3. Measurement of transverse momentum spectra 57
3.7. Track-level corrections
3.7.1. Tracking Efficiency
The correction for tracking efficiency is based on Monte Carlo information from simulated data using the full chain of Monte Carlo Event Generators (PYTHIA, HIJING, DPMJET) together with the detector simulation (based on GEANT) and the same reconstruction algorithms that are used for real data.
Within the acceptance defined by the kinematic range (usually0≤ φ <2π, η
<0.8and pT >0.15 GeV/c) the overall efficiency accounts also for acceptance limitations. These can result from dead areas in the SPD and occur also at the edges of the TPC readout chambers.
In this thesis the termtracking efficiencyalways refers to this overall efficiency.
78 3. Measurement of transverse momentum spectra
The tracking efficiency " and corresponding multiplicative correction factor ceff is obtained from simulations using all triggered events passing the event selection criteria. It depends on the kinematic variablespT, pseudorapidityη, z-position of the primary vertexVz and multiplic-ity classM and is calculated as the ratio of reconstructed primary tracks to generated primary particles:
" pT,η,Vz,M
= 1
ceff pT,η,Vz,M = Nprim,recMC pTMC,ηMC,VzMC,M
Nprim,genMC pMCT ,ηMC,VzMC,M (3.4) The corrections are calculated using histograms that are filled for all generated tracks (avail-able through the particle stack) and in addition for tracks that have been reconstructed. All correction matrices are obtained using the true track parameters (pTMC,ηMC) from the simula-tion. When the correction is applied to the data the reconstructed track parameters (pT,η) are used. In principal one could use the MC truth track parameters for the generated primaries and the measured parameters for the reconstructed primaries. Using this approach a combined effective correction for efficiency and resolution effects is obtained. The usage of the true track parameters, as it was done for this analysis, allows for a separate treatment of efficiency and momentum resolution effects. This is required since thepTresolution is not properly modeled in the simulations and an effective correction depends also on the shape (steepness) of the spectrum, which is not well described by the MC generators used.
Multiplicity classes are defined in the same way in data and simulations. Not all of the variables in equation 3.4 need to be kept for the corrections. Even though efficiency itself is also strongly φ-dependent, the fact that (averaged over many events) data and simulations have the same φ-distribution of tracks (which is of course flat) allows to average over φ. The same can be done for all variables whose distributions are either well described in simulations or for which the efficiency is constant. This is the case for the dependence of the efficiency onVz where the simulations take the measuredVz-distribution as an input.
For pp and p–Pb no dependence of the efficiency on multiplicity was observed and an ef-ficiency averaged over all M, and depending only on pT and η has been used. For Pb–Pb efficiency corrections were evaluated in centrality intervals, which are chosen to have similar track multiplicities as the corresponding intervals in data.
As mentioned before the tracking efficiency depends also on the particle type under consider-ation. Figure 3.15 shows the pT dependence of the tracking efficiency for different particles exemplary for pp withp
s=7TeV. PYTHIA6 and PHOJET have been used as event generators.
Different low momentum cut-offs (increasing with particle mass) for pion, kaons and protons are visible, while at large momenta the efficiency is universal. The different pT dependence of the kaon efficiency is a consequence of the decay probability (see also Figure 3.2). For the most frequently produces particles (π, K,p) the simulated efficiencies do not depend on the employed event generator. For electrons, muons and strange baryons, labeled “other” in the plot, the difference between the generators is the result of varying relative production yields of these particles.
The overall efficiency for primary charged particles is the weighted average of the individual particle-type efficiencies weighted with their abundances. Except for the lowerpTbin, where it
3.7. Track-level corrections 79
(GeV/c) pT
10-1 1 10
tracking efficiency
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
| < 0.8 = 7 TeV, |η s MC, pp, PHYTIA π p K other
PHOJET π p K other
Figure 3.15.: Tracking efficiency for different primary charged particle species obtained from simulations of pp collisions atp
s=7TeV.
reaches only≈40%, the tracking efficiency is generally in the range55−80% for all energies and collisions systems.
The pT-dependence of the tracking efficiency is shown in Figure 3.16 for pp collisions at the three energies. Efficiencies at 0.9 TeV and 7 TeV (2010 data) are very similar, while it is strikingly smaller for 2.76 TeV (2011 data). This is a result of the increased dead area of the SPD detector after the first heavy ion run. As the statistics available in the minimum bias simulations is limited at highpT and no strong pT dependence of the efficiency is seen above 4GeV/c, a constant efficiency is assumed forpT > 4GeV/c.
The centrality andpTdependence of the overall tracking efficiency in Pb-Pb collisions is shown in Figure 3.17, there are only minor differences the different centrality classes. Figure 3.18 shows the ratio of the tracking efficiency in a given centrality interval to the average (minimum bias) efficiency. Efficiency variations for the different centralities are within±2% and exhibit only a marginalpT dependence.
Similarly, Figure 3.19 visualizes the efficiencies obtained for p–Pb collisions in the different pseudorapidity intervals using the MC samples corresponding to the 2012 data. They are significantly larger as in the preceding pp and Pb–Pb data thanks to the increased active area of the SPD after a repair of the cooling system performed in the winter shutdown beginning of 2012.
For the study of the multiplicity dependence of the average transverse momentum (see sec-tion 5), which used the p–Pb data collected in 2013, the tracking efficiency was estimated based on the measured fractions of pions, protons and kaon [161]. The tracking efficiencies
80 3. Measurement of transverse momentum spectra
(GeV/c) pT
10-1 1 10
tracking efficiency
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
| < 0.8 MC, pp, |η PHYTIA Perugia0
= 0.9 TeV s
= 2.76 TeV s
= 7 TeV s
Figure 3.16.:pT dependence of the tracking efficiency for primary particles as obtained from simulations of pp collisions at the various energies. The assigned averaged effi-ciencies for pT >4 GeV/c that are used for the corrections are overlayed with the ones higher granularity pT bins as used for the spectra.
for single particles are still based on simulations, but the measurement has been incorporated using a re-weighting procedure for the tracking efficiency:
"ch(pT) ="otherMC (pT)·nMCother(pT)
nMCall(pT) +nMCπ+K+p nMCall
X
i=π,K,p
"iMC(pT)·nmeasuredi (pT)
nmeasuredπ+K+p (pT) (3.5) Here"denotes the efficiency, that is always obtained from simulations, and the particle abun-dances are denoted by n. The sum (for the efficiency the weighted average) of primary par-ticles that are not pion, kaons or proton are labeledother. The efficiencies in Equation (3.5) are only functions ofpT. For the dependence onηthe shape obtained from MC simulations is used.
The measurement of identified particles [161] reports d2N/(d y d pT) for the rapidity range 0< y <0.5. For the use in Equation (3.5) the measured d2N/(d y d pT)was fitted by a blast-wave [75] inspired function and converted tod2N/(dηd pT). The effect of the difference in the acceptance (0 < y < 0.5 vs. |ηcms| < 0.3) has been neglected and the particle ratios were assumed to be equal in these two kinematic ranges. Outside thepT range covered by the measurement, the particle fractions are assumed to remain constant. The relative difference between the pure MC efficiency and the re-weighted one turned out to be up to 2% at low pT and drops below 0.5% forpT>3GeV/c.
3.7. Track-level corrections 81
efficiency
0.3 0.4 0.5 0.6 0.7 0.8
0-5%
efficiency
0.3 0.4 0.5 0.6 0.7 0.8
20-30%
(GeV/c) pT
10-1 1 10
efficiency
0.3 0.4 0.5 0.6 0.7 0.8
50-60%
0.3 0.4 0.5 0.6 0.7 0.8
5-10%
0.3 0.4 0.5 0.6 0.7 0.8
30-40%
(GeV/c) pT
10-1 1 10
0.3 0.4 0.5 0.6 0.7 0.8
60-70%
0.3 0.4 0.5 0.6 0.7 0.8
10-20%
0.3 0.4 0.5 0.6 0.7 0.8
40-50%
(GeV/c) pT
10-1 1 10
0.3 0.4 0.5 0.6 0.7 0.8
70-80%
Figure 3.17.: Tracking efficiencies for primary charged particles in Pb–Pb collisions obtained from simulations with HIJING and GEANT3 for different centrality classes.