7.2 Results of the fitting
9.1.4 Pair-level selection criteria
The accepted particles from each event were combined in pairs and the correlation functions were calculated according to Eq. (6.3). Figure 9.3 shows the pΛ correlation function as a func-tion of k∗= q/2 for the 0–10% centrality range, after applying the single-track selection criteria only. A significant peak around k∗ = 0.05 GeV/c, not expected in the pure pΛ correlations, is clearly visible. There are two possible explanations of the origin of this effect, which do not
9.1. DATA ANALYSIS
k* (GeV/c)
0 0.1 0.2 0.3 0.4 0.5
C(k*)
1 1.1 1.2
pΛ Λ + p = 2.76 TeV, Centrality 0-10%
sNN
Pb-Pb at
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Figure 9.3: The combined pΛ+pΛ correlation function for the most central collisions (0−10% centrality range). The peak at k∗= 0.05 GeV/c due to splitting and residual correlations is visible.
exclude each other: the so-called proton-proton residual correlation and splitting of primary proton tracks. In addition, merging of primary tracks and the ones associated with the V0 can also be present in the analyzed correlations. In order to account for all these effects a dedicated study was performed.
Removing the merging effect
In order to remove the effect of track merging in the analyzed correlations, the average separa-tion distance in the TPC between primary p (p) and same-signΛ (Λ) daughters, was calculated.
Figure 9.4 shows the ratio of the same event pairs over mixed event pairs as a function of the average distance between a primary proton and a positive pion (Λ daughter) in the study of pΛ correlations. The merging effect, manifested as anticorrelation appearing below ≈ 11 cm, is clearly visible. Therefore, only those pairs with the average separation larger than 11 cm were accepted.
Average separation (cm)
0 5 10 15 20 25 30 35 40 45
mixed event pairssame event pairs
0.6 0.8 1
pairs = 2.76 TeV, Centrality 0-10%, pΛ sNN
Pb-Pb at
daughter) Primary proton - Positive pion (Λ
06/09/2012
ALI−PERF−41661
Figure 9.4: The correlation function (ratio of the same event pairs over mixed event pairs) as a function of the average separation distance in the TPC between the primary protons and the positive pions recon-structed asΛ daughters. The anticorrelation observed for the low values of average separation distance originates from the merging effect.
9.1. DATA ANALYSIS
Table 9.1: List of possible residual correlation sources contributing to the pΛ (and pΛ) system. The fractions correspond to addmixture of these pairs in the measured pΛ (pΛ) correlation. Table from Ref. [294].
Pair Fraction Decay momentum (MeV/c)
pΛ 15% 0
ΛΛ 10% 101
Σ+Λ 3% 189
pΣ0 11% 74
ΛΣ0 7% 101, 74
Σ+Σ0 2% 189, 74
pΞ0 9% 135
ΛΞ0 5% 101, 135
Σ+Ξ0 2% 189, 135
pp 7% 101
Residual correlations
From the experimental point of view, not all of the V0s, reconstructed by the dedicated algo-rithms, correspond to real neutral strange particles. In fact, even after applying the strict se-lection criteria introduced in Sec. 9.1.3, some of the wrongly reconstructed V0s remain. These artifacts lead to the admixture of direct protons (antiprotons) in theΛ (Λ) sample, yielding the primary proton residual correlation contributing to the measured pΛ correlation function. Other possible sources of residual correlations are protons which are identified as primary but in prac-tice come from decays of heavier baryons, such asΛ and Σ+. The same mechanism applies to Λ hyperons, which can originate from Σ0orΞ0decays.
In fact, the residual correlations are not limited to baryons only; they are present essen-tially in all systems. For example in the case of two-pion correlations, the possible residual correlation originates from muons decaying into pion pairs. Neveretheless, the admixture of these non-primordial pions is practically negligible. In the case of baryons there are, however, many sources of non-primary particles which significantly affect the measurements. In the pΛ (and pΛ) systems the possible sources of residual correlations were estimated by the STAR experiment [294] and are presented in Table 9.1.
The potential primary proton residual correlation in the experimental pΛ correlation func-tion can be manifested as a significant correlafunc-tion peak around k∗ ≈ 0.05 GeV/c visible in Fig. 9.3. In order to test this assumption the following procedure was employed.
First, we calculated the theoretical pp correlation function using the CorrFit [295] tool.
However, the pΛ and pp correlation functions are calculated in different reference frames. The latter is calculated as a function of k∗pp, which is defined as the relative momentum between the two protons, while the pΛ correlation function is calculated as a function of k∗pΛ, defined as the relative momentum between a primary proton and a lambda. Therefore, in order to compare the two correlation functions, one needs to apply a dedicated transformation procedure of the pp correlation function from k∗ppframe to k∗pΛ. This transformation requires calculation of the Λ decay kinematics, which was obtained from the THERMINATOR 2 model [286]. This decay kinematics, shown in Fig. 9.5, is represented as a two-dimensional correlation matrix T(kpp∗ , kp∗Λ). The transformation is then defined as a weighted average: for each value of k∗pΛ, Cpp(k∗pΛ) is determined as a sum over all kpp∗ values of Cpp(k∗pp) scaled by factors taken from a two-dimensional transformation matrix T (kpp∗ , kp∗Λ). This leads to the following transformation formula:
Cpp(kp∗Λ)=X
k∗pp
Cpp(kpp∗ )T (k∗pp, kp∗Λ). (9.1)
We note that Eq. (9.1) assumes normalization of the transformation matrix:
X
k∗pp
T(k∗pp, k∗pΛ)= 1. (9.2)
The result of the transformation is shown in Fig. 9.6. The theoretical pp correlation function is plotted as a function k∗pp (red full symbols) and, after the transformation procedure, as a function of k∗pΛ(green open symbols). One should notice that the peak around 0.02 GeV/c in kpp∗ transforms into the peak around 0.05 GeV/c in k∗pΛ. This calculation is consistent with the experimental result shown in Fig. 9.3.
The procedure was then applied to the experimental data by removing the proton pairs with kpp∗ < 0.04 GeV/c, which includes the whole correlation peak in the pp correlation function. We note that this procedure also removes the split tracks, which by construction have close relative momenta. We can clearly see in Fig. 9.7 that the peak around 0.05 GeV/c in k∗pΛ, which was present in Fig. 9.3, is removed and a clear enhancement at low k∗is visible.
9.1. DATA ANALYSIS
Figure 9.5: TheΛ kinematics decay matrix T(k∗pp, k∗pΛ) calculated using the THERMINATOR 2 model.
(GeV/c)
pΛ pp, k*
k*
0 0.05 0.1 0.15 0.2
) Λp), C(k* ppC(k*
1 1.1 1.2 1.3
Λ) C(k*p
pp) C(k*
Figure 9.6: The pp theoretical correlation function from CorrFit as a function of k∗pp(red full points) and k∗pΛ(green open symbols).
k* (GeV/c)
0 0.1 0.2 0.3 0.4 0.5
C(k*)
1 1.1 1.2 1.3
0-10%
10-20%
20-30%
30-40%
0-10%
10-20%
20-30%
30-40%
0-10%
10-20%
20-30%
30-40%
0-10%
10-20%
20-30%
30-40%
= 2.76 TeV sNN
, Pb-Pb at pΛ
Λ + p ALICE
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Figure 9.7: The combined pΛ+pΛ correlation functions for centralities 0–10%, 10–20%, 20–30%, and 30–40%.