selection variable value TPC PID signal required
TPC Nσ(e) ≤4.0
TPCNσ(e),p <0.4 GeV/c ≤3.0
TPCNσ(π) ≥1.0
TPCNσ(K) ≥1.0
TPC Nσ(p) ≥1.0
TOF PID signal if present
TOF Nσ(e) ≤3.0
Table 7.1: PID selection criteria for the photon conversion candidate daughters applied on the analysis level.
dEdx(neg)
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dEdx(neg) vs dEdx(pos)
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pos. daug. dE/dx (a.u.)
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after PID dEdx(neg) vs dEdx(pos)after analysis level PID
neg. daug. dE/dx (a.u.)
pos. daug. dE/dx (a.u.)
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!
!
A
!
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Figure 7.1: Effect of the imposed PID on the conversion candidate sample visualized as the correlation between the dE/dxof the positive photon candidate daughter vs. the one of the negative daughter before (left) and after (right) the criteria listed in Table 7.1 were applied. All momenta are shown here, the electrons are ultra-relativistic and have a constant energy loss dE/dx, independent of momentum. The electron inclusion criterion of TPC Nσ(e)≤4.0 does not lead to a sharp cut-off in the right panel since the Nσ variable also takes into account the precision of the dE/dxmeasurement for each track independently.
7.2 EMCal Photon Candidate Selection
7.2.1 Charged Particle Veto
Utilizing a Charged Particle Veto (CPV) detector located in front of an electromagnetic calorimeter has a long tradition in heavy-ion physics and was, e. g., applied by WA98 experiment at the SPS [363] and STAR [364] and particularly PHENIX at RHIC [365]. In ALICE, the so far largest CPV detector for a dedicated heavy-ion experiment was built, namely the TPC. Fig. 7.2
(left) shows for each calorimeter cluster the distance in (η, ϕ) to the closest charged track extrapolated from the TPC. The histogram is well described by a two-dimensional Gaussian fit, which for this particular pT selection yields a width which is applied both in ∆η and
∆ϕ of σ = 0.0088±1×10−5. Fig. 7.2 (right) shows the distribution of the distance inη of the cluster to the nearest track as a function of pT in the colored histogram. Apparent is a reduction in statistics for the bin 0.0≤pT (GeV/c)<0.5. Primary tracks need a minimum pT,min = 0.675 GeV/cto not curl up before hitting the EMCal surface at a radius R= 4.5 m.
Therefore, tracks withpT <0.5 GeV/c that reach the detector must be secondary and must stem from a decay vertex considerably far away from the primary interaction point. Also shown is the width of the aforementioned two-dimensional Gaussian as a black graph and a functional fit of the form f(pT) =a+b/pT to the graph in the white, dashed line; theχ2 minimization gives as parameters a= 3.3×10−3 andb= 5.9×10−3. Rejecting clusters for which the nearest charged track extrapolation falls below this simple pT-dependent parametrization constitutes a simple and effective procedure for a charged particle veto.
counts
0 200 400 600 800 1000
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∆
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counts
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) c (GeV/
pT
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Figure 7.2: Track cluster matching in the ALICE calorimeters. Left: (∆η,∆ϕ) of the cluster in the calorimeter to its nearest charged track extrapolation from the TPC for 0.5≤pT (GeV/c)<1.0 together with a two-dimensional Gaussian fit. Right: ∆η of the calorimeter cluster to its nearest TPC track extrapolation as a function ofpT in the colored histogram. Also shown is the width in ∆η of the two-dimensional Gaussian fit of the left panel as a black graph together with a functional fit to the graph with f(pT) =a+b/pT in the white, dashed line.
7.2.2 Shower Shape Analysis
The left panel of Fig. 7.3 shows the two-dimensional, transverse and vertical, profile of an air shower of a 1 TeV gamma ray and a 1 TeV nucleon. The most prominent feature is the much narrower energy distribution in the electromagnetic shower of the hard photon. The energy loss of the photon cascade is dominated by pair creation γ →e+e− and bremsstrahlung e→e+γ.
7.2 EMCal Photon Candidate Selection 147
Both of these processes do not produce particles with a significant amount of transverse momentum. The physics processes of hadronic shower are much richer, they can however be roughly grouped into two classes. The first category consists of production of energetic secondary hadrons, which typically carry a fair fraction of the primary particles momentum. The second kind of processes are interactions with the traversed material like excitation, evaporation, spallation, et cetera, see the review article on calorimetry by C.W. Fabjan and F. Gianotti [366].
A 1 TeV proton, as it is depicted in Fig. 7.3 (left), typically stems from a galactic source [367].
The mean transverse momentum in a collision of such a 1 TeV proton with a hydrogen nucleus at rest in the atmosphere is considerably large. The center of mass energy for such a collision is √
s= q
2m2p+ 2Epmp = 43.3 GeV which corresponds to the energy range probed by the pioneering measurements at the CERN Intersecting Storage Rings (ISR). It was at the ISR where the mean transverse momentum in such hadronic collisions was quantified to be about 0.35 GeV/c [368, 369]. In contrast, the average transverse momentum in the electromagnetic pair-creation and bremsstrahlung processes is only on the order of the electron mass [370]. Thus, the transverse shower profile is a potent discriminator between electromagnetic and hadronic showers.
M20
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
M02
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
/ allγ
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
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Figure 7.3: Left: Air shower for a gamma ray and a nucleon, both of 1 TeV. The energy of the gamma is dissociated in a much narrower area than for the nucleon.
Taken from [371]. Right: Ratio of the number ofγ over all particles as a function of the shower shape parameters M0,2 andM2,0, see Eq. 7.1, from a Monte-Carlo simulation including the full detector response. We see the precedence of the photons for small M0,2.
Let us denote byM0,2 andM2,0 the second moments along the major and minor axis of the
shower ellipse which shall be perpendicular to the particle’s propagation [372]:
Mp,q = Z +∞
−∞
Z +∞
−∞
upvqf(u, v) dudv, (7.1)
here urepresents the coordinate along the minor axis,v follows the major axis,pandqtake the values 0 and 2, andf(u, v) is the distribution of energy within the cluster.1 The particles from a hadronic shower are generally less abundant but more energetic and carry more transverse momentum when compared to an electromagnetic shower, as discussed before. Thus, it is expected that the second moment of the principal axis is large for a hadronic shower but small for an electromagnetic shower. This presumption is certified by the results of a Monte Carlo simulation of Pb-Pb events including the full detector response, presented in Fig. 7.3 (right). We see that the ratio of γ over all mother particles generating the shower, i. e. the purity, is augmented for small values ofM0,2. A detailed inspection reveals that the significance ζ = √S
S+B is maximized by the requirement M0,2 ≤0.44. The typical purity of the photon candidate sample in this selected region is about 60–100%. We recognize the dependence of the photon purity in Fig. 7.3 (right) on M2,0 and note that a more elaborate selection which includes both moments like a weighted sum or a weighted sum of squares of the two moments appears to be a more favorable selection criterion for future studies.
7.2.3 Energy Calibration of the ALICE EMCal
Within the ALICE software, the so called EMCal tender allows to utilize an energy response function which was determined from an electron test-beam campaign. The deviation from a simple linear correspondance between the measured Analogue to Digital Counts (ADCs) and the energy of the incident electron of the test beam is shown in full black dots in Fig. 7.4 (left);
the open circles represent the deviation from a cubic parametrization. We note the depression of the full symbols below unity for energies smaller or equal 10 GeV. For the given granularity of the data, i. e. the two data points at 5 and 10 GeV, the cubic energy response function allows to correct for the energy inefficieny attributed to threshold effects and possible light-transmission losses [256].
With the cubic energy response function applied, Fig. 7.4 (right) shows the mean of Gaussian fits to the peaks in the two photon-candidate invariant mass spectrum vs. the mean cluster energy of the photon candidates in highly symmetric decays where the energy difference of the two photon candidates was less than 10% for the investigated Pb-Pb collision data sample.
The full red dots signify that a π0 peak was doubtlessly identified; the open circles give the result of the fit, however due to the particular shape of the invariant mass distributions and a bad signal to background ratio it is not given with certainty that the values represent the
1Within ALICE,M0,2 is also denoted withλ20 andM2,0 withλ21. A technical implementation can be found in, e. g., [274].
7.2 EMCal Photon Candidate Selection 149
position of peaks fromπ0. If the test-beam response function covered all systematic effects, the mass of theπ0 should correctly show up at the value given by the particle data group of 134.98 MeV/c2. Unfortunately, we see that the π0 mass is systematically underestimated.
)/2 (GeV) Ecl2 cl1+ (E
0 1 2 3 4 5 6 7 8
)2c (GeV/0πm
0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14
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π0 certain
π0 speculative cubic splines log fit PDG mass
Figure 7.4: Left: Deviation from a linear correspondance between the reconstructed energy and the incident energy of the electron beam in an EMCal test-beam campaign in full black circles and deviation of the reconstructed energy from a cubic energy response function in open symbols. Taken from [256]. Right: Reconstructed mass of the neutral pion as a function of the mean cluster energy in highly symmetric decays into two photon candidates. The PDG mass of 134.98 MeV/c2 is underestimated over the full dynamic range. Compare to the very similar dependence obtained in [373] for pp and p-Pb collisions.
A remedy is to apply a non-linearity correction, i. e. to simply multiply the reconstructed cluster energy by an additional correction factor. Since Fig. 7.4 (right) shows only highly sym-metric decays, this correction factor is the ratio of the PDG mass over the shown reconstructed π0 mass. In order to take into account the finite binning, the spline fit (shown in the right panel of Fig. 7.4 as a black line) is used for cluster energies from 0.8 GeV/c2 and above. Below, the spline is smoothly connected to the log fit (shown as a blue line in the figure). The spline was chosen over any other function since it does not bias the correction factor to follow a particular functional shape. Additionally, the spline is easily handleable in the fitting procedure.
A log-like (or similarily shaped) decrease in theπ0 mass with decreasingpT was observed in a dedicated study of the EMCal energy response in pp and p-Pb collisions [373]. Clearly, the ad hoc energy calibration of the EMCal performed here can only be an intermediate solution and should be replaced by a centrally organized calibration of the detector.