Net-charge fluctuations in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV

We report the first measurement of the net-charge fluctuations in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV, measured with the ALICE detector at the CERN Large Hadron Collider. The dynamical fluctuations per unit entropy are observed to decrease when going from peripheral to central collisions. An additional reduction in the amount of fluctuations is seen in comparison to the results from lower energies. We examine the dependence of fluctuations on the pseudorapidity interval, which may account for the dilution of fluctuations during the evolution of the system. We find that the fluctuations at LHC are smaller compared to the measurements at the Relativistic heavy Ion Collider (RHIC), and as such, closer to what has been theoretically predicted for the formation of Quark-Gluon Plasma (QGP).

The ALICE experiment [1] at the Large Hadron Collider (LHC) is a multi-purpose detector designed to study the formation and evolution of nuclear matter at high temperatures and energy densities. One of the major goals of the experiment is to explore as many signals as possible towards characterizing the properties of the Quark-Gluon Plasma (QGP), the deconfined state of quarks and gluons, produced in high energy heavy-ion collisions. The study of event-by-event fluctuations provides a powerful tool to characterize the thermodynamic properties of the system. The fluctuations of conserved quantities in a finite phase space window, like net-charge of the system, are predicted to be one of the most sensitive signals of the QGP formation and phase transition, and may provide complementary understanding of strong interactions [2][3][4][5][6][7][8][9].
In the QGP phase, the charge carriers are quarks with fractional charges, whereas the particles in a hadron gas (HG) carry unit charge. The fluctuations in the netcharge depend on the squares of the charge states present in the system. Consequently, the net-charge fluctuations in the QGP phase are significantly smaller compared to that of a HG [2]. At the same time, if the initial QGP phase is strongly gluon dominated, the fluctuation per entropy may further be reduced as the hadronization of gluons increases the entropy [3]. Thus the net-charge fluctuations are strongly dependent on which phase they originate from. However, the net-charge fluctuations may get affected by uncertainties arising from volume fluctuations, so one considers the fluctuations of the ratio, R = N + /N − . Here N + and N − are the numbers of positive and negative particles respectively, measured in a specific transverse momentum (p T ) and pseudorapidity (η) window. The parameter R is related to the fluctuations of the net-charge via the D-measure as per the following expression [2,4,5]: which provides a measure of the charge fluctuations per unit entropy. Here the ... denotes an average of the quantity over an ensemble of events. The term δQ 2 is the variance of net charge, Q = N + − N − and N ch = N + + N − . The D-measure has been estimated for several different theoretical considerations including those of the lattice calculations. In a simple picture by neglecting quark-quark interactions, D is found to be approximately 4 times smaller for a QGP compared to a HG [2]. Lattice calculations which include the quark-quark interactions give a quantitatively different estimate for a a M.V.Lomonosov Moscow State University, D.V.Skobeltsyn Institute of Nuclear Physics, Moscow, Russia b University of Belgrade, Faculty of Physics and "Vinca" Institute of Nuclear Sciences, Belgrade, Serbia QGP phase, still significantly smaller than for a HG. It has been shown that D = 4 for an uncorrelated pion gas, and after taking resonance yields into account, the value decreases to D ≃ 3. For a QGP, D is significantly lower and has been calculated to be D ≃ 1.0-1.5 where the uncertainty arises from the uncertainty of relating the entropy to the number of charged particles in the final state [5]. Thus, a measurement of D can be effectively used as a probe for distinguishing the two phases, the HG and the QGP. However in reality, these fluctuations may get diluted in the rapidly expanding medium due to diffusion of particles in rapidity space [8,9]. Several other effects, such as collision dynamics, radial flow, resonance decays and final state interactions may also affect the amount of measured fluctuations [2,[10][11][12].
In the experiment, the net-charge fluctuations are best studied [12][13][14][15][16][17] by calculating the quantity ν (+−,dyn) defined as: which is a measure of the relative correlation strength of particle pairs. A negative value of ν (+−,dyn) signifies the dominant contribution from correlations between pairs of opposite charges. On the other hand, a positive value indicates the significance of the same charge pair correlations. The ν (+−,dyn) has been found to be robust against random efficiency losses [17][18][19]. D-measure and ν (+−,dyn) are related to each other by [5]: The values of ν (+−,dyn) need to be corrected for global charge conservation [17]. The predictions for the Dmeasure are based on the assumption of vanishing netcharge in the system. However, in a realistic situation, the system under consideration has a small but finite netcharge. A correction due to finite net-charge effect also needs to be applied [4].
In this letter, we report the first measurements of netcharge fluctuations, by calculating ν (+−,dyn) and the Dmeasure, as a function of collision centrality in Pb-Pb collisions at √ s NN = 2.76 TeV at the LHC with the AL-ICE detector. We also make a comparison of the experimental results to the theoretical predictions.
Details of the ALICE experiment and its detectors can be found in [1]. For this analysis, we have used the Time Projection Chamber (TPC) [20] to reconstruct charged particle tracks. The detector provides a uniform acceptance with an almost constant tracking efficiency of about 80% in the analyzed phase space (|η| < 0.8 and 0.2 GeV/c < p T < 5 GeV/c). The interaction vertex was measured using the Silicon Pixel Detector (SPD), the innermost detector of the Inner Tracking System (ITS).
In the analysis, we have considered events with a vertex |v z | < 10 cm to ensure a uniform acceptance in the central pseudo-rapidity region. The minimum bias trigger consisted of a coincidence of at least one hit on each of the two VZERO scintillator detectors, positioned on both sides of the interaction point, while at the startup of data taking period an additional requirement of having a coincidence with a signal from the SPD was also introduced. The background events coming from parasitic beam interactions are removed by a standard offline event selection procedure, which requires the VZERO timing information and hits in the SPD.
We present the results as a function of centrality that reflects the collision geometry. The collision centrality is determined by cuts on the VZERO multiplicity [21]. A study based on Glauber model fits [22][23][24] to the multiplicity distribution in the region corresponding to 90% of the most central collisions, where the vertex reconstruction is fully efficient, facilitates the determination of the cross section percentile and the number of participants. The resolution in centrality is found to be < 0.5% RMS for the most central (0-5%) collisions, increasing towards 2% RMS for peripheral (70-80%) collisions [21].
We require tracks in the TPC to have at least 80 reconstructed space points with a χ 2 per TPC cluster of the momentum fit less than 4. We reject tracks with distance of closest approach (dca) to the vertex larger than 3 cm both in the transverse plane and in the longitudinal direction. We have performed an alternative analysis with tracks reconstructed using the combined tracking of ITS and TPC. In this case, the dca cuts were 0.3 cm in the transverse plane as well as in the longitudinal direction. The results obtained with both tracking approaches are in agreement.
The data analysis has been performed for Pb-Pb collisions at √ s NN = 2.76 TeV and pp collisions at the same centre-of-mass energy. An identical analysis procedure has been followed for both the data sets. We calculate the ν (+−,dyn) from the experimental measurements of positive and negative charged particles counted in ∆η windows, defined around mid-rapidity (for example, ∆η = 1 corresponds to −0.5 ≤ η ≤ 0.5) and in the p T range from 0.2 to 5.0 GeV/c. Consistency checks had been performed for another p T window, viz., 0.3 GeV/c < p T < 1.5 GeV/c. The differences in the fluctuation results are small, and included in the systematic errors. In Figure 1, we present the ν (+−,dyn) as a function of centrality, expressed in terms of the number of participating nucleons. Moving from left to right along the x-axis of the figure corresponds to moving from peripheral to central collisions. The results are presented for ∆η = 1 and 1.6, for both Pb-Pb and pp collisions. In all cases, the magnitude of ν (+−,dyn) is observed to be negative, indicating the dominance of the correlation term in Eq. 2. The absolute values of ν (+−,dyn) for pp collisions are larger compared to those measured for Pb-Pb collisions. When going from peripheral to central events, the absolute values of ν (+−,dyn) are seen to decrease monotonically. The values of ν (+−,dyn) have to be corrected for global charge conservation and finite acceptance [17]. If all charges were accepted, the global charge conservation would lead to vanishing fluctuations. This will yield the minimum value of ν (+−,dyn) to be -4/ N total , where N total is the average total number of charged particles produced over full phase space. The corrected ν (+−,dyn) is The values of N total for Pb-Pb collisions have been estimated from the experimental data [25], whereas for pp collisions, it is taken from PYTHIA [26] event generator. As a reference, N ch for ∆η=1 and N total values are 1637±61 and 17165±772 for most central (0-5%) Pb-Pb collisions, and 4.8±0.2 and 36.0 for pp collisions. These are systematic errors, statistical errors are negligible. The corrected values, ν corr (+−,dyn) , are plotted in Figure 1 as a function of the number of participating nucleons for Pb-Pb and pp collisions. The absolute values of ν corr (+−,dyn) are smaller compared to ν (+−,dyn) in all cases. The differences are more apparent for pp and peripheral Pb-Pb collisions than for central collisions.
Taking the above corrections into account, we obtain, Alternatively, corrections to D-measure may also be ob- tained using [4]: where C µ (= N+ 2 N− 2 ) corrects for the effects of the finite net charge, and C η (=1− N ch N total ) accounts for finite bin size in rapidity as well as global charge conservation. Differences in the two corrected values, D ′ and D ′′ , are within 4-9%, depending on ∆η. Subsequently, mean values of D ′ and D ′′ are plotted in the figures as D, and differences of those have been included as systematic errors.
The systematic uncertainties have additional contributions from the following sources: (a) uncertainty in the determination of the interaction vertex, (b) different magnetic field polarities, (c) contamination from secondary tracks (dca cuts), (d) centrality definition using different detectors, (e) selection criteria at the track level, (f) different tracking scenarios, and (g) two different p T windows. The total systematic error on ν corr (+−,dyn) amounts to 6-10% in going from peripheral to central collisions. The error on the product of number of charged particles and ν corr (+−,dyn) remains within 7-13% at all centralities. The systematic and statistical uncertainties in all the figures are represented by boxes and error bars, respectively. The statistical errors are small and within the sizes of the symbols in most cases. Figure 2 presents the values of N ch ν corr (+−,dyn) and D in the left and right axes, respectively, as a function of the number of participating nucleons. The N ch values have been measured for different centralities and ∆η windows, and corrected for detector inefficiencies [21]. Both the results from the Pb-Pb and pp analyses are shown. The shaded bands in the figure indicate the predictions for a HG and a QGP. Results from the HIJING event generator [27] at ∆η = 1 and 1.6 are observed to be close to the HG line and at the same time independent of centrality. The pp results agree well with the HG prediction. The experimental results for Pb-Pb for both the ∆η windows are observed to be below the HG predictions and above those of the QGP. The values of D for ∆η = 1.6 are lower compared to those for ∆η = 1 for all centralities.
A decreasing trend of D has been observed while going from peripheral to central collisions, as seen in Figure 2. This centrality dependence may arise partly because of the presence of radial flow [10]. The radial flow velocity could lead to the kinetic focussing of the produced particles, causing a narrowing of the opening angles. This may affect the magnitude of net-charge fluctuations. The effect of radial flow on ν (+−,dyn) has been estimated by using an afterburner [28] on the HIJING events where the particles get a boost in the transverse momenta because of the radial flow velocity. We observe no significant difference between the results from pure HIJING and HIJING with the afterburner. This indicates that the presence of radial flow may not be responsible for the centrality dependence of the D-measure.
The measured fluctuations may get diluted during the evolution of the system from hadronization to kinetic freeze-out because of the diffusion of charged hadrons in rapidity. This has been addressed in refs. [8,9], where a diffusion equation has been proposed to study the dependence of net-charge fluctuations on the width of the rapidity window. Taking the dissipation into account, the asymptotic value of fluctuations may be close to the primordial fluctuations. This has been explored for the ALICE data points by plotting N ch ν corr (+−,dyn) and D as a function of ∆η for three centrality bins, as shown in Figure 3. We observe that for a given centrality bin, the D-measure shows a strong decreasing trend with the increase of ∆η. In fact, the curvature of D has a decreasing slope with a flattening tendency at large ∆η windows. Following the prescriptions of [8,9], we fit the data points with the functional form, erf(∆η/ √ 8σ f ), which represents the diffusion in rapidity space. Here, σ f characterizes the diffusion at freeze-out. The evolution of the net-charge fluctuations with beam energy can be studied by combining the ALICE data with those of the STAR experiment [12] at RHIC. In  The results from the STAR [12] and ALICE experiments are presented for ∆η = 1 after the correction for charge conservation. The ALICE result for ∆η = 1.6 is also shown. Both statistical (error bar) and systematic (box) errors are plotted.
tions per entropy, is calculated from ν corr (+−,dyn) and from the measured average charged particle multiplicity. A decreasing trend of D is observed in going from peripheral to central collisions. Model studies indicate that the presence of radial flow may not be the cause of this decrease. The dissipation of signal during the evolution of the fireball from the hadronization to freeze-out has been estimated by fitting D as a function of the ∆η window. The extrapolation of the fit function yields the asymptotic value of D, which is not very different from the measurement at ∆η = 1.6. The beam energy dependence of charge fluctuations has been studied by comparing the ALICE data with those from the STAR experiment at RHIC for Au-Au collisions at four energies. A monotonic decrease in the value of D, measured at ∆η = 1, has been observed. The STAR data points at RHIC top energy are close to the prediction for a hadron gas. This may be due to the fact that the fluctuation may be not strong enough to be measured or because of the dilution of fluctuation during the evolution process. The fluctuations at √ s NN = 2.76 T eV for ∆η = 1.0 are below the measurements at RHIC. These data points show an additional decrease at ∆η = 1.6, where D turns out to be 2.3±0.02(stat.)±0.21(sys.) for top central collisions. The fluctuations at the LHC energy might also have been diluted because of various effects as discussed earlier. As these fluctuations are smaller than the theoretical expectations for a HG, and show for the first time at the LHC energy a clear tendency towards expectations from a QGP, we may infer that they have their origin in the QGP phase. Dynamical model calculations are needed to understand the results better.
The ALICE collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex.