2. The ALICE experiment at the LHC 41
2.7. Centrality determination in ALICE
The centrality determination in ALICE is described in detail in ref. [144], only a short descrip-tion based on this reference is given here.
Centrality is defined as the percentage of the total nuclear cross section and allows to relate measured signals in the detector to geometrical quantities that can not be directly observed.
In particular the impact parameter b, the number of participating nucleonNpartor the number of binary collisions Ncoll or the nuclear overlap TAA can be obtained (see section 1.7 for a definition of these quantities). Various detectors with different pseudorapidity coverage are used to estimate the centrality of a Pb–Pb collision, including the ZDC, VZERO, TPC and SPD.
The different centrality estimators are implemented and calibrated in a central framework
2.7. Centrality determination in ALICE 53
CENTRALITY DETERMINATION OF Pb-Pb COLLISIONS . . . PHYSICAL REVIEW C 88, 044909 (2013)
VZERO amplitude (arb. units)
0 20 40 60 80 100 120 140 160 180
Purity
0 0.2 0.4 0.6 0.8 1
All events 2-out-of-3 V0AND 3-out-of-3 V0AND + TPC V0AND + ZDC
ALICE
=2.76 TeV s
NNPb-Pb at
90% of total cross section
FIG. 9. (Color online) Purity of the three online interaction trig-gers (2-out-of-3, V0AND, and 3-out-of-3) and other event selections used for Pb-Pb collisions as a function of the VZERO amplitude calculated with HIJING, STARLIGHT, and QED simulations. The dashed line indicates 90% of the hadronic cross section.
of the VZERO amplitude ( V ), is defined as the fraction of hadronic collisions over all the events selected with a given condition,
purity =
dNx
dV
H σH
NH
dNx
dV
H σH
NH
+
dNdVxSNS σSNS
NSNS
+
dNdVxSND σSND
NSND
+
dNdVxQ σQ
NQ
, (4) where σ
xand N
xare the cross sections and number of events for a given process, x , where x = H , SNS, SND, and Q , for HIJING, STARLIGHT single, STARLIGHT double, and QED, respectively.
The purity of the event sample can be verified using the correlation of the energy deposition in the two sides of the ZN calorimeter, similar to the one shown in Fig. 6. Single-neutron peaks are visible in the 80–90% centrality class, which may indicate some remaining contamination from EMD events.
However, their origin can be also attributed to asymmetric Pb-Pb events, as well as a pile-up of an EMD and a hadronic collision. Since this contamination cannot be easily removed, analyses that use peripheral classes like 80–90% assign an additional 6% systematic uncertainty on the event selection to take into account the possible contamination from EMD.
B. Method 2: Fitting the multiplicity distribution
Another independent way to define the AP uses a phe-nomenological approach based on the Glauber Monte Carlo to fit the experimental multiplicity distribution. The Glauber Monte Carlo uses the assumptions mentioned above plus a convolution of a model for particle production, based on a negative binomial distribution (NBD). This latter assumption is motivated by the fact that in minimum bias pp and pp collisions at high energy, the charged-particle multiplicity dσ/dN
chhas been measured over a wide range of rapidity and is well described by a NBD [31,32]. This approach allows one to simulate an experimental multiplicity distribution (e.g.,
FIG. 10. (Color online) Distribution of the sum of amplitudes in the VZERO scintillators. The distribution is fitted with the NBD-Glauber fit (explained in the text), shown as a line. The centrality classes used in the analysis are indicated in the figure. The inset shows a zoom of the most peripheral region.
VZERO amplitude), which can be compared with the one from data.
Figure 10 shows the distribution of VZERO amplitudes for all events triggered with the 3-out-of-3 trigger (see Sec. III B) after removing the beam background (see Sec. III C1), part of the EM background with the ZDC cut (see Sec. III C2), and a Z -vertex cut |z
vtx| < 10 cm. The multiplicity distribution has the classical shape of a peak corresponding to most peripheral collisions (contaminated by EM background and by missing events due to the trigger inefficiency), a plateau of the intermediate region, and an edge for the central collisions, which is sensitive to the intrinsic fluctuations of N
partand dN
ch/dη and to detector acceptance and resolution.
The Glauber Monte Carlo defines, for an event with a given impact parameter b , the corresponding N
partand N
coll. The particle multiplicity per nucleon-nucleon collision is parametrized by a NBD. To apply this model to any collision with a given N
partand N
collvalue we introduce the concept of
“ancestors,” i.e., independently emitting sources of particles.
We assume that the number of ancestors N
ancestorscan be parameterized by N
ancestors= f N
part+ (1 − f ) N
coll. This is inspired by two-component models [33,34], which decompose nucleus-nucleus collisions into soft and hard interactions, where the soft interactions produce particles with an average multiplicity proportional to N
part, and the probability for hard interactions to occur is proportional to N
coll. We discuss the independence of the fit results of this assumption below (Sec. IV B1).
To generate the number of particles produced per interac-tion, we use the negative binomial distribution
P
μ,k( n ) = ( n + k ) ( n + 1) ( k )
( μ/k )
n( μ/k + 1)
n+k, (5) which gives the probability of measuring n hits per ancestor, where μ is the mean multiplicity per ancestor and k controls the width. For every Glauber Monte Carlo event, the NBD is sampled N
ancestorstimes to obtain the averaged simulated VZERO amplitude for this event, which is proportional to the number of particles hitting the hodoscopes. The VZERO 044909-9
Figure 2.5.: Distribution of the VZERO amplitudes (sum of V0A and V0C) measured in Pb–Pb collisions atpsNN = 2.76 TeV together with the NBD-Glauber-Fit. The centrality intervals obtained from the VZERO amplitudes are indicated. The insert shows the most peripheral centrality intervals.
Figure taken from [144].
and can be used in the data analysis. All methods are based on a monotonic behavior of the detector signal on the collision centrality.
The best centrality resolution is achieved for the combined multiplicity (V0M) of the V0A and V0C detectors. For this analysis this V0M is used as a estimator for the collision cen-trality, which represents also the main method used by ALICE. Part of the machine induced background and electromagnetic dissociation is removed with cuts on the ZDC signals.
The multiplicity distribution in Pb–Pb collisions can be well described by a convolution of a Monte Carlo Glauber model with a negative binomial distribution (NBD) for particle produc-tion. The distribution of the signals in the VZERO detectors is shown in Figure 2.5 along with a NBD-Glauber-Fit. Only the range of 0-90% of the total cross section is used for the fit, as the contamination with background events from Electromagnetic (QED) processes and beam-gas collisions and trigger inefficiencies are negligible in this range. The lower end of the fit range (90%) is called the Anchor Point (AP).
Centrality percentiles as indicated in Figure 2.5 are obtained by sharp cuts on the V0M dis-tribution, the corresponding geometrical quantities are obtained via the NBD-Glauber-Fit. A pure MC Glauber model with centrality intervals obtained from slicing in the impact param-eter b and without fit to the data results in geometrical quantities that are only marginally5 different from those obtained with the NBD-Glauber-Fit.
The parameters used in the MC Glauber model of ALICE are the nucleon-nucleon cross section ofσinelNN = (64±5)mb and the Woods-Saxon parameters r0= (6.62±0.06)fm for the nuclear radius and a = (0.546±0.010) fm for the skin thickness. In addition a minimal exclusion
5 The relative difference is<1%for 0-50% centrality and<2%for more peripheral collisions.
54 2. The ALICE experiment at the LHC
distance for two nucleons ofdmin= (0.4±0.4)fm is required. All parameters have been varied by their quoted uncertainties to estimate the systematic uncertainties of the centrality-related geometrical quantities. Values and systematic uncertainties of of〈TAA〉,〈Npart〉and〈Ncoll〉that are relevant for this thesis are listed in Table 4.2 of section 4.4, where the results in Pb–Pb collisions are presented.
2.7. Centrality determination in ALICE 55