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5.2 Primary Proton Identification

5.2.5 Proton Feed-Down

A large fraction of the selected primary proton candidates emanates not from the fireball itself but is a product from the weak decays of (mostly) lambda particles. Two efforts concerning the contamination by feed-down are carried out within this thesis. Firstly, its contribution should be suppressed in order to enhance the significance of the signal from pairs of primary protons and Λ in the correlation function and secondly, it should be quantified so that it can be corrected for (see Section 6.5). Both can be achieved with the Distance of Closest Approach (DCA) of the track extrapolation to the primary vertex, see Fig. 3.5 for a sketch of the DCA.

10It was shown by the NA49 Collaboration that within the uncertainties of their data, no kaon-lambda or pion-lambda correlation is present [294, 295].

5.2 Primary Proton Identification 95

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purity: 99.9%

10/10/2012

ALI−PERF−43422

Figure 5.5: Left: Measured TOF β for the 2011 Pb-Pb run, calculated as follows from Eq. 3.7. The bands for the different species get closer as the momentum increases, but the protons appear separated up to p = 5.0 GeV/c. The mismatch decreases drastically with increasing momentum. Right: Exemplary TOF spectrum with the expected time for protons t(p)exp subtracted from the measured timetfor the momentum bin 1.75≤p(GeV/c)<2.0 with a fit decomposing the different contributions.

The DCA generally is the length of a three-dimensional vector. Due to the rotational symmetry in azimuth of ALICE it simplifies the analysis to reduce thex and y components to a single transverse element DCAxy. It is a common approach in ALICE to only study this transverse component [290] since it alone provides enough separation power to distinguish between primary protons,11 protons from weak decays, and protons from an interaction with the detector material. In this thesis, an additional effort was made to not only employ the transverse DCAxy but also make use of the longitudinal DCAz. The two-dimensional DCA of protons was obtained for three centrality classes, 0–10%, 10–30%, and 30–50% most central events, differential in rapidity and transverse momentum and separately for the particles and anti-particles. In Fig. 5.6 (left) the two-dimensional (DCAxy,DCAz) distribution of protons relative to the primary vertex for an exemplary phase space bin is projected on the DCAxy

component. The data, shown in black, are well described by a fit (magenta) consisting of Monte-Carlo templates for primary protons (red), protons from weak decays (green), and protons from material (blue); the symbols for the Monte-Carlo distributions are connected with lines for better visualization. The templates were obtained by analyzing simulated Hijing events, anchored to the Pb-Pb data taken in 2011.12 The same track selection criteria were applied to the Monte-Carlo samples as on the Pb-Pb data, only the particle identification was performed with the information from the event generator. The single components all display a distinct shape in DCA, which is almost flat for the contribution from material, shows broad shoulders for the weak decays and is very peaked for the primary protons. Visible for the contribution

11Note that according to an ALICE definition, primary particles include particles from decays, except weak decays of light flavor (u, d, s) hadrons and muons.

12All periods from LHC12a17a fix to LHC12a17i fix were analyzed.

from material interactions is a peaked structure for DCAxy <0.1 cm. It was found in [296]

(see the discussion in Section 3.2.3 therein), that it originates in the fake association of a SPD cluster from a primary track to the trajectory of the secondary particle. In the two-dimensional fit to the data, only three parameters in each bin are left free, which are the scaling factors of the MC templates. The progressive binning in the DCA variables, e. g. bin widths of 0.2 cm in DCAxy for |DCAxy|> 2.0 cm down to widths of 0.02 cm for|DCAxy|< 0.1 cm, allowed for an additional sensitivity in the interesting region of small distances while keeping the data structures small enough to handle them effectively.

When deciding on a cut value in DCA, an objective criterion for the determination of the best cut value is beneficial. Let us consider the background in the proton sample to be uncorrelated with the lambda particles (this assumption will be verified in Section 5.2.5). Then, the height of the correlation function above one, H, is proportional to the purity of the sample:

H ∼ pur = S/(S +B). The number of pairs found in real events Npairreal is proportional to the number of selected protons Npairreal ∼ Np = S+B. Its uncertainty is driven by Poisson statistics, since we are still just counting pairs, hence ∆Npairreal = q

Npairreal ∼√

S+B. When utilizing the event mixing technique, the uncertainty on the ratio of real over mixed events is usually dominated by the uncertainty of the real events as the mixed events typically have a factor of ten more statistics:

∆ Npairreal Npairmixed

!. Npairreal Npairmixed

!

=r

∆(Npairreal)/Npairreal2

+

∆(Npairmixed)/Npairmixed2

(5.6)

=√

1 + 0.1·1.q

Npairreal ≈1.q

Npairreal. (5.7) We see that the uncertainty on the correlation functionE consequently is E ∼1/q

Npairreal ∼ 1/√

S+B. Therefore, the ratio of the correlation function above one to the uncertainty of the correlation function is:

H/E∼ S S+B

√S+B = S

√S+B :=ζ, (5.8)

where ζ is the commonly used significance of the single-particle sample. In order to obtain the most accurate measurement, the single-particle significance ζ has to be maximized.

Fig. 5.6 (right) shows the significanceζas a function of the cut value in|DCAxy|and|DCAz|. One sees that a selection on the |DCAxy| and/or |DCAz| on the order of 0.5 cm provides a good significance. It is important to note that a too strict selection should be avoided, as the significance drops rapidly for |DCAxy|and/or |DCAz|smaller than on the order of 0.01 cm. It turns out that a maximum exists in the distribution of ζ, according to which the selection was chosen to be |DCAxy| ≤0.1 cm and|DCAz| ≤0.15 cm for protons. For the anti-protons, the contribution from material interactions does not play a role, therefore a slightly looser selection

5.2 Primary Proton Identification 97

of|DCAxy| ≤0.15 cm and|DCAz| ≤0.20 cm was applied, yielding a maximumζ.

The feed-down fraction in the proton samplefp should be defined as the number of particles from material interactions and weak decays over the number of all particles and is thus a measure of the uncorrelated background. The DCA fits allow to obtainfp within the aforementioned selection windows in DCA. For the example shown in Fig. 5.6 (left), the feed-down fractionfp

amounts to 15%, where the main feed-down contributors are from weak decays, with less than 1% of fp coming from interactions with detector material.

The feed-down fraction exhibits a dependence on phase space, which is shown in Fig. 5.7 for protons in the 0–10% most central events. The most prominent feature of the distribution is the increased feed-down at central rapidity|y|<0.5 and low transverse momentumpT <0.5 GeV/c.

This contribution arises from protons which were knocked-out from the detector. This conclusion emerging from the DCA fits is confirmed by the fact that the anti-protons do not show such a behavior. Due to the significant amount of feed-down, protons, but not anti-protons, with

|y|<0.5 andpT <0.5 GeV/care rejected from the sample as indicated by the hatched overlay in the figure. Loading such a histogram in the analysis to look up the feed-down fraction for each single particle allows to correct the correlation function for the uncorrelated background in a later stage, see Section 6.5. The selection on the DCA concludes the proton selection.

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Figure 5.6: Left: Transverse DCA distribution of protons in an exemplary phase space bin for the 0–10% most central events with a fit using Monte-Carlo templates.

See text for the discussion. Right: Significance ζ as a function of the cut values in DCAxy and DCAz for protons in 0–10% most central events. Mirrored around (0,0).

A maximum inζ exists for|DCAxy| ≤0.1 cm and|DCAz| ≤0.15 cm.

pffeed-down fraction

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protons This Thesis

Figure 5.7: Evolution of the feed-down fraction fp as determined by DCA fits with phase space.