energy sum sig- nal. A typical threshold setting at Eveto ≤ 8 TeV corresponds to about 4 % of the Pb+Pb interaction cross section and an impact parameter below 3 fm.
A series of Beam P osition Detectors (BPD) an Cerenkov-counters are used for the data acquisition. The BPD is a two dimensional multi-wire proportional counter with a area of 3×3 cm2 giving x and y coordinates of the beam. Two orthogonal sense wire planes with a 2 mm pitch are sandwiched between three cathode planes. Each lead ion passing through the three BPDs can be projected to the target z position giving an independent measurement of the primary interaction vertex. The resulting precision of the beam position extrapolated to the target is 40 μm for Pb beams.
In order to select central lead-lead events and to trigger the read-out, a combina- tion of the signals of th Cerenkov-counters S1, S2′, S3 and the Veto-Calorimeter is used. It is possible to determine the charge of the beam particles with the Cerenkov-counters. Therefore the signals of S1 and S2 are used to select the lead-ions. The lead target is actually contained within the counter S3 and has a thickness of 207 μm and an interaction rate of about 1%. Cerenkov light is reflected towards a photomultiplier tube by a mylar strip with a thickness of 25 μm, which ensures that no more extra material is placed in the beamline than necessary. For lead-lead collisions the interaction in the target is selected with the S3 counter, which is switched in anti-coincidence with S1 and S2.
2.2. Time Projection Chambers
The majority of particle detection in NA49 is done with the four large volume TPCs. These devices combine technology of drift chambers and multi-wire proportional counters. The TPC is capable of recording the trajectory of charged particles in three dimensions.
A TPC consists of a gas filled box lain in an electric field (E) with one face chosen as the readout plane. The basic idea behind TPC operation is illus- trated in figure 2.3. A charged particle passing the gas box will interact with the gas causing it to be ionized. Electrons from this ionization drift (upwards) towards the readout plane under the influence of the field. The field is main- tained by a potential difference between the bottom of the TPC and a gating grid of wires near the cathode plane and this defines the drift region. Beyond the gating grid lies a series of sense wires held at a high voltage. When the drifting electrons pass the gating grid, they are rapidly accelerated towards the sense wires until they have sufficient energy to cause secondary ionization. If the accelerating potential is held constant, the amount of secondary ionization produced is proportional to the original number of drifting electrons. This is the principle behind the proportional counter.
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Figure 2.3.: Schematic layout of the TPC readout chambers.
When electrons from the secondary ionization reach the sense wires, the total charge can be read out. By providing several such wires along the top plane of a TPC, the location of the original ionization in the two dimensions orthogonal to the drift direction can be obtained. An alternative approach is to use a plane of pads situated just above the sense wires. Movement of the positive ions from the secondary ionisation induces charge on the pads which are then read out. In principle, covering the detection plane with rows of these pads gives position information in the two directions orthogonal to the drift direction. The location of the original ionization in the drift direction is obtained from the product of the drift time and drift velocity. Thus, determination of the original particle ionization in all three spatial dimensions is possible with a TPC.
2.2.1. The NA49 TPCs
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Table 2.1 shows the physical properties of the NA49 TPCs41. Both Main TPCs (MTPC) consist of 25 (5×5) sectors and the VTPCs consist of 6 (2×3) sectors as shown in figure 2.2. Generally, each MTPC sector is subdivided into 18 rows of 128 pads and is correspondingly classified as standard resolution (SR). However, the five sectors closest to the beamline are higher resolution (HR) sectors and contain 192 pads per padrow. Furthermore, all sectors in the VTPCs consist of 24 rows of 192 pads. Increased resolution is desirable close to the beamline because the track density is higher there. Both of the VTPCs are split into two equal halves on either side of the beamline, with a separation gap of 20 cm. This space is to avoid deposition of charge in the sensitive volume by the beam. This problem is also avoided with the MTPCs since they are situated on either side of the beamline. The choice of gas used in the TPCs is a critical design consideration. Both the velocity and diffusion of the drifting electrons depend on the mixture and pressure of the selected gas42. The chosen gas mixture is Ne/CO2 (90/10) for the VTPCs and Ar/CH4/CO2 (90/5/5) for the MTPCs. With the selected gas mixture the FWHM of the charge distribution can be limited to about 5 mm both in transverse and logitudinal drift direction
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Table 2.1.: Physical properties of the NA49 TPCs.
2.3. Event Reconstruction
During the production of data, which was carried out at CERN for the analysis described in this thesis, raw events are processed through the NA49 recon- struction chain which reconstructs each event. The reconstruction chain itself consists of a series of software packages which process this data performing a
2.3. Event Reconstruction
variety of different tasks, such as cluster finding, track finding and fitting, pri- mary vertex location,dEdx determination,TOFinformationandstrangeparticle reconstruction.
Before the first event of raw data is read in, other information is also loaded. These constants comprise the magnetic field maps, detector geometry informa- tion and program parameters which are used by the software packages in the production. Once completed, the reconstructed event is written to an output Data Summary Tape (DST). Typically three Mbytes of DST data are written per event. The information which is saved in the DSTs is important for the calculation of the track information, but too much for the analysis especially for the analysis of millions of events. Because of this reason, miniDSTs are used for the analysis, which implies the subset of all information that is really needed.
The miniDSTs are saved as ROOT-Trees [[43]]. ROOT [[44]] [[45]] is an object orientated analysis environment which is based on the programming language C++. Adapted classes to the detector are developed in NA49 to save event and track information [[43]]. These classes are used for the analysis in this thesis.
Details of the reconstruction chain are already discussed in different diploma and Ph.D. theses (e.g. [[46]]). Therefore just the important aspects of the re- construction, which are used for the analysis, will be discussed. In order to make the maximum use of the available infomation it is necessary to combine the data measured by the four local TPCs and treat the whole NA49 setup as one global detector system. The analysis software providing the unification of the detector system will thus be refered to as the Global Tracking Chain47.
This serves the approach to combine the superior momentum determination of the VTPCs+MTPCs (with a momentum resolution of dp/p2 = 0.3 × 10−4 (GeV/c)−1 ) with the excellent particle identification capabilities of the large volume MTPCs and it also facilitates the pattern recognition by extrapolating well separated tracks in one detector to the high track density region of another.
The NA49 global tracking is based on a strategy of data reduction by first trans- lating the hits in the detector into space points and then connecting these by pattern recognition algorithmus. The space points are generated by identifying continous regions of charge pixels above threshold, so called ”clusters”, which are then connected to ”tracks”. The algorithmus used are set up to search for tracks oncoming from the main vertex first, because they offer the best con- straints for momentum reconstruction and are thus easiest to find. Removing the easy and well defined tracks from the sample leaves a moderate multiplicity of special cases.
The MTPCs have a simple track model (straight-lines) which eases pattern recognition. Due to the absence of a magnetic field in the detector only tracks originating from the main vertex can be assigned a momentum that defines a unique trajectory. The VTPCs have a good momentum resolution (dp/p2 =
7.0 × 10−4 (GeV/c)−1 ) independent of the main vertex because of the direct
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Figure 2.4.: The NA49 reconstruction chain.
measurement of the track bending, but suffer from a high track density and a complex track model of a helix distorted by inhomogenities in the magnetic field. Figure 2.4 shows the NA49 reconstruction chain.
2.3. Event Reconstruction
2.3.1. V0 Reconstruction
Three neutral single strange hadrons (Λ,Λ and K0 s)canbestudiedatNA49. These particles are uncharged and therefore do not cause ionisation in the TPC gas themselves. Instead, they are recognized by their weak decay into two op- positely charged daughters in a characteristic ”∨” shape. They are collectively referred to as V0s. Table 1.2 shows the properties of the V0 candidates. The weakly decaying charged hyperons Σ+ and Σ− are not reconstructable due to the fact that only one daughter is charged. Neutral Σ0 hyperons decay elec- tromagnetically via Σ0 → Λ + γ and, because of the shorter time scale of the electromagnetic interaction, it is experimentally indistinguishable from the weakly decaying Λ hyperon. Consequently, measurements of Λ andΛ hyperons represent the summed contribution from Λ + Σ0 andΛ + Σ0 respectively.
2.3.2. V0 Finding
V0 candidates are found from particle tracks by taking each positively charged track in combination with each negative track and tracking them through the NA49 magnetic field. In the V0 finding software, v0f ind, particles are tracked from the first measured point in the TPC in the direction towards the target to the minimum allowed z position in steps of 2 cm. The separation of each positive-negative pair in x and y are compared at each z position and a mini- mum is found if one exists. At the minimum, the distance of closest approach (DCA) of the pair in x and y (dcax and dcay) is found. If the DCA is smaller than 0.5 cm in x and 0.25 cm in y, the pair are considered as a V0 candidate. For kinematic analysis of V0s, it is important to know the momentum of the daughter tracks, so v0f ind insists the global tracks has a minimum of 10 points in VT1 or 20 points in VT2.
The following, basically geometrical, V0 finding criteria are selected in such a way to find as many V0 candidates as possible but still reduce the combi- natorial background. The first geometrical criterion is the z position of the determined V0 vertex. This quantity has to be larger than -555 cm for all V0 candidates. If the crossing point of a track pair is before this point it will be rejected. It is also requested that the extrapolated daughter track has a min- imum distance in the target plane. The distance in y direction is larger than 0.75 cm. This cut makes sure that both tracks are not from the main vertex. The extrapolated track of the mother particle has to be in a certain range of the main vertex in x and y direction. Detailed descriptions about the φ angle, dip-cut and the armenteros criteria can be found here [48, 49]. Table 2.2 shows a summary of the used cuts in the V0 finder. These cuts are referred as the GSItype and are used for the further analysis.
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Table 2.2.: V0 cuts (for lead-lead-collisions) of the Λ hyperons.
2.3.3. V0 Fitting
Found V0 candidates are presently fitted geometrically with the client v0f it. Each V0 daughter track is associated with one extra point (the V0 decay ver- tex). From this additional constraint a better determination of the true V0 momentum is expected if the V0 candidate is really a decaying particle. V0s are fitted with a nine parameter Levenburgh-Marquardt fitting procedure50. The nine variables are the three coordinates of the decay vertex and three mo- mentum components from each of the two charged daughters.
2.3.4. Multi-Strange Hyperon Reconstruction
In addition to singlely strange V0s, there are multi-strange hyperons which can be reconstructed additionally in NA49. Properties of the doubly strange Ξ, triply strange Ωs and their antiparticles are shown in Table 1.2. It is not possible to measure the uncharged Ξ0. The π0 is uncharged and cannot be detected in the NA49 TPCs. Thus, only the charged Ξs in the decay modes shown in Table 1.2 can be considered. As an example, the topology of the decay process for the Ξ is illustrated in figure 2.5.
2.3.5. Ξ Finding
The Ξ reconstruction is performed with the program xi find and is based on locating the decay vertices in an analogous way to V0 finding (see subsec- tion 2.3.2). Here, V0 candidates are reconstruced first from global tracks and V0 vertices are obtained. Ξ candidates are found by taking suitable V0s in
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Figure 2.5.: Decay topology of the Ξ hyperon and definition of target and decay length which are applied in the analysis.
combination with charged tracks. From table 1.2, a charged Ξ will decay into Λ andΛ and a charged pion. The distance of every pion and V0 candidate in x- and y-direction will be compared at every z position to find the distance of closest approach (dcax, dcay). The two-dimensional separation is deduced in the plane orthogonal to the beam direction and consecutive steps are compared in the search for a minimum and hence a DCA. If a minimum is located and the x and y separation components are both less than 1 cm, the V0 and charged track are considered as a Ξ candidate.
The minimum number of reconstructed points, npoint, is applied to all three reconstructed tracks in either VTPC (see Fig. 2.6). If desired, three different npoint parameters can be applied to the separate daughter tracks, but for the current cuts used these values are kept the same.
A further cut is applied to select only those V0s which appear to be Λ orΛ particles. For Ξ candidates the V0 invariant mass under the Λ hypothesis (MΛ) must be in the range 1.101 ≤ MΛ ≤ 1.131 GeV/c2.
In the rest frame of the decaying parent particle, conservation of momentum dictates that the daughters are emitted back-to-back. For the case of a relativistic particle traveling through a TPC, the decay frame is not stationary in the laboratory frame and a transformation must be made between the two. Specifically, in the laboratory frame there will be a Lorentz boost in the direction given by the parents velocity just before decay.
Podolanski and Armenteros51 calculated the transverse momentum, pArmt as:
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Figure 2.6.: The number of reconstructed points distribution for the three dif- ferent daughter tracks in either VTPC.
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Figure 2.7.: The Armenteros-Podolanski plot for V0s candidates (left) and Ξ candidates (right) after V0 finder, Ξ finder and analysis cuts.
where a daughter with respect to the parent’s momentum vector and a variable is defined as:
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with the fractional difference of longitudinal momentum shared between the daughters. Here, p|| is the component of the daughter’s momentum along the original direction of the parent. Particle (1) is customarily chosen as the most
positively charged daughter. Plots of pArmt against α describe ellipses which are unique for different decaying systems. Figure 2.7 shows the ArmenterosPodolanski plot for V0s (left) and Ξ, Ω (right) after V0 finder, Ξ finder and analysis cuts. Table 2.3 summarize the used cuts in the Ξ finder.
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Table 2.3.: Ξ finder cuts (for lead-lead-collisions) of the Ξ hyperons.
3. Data Analysis
3.1. Data sets
To study the energy and system size dependence of the Ξ production, 5 different data sets in the beam energy range 20 − 158 AGeV were analyzed for the energy dependence in Pb+Pb collisions and two minimum bias Pb+Pb data sets with a beam energy of 40 and 158 AGeV. At 40 AGeV both polarities of the magnetic field are available. Besides Pb+Pb NA49 took also Si+Si collisions at 158 AGeV. The magnetic field configuration is denoted with std+, respectively std−, where std refers to the magnetic field at 158 AGeV. The corresponding number of wounded nucleons 〈NW〉 (see subsection 5.3.1) for the 7.2 % most central data set is 〈NW〉 = 349. For the 23.5 % most central data set 〈NW〉 is 262, whereas the 10% selection has a 〈NW〉 of 335. For the semi-central Si+Si data set 〈NW 〉 is 37. The system, number of events, the magnetic field configuration, the centrality and the production key for the different data sets are shown in Table 3.1.
System Beam Energy Magnetic Field σ/σtot (%) Nevt Prod. Key
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Table 3.1.: Data sets on nucleus-nucleus collisions used for this thesis.
h) baryons formed
respectively by a quark-antiquark (q q) pair or three quarks (qqq). Some of the family of baryons that form the (spinparity) Jπ =1 + octet, the Jπ = 0− nonet and the Jπ =3 + decuplet are illustrated in Figure 1.2. The 3rd component of isospin, I3, is assigned to light quarks (u =12,d=-2 )andSisthestrangeness of the hadron. Any baryon with non-zero strangeness, is generically referred to as a hyperon. The two hyperons with S = -1, I3 = 0 in Figure 1.2a are different because the ud pair is in a spin 0 state for the Λ, but is in spin 1 state for the Σ0. Properties of some of the strange hadrons encountered in this thesis are given in Table 1.2. Strange quarks decay via the weak interaction in which quark flavor is not conserved. Also given in the table are the principle decay channels and branching ratio for decaying strange hadrons, along with the mean lifetime, c. Lifetimes are often given as cτ in units of cm. All values are taken from the particle data book5.
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