Kinetic freeze-out forms a frontier for momenta that cannot be looked past with strongly interacting probes. Only model comparisons let us indirectly infer properties of the deconfined phase. We are stuck with the paradox that we can study the strong interactions only after they have ceased. A salvation can be found in studying probes that do not interact strongly like leptons or photons. The solution to go back to the beginning of femtoscopy and study correlations of photons, like Hanbury Twiss and Brown did, is at hand. As the thermal emission rate in a thermodynamical equilibrium is proportional to the fourth power of the temperature, the hope exists that a photon-photon correlation study can provide an image of the fireball at earlier times than it is accessible with hadronic probes. Fig. 2.13 shows the photon yield as obtained from theory in [198] as a function of transverse energy for RHIC and LHC energies.
One sees that in both cases, photons from the late, confined phase are most copious at low
2.7 Photon Sources 39
Figure 2.12: Left: One-dimensional radius parameters obtained from two-particle correlations of pions, neutral and charged kaons, and protons shown as a function of transverse mass [195, 196]. Right: Final state eccentricity from azimuthally sensitive ππ HBT as a function of energy. Taken from [197].
transverse energies less or equal 1 GeV. For higher photon energies, thermal radiation from the QGP phase is most abundant; at the LHC to more than 5 GeV, at RHIC up to about 3 GeV, where at RHIC hard, primordial γ rays are presiding. This means a sweet spot at RHIC for studying the deconfined medium between 1 to 3 GeV transverse photon energy and a broad range from 1 to more than 5 GeV at the LHC.
Two observations regarding photons are not easily understood theoretically and were consequently dubbed the photon puzzle. The PHENIX collaboration measured the direct photon yield and extracted an inverse slope parameter of the transverse momentum spectrum in central Au-Au collisions ofT = 221±19 (stat.)±19 (syst.) MeV [199]. This inverse slope parameter can be interpreted as an effective temperature, since it is a time-integrated observable.
Compared to the critical temperature of deconfinement of about 160 MeV, the inverse slope points to rather early production of the photons. Contrarily, the measurement of the direct photon elliptic flow [200], which yields values comparable to the flow of hadrons, suggests a late production. Although recently the evaluation of systematic uncertainties was criticized [201], the ALICE collaboration qualitatively sees the same patterns of a high effective temperature of T = 304±51 (syst.+ stat.) MeV [202] andv2 consistent with the one of hadrons [203].
An explanation for this puzzle could be that the photons are emitted at a later stage and the effective temperature has a significant contribution from flow [204]. In Fig. 2.14 this possible blue shift by radial flow for photons is displayed. The calculations show that the temperature of the medium drops rapidly as a function of proper timeτ and that a temperature ofT = 221 MeV at RHIC exists only as early as τ .1 fm/c and similarly at the LHC T = 304 fm/c is only reached even earlier. The experimental slope however corresponds to the effective temperature, which carries a large imprint from the expansion. To be consistent with the experimental
Figure 2.13: Photon yields from different sources as a function of transverse energy of the photon for central collisions of Au-Au at RHIC (left) and Pb-Pb at the LHC (right).
For RHIC one sees that up to a transverse energy of about 1 GeV, the contribution from the late hadron gas is dominant. In an intermediate range from 1 to 3 GeV, the thermal photons from the QGP prevail; for higher energies the direct photons from initial, hard pQCD processes are governing the total spectrum. At the full LHC energy of √sNN= 5.5 TeV, the majority of photons comes from hadronic sources up to about 1 GeV, but the reign of thermal photons is much extended towards higher transverse energies as compared to RHIC of more than 5 GeV. Taken from [198].
inverse-slope measurements, the photons in the model could be instantaneously ejected as late asτ = 10 fm/cboth at RHIC and the LHC.
The problem however is that models do not show such a late production and subsequently fail to describe the v2 and/or do not yield enough photons to reproduce the pT spectra. Fig. 2.15 evidences the deviation between data and an exemplary calculation [205]; various other models fail to reproduce the photon data as well [206–208]. An HBT measurement of photons could unveil the origin of these gauge bosons, resolving the puzzle. Such a measurement was already carried out successfully by the WA98 Collaboration [209] at the SPS, presented in Fig. 2.16.
Within the study, both photons were reconstructed with the electromagnetic calorimeter of WA98. While the data forQinv.20 MeV/c were found to be affected by detector resolution effects, the excess seen for intermediate relative momenta up to Qinv.90 MeV/c was observed to be stable against all variations of the selection criteria. It was thus attributed to the quantum statistical correlation of primary photons. The hope for such a measurement with ALICE at the LHC would be to extract a radius of the photon source. A large radius would then reveal a late hadronic production mechanism of the photon excess and a small size prove the early photon genesis.
2.7 Photon Sources 41
Figure 2.14: Blue shift of photons at RHIC (left) and LHC (right) in a hydrodynamic calculation [204]. Shown is the average temperature as a blue line and the apparent, effective temperature, i. e. the inverse slope parameter of the photon pT spectrum, without viscous corrections as white dots and including viscous effects as red dots together with the experimental, integrated value as green line. We see that although the temperature drops monotonically with proper time τ, the effective temperature stalls for 2.τ (fm/c).8. The temperature agrees in numbers with the experimental inverse slope for proper times of ∼1 fm/c, but the effective temperature is still consistent as late as τ ≈10 fm/c. Taken from [204].
Figure 2.15: Elliptic flow of direct photons as a function of transverse momentum as measured by PHENIX [200] at RHIC (left) and ALICE [203] at the LHC (right) compared to a hydrodynamical, event-by-event calculation [205]. The discrepancy, called the photon puzzle, is obvious. Taken from [205].
Figure 2.16: γγ correlation measurement by WA98 [209].
Chapter 3
ALICE at the LHC
TPC TRD EMCAL
TOF
PHOS
ITS
Muon Trigger Muon Filter
Absorber Solenoid
Dipole
Muon Tracking
Figure 3.1: Setup of A Large Ion Collider Experiment
ALICE — A Large Ion Collider Experiment — is located at the second interaction point (Point 2) of the Large Hadron Collider (LHC). The ALICE setup [99] is shown in Fig. 3.1.
The LHC was built into the existing tunnel of the Large Electron Positron Collider (LEP), 43
and ALICE inherited its main magnet from the LEP L3 experiment, which was located at the same interaction point as ALICE now is. The magnet was modified for ALICE to improve the uniformity of the magnetic field by adding plugs to the octagonal shaped opening of the yokes of the magnet [210]. It is one of the largest non-super-conducting magnets. The magnetic field of 0.5 T is at the upper limit of the 6000 A current which the magnet can hold. While for low-pT observables a lower magnetic field of∼0.2 T would be desirable [114], the strong field gives better resolution for high-pT observables which generally have low statistics. The interaction point is surrounded by a beam pipe. Its outer diameter amounts to 60 mm; it is 800µm thin.
A significant part of ALICE consists of the muon arm depicted on the right hand side of Fig. 3.1. However, the studies performed within this thesis do not comprise any analysis of muons. The muon setup is therefore not covered here; for details see e. g. [211, 212].
3.1 Coordinate Systems
The global ALICE coordinate system is a right-handed and Cartesian one with the origin x =y =z= 0 at the nominal interaction point. The z axis follows the beam direction, the muon arm is at negative z. The x axis is aligned horizontally, perpendicular to thez axis and points towards the center of the LHC ring. The y axis is perpendicular to the other two and points upwards. The azimuthal angle ϕis zero at the positivex axis and increases from there towards the positive y axis. The polar angle θis zero at the positive z axis,π/2 in the (x, y) plane and π at the negativez axis [213]. Within the ALICE software, coordinate values are usually in cm. Unless specified differently, the global coordinate system is used. Especially for tracking the particles through the detectors, a local coordinate system exits. It is also Cartesian and right-handed, and even the z axis agrees with the global coordinate system, but the local system is rotated around the z axis by an angleα with respect to the global system.
The definition ofα changes with the radius r=x2+y2. For r <45 cm, i. e. within the ITS, the rotation is such that thex axis points in the direction of the projection of the momentum vector of the particle on the transverse plane. For r≥45 cm, the azimuth is segmented 18-fold with the zeroth segment starting at ϕ= 0. Here the rotation α is the angle of the center of the segment in which the point (x, y, z) lies. The segments correspond to the azimuthal TPC sectors and TRD supermodules. This brings the advantage that all azimuthal TPC sectors and TRD supermodules have the same coordinates in the local coordinate system, simplifying the tracking codes.