We present the first azimuthally differential measurements of the pion source size relative to the second harmonic event plane in Pb-Pb collisions at a center-of-mass energy per nucleon-nucleon pair of $\sqrt{s_{\rm NN}}=2.76$ TeV. The measurements have been performed in the centrality range 0-50% and for pion pair transverse momenta $0.2 < k_{\rm T} < 0.7$ GeV/$c$. We find that the $R_{\rm side}$ and $R_{\rm out}$ radii, which characterize the pion source size in the directions perpendicular and parallel to the pion transverse momentum, oscillate out of phase, similar to what was observed at the Relativistic Heavy Ion Collider (RHIC). The final-state source eccentricity, estimated via $R_{\rm side}$ oscillations, is found to be significantly smaller than the initial-state source eccentricity, but remains positive; indicating that even after a stronger expansion in the in-plane direction, the pion source at the freeze-out is still elongated in the out-of-plane direction. The 3+1D hydrodynamic calculations are in qualitative agreement with observed centrality and transverse momentum $R_{\rm side}$ oscillations, but systematically underestimate the oscillation magnitude.
The azimuthal dependence of $R_{out}^{2}$ as a function of $\Delta\varphi=\varphi_{\mathrm{pair}}-\Psi_{\mathrm EP,2}$ for the centrality 20--30% and different $k_{\mathrm{T}}$ ranges.
The azimuthal dependence of $R_{out}^{2}$ as a function of $\Delta\varphi=\varphi_{\mathrm{pair}}-\Psi_{\mathrm EP,2}$ for the centrality 20--30% and different $k_{\mathrm{T}}$ ranges.
The azimuthal dependence of $R_{out}^{2}$ as a function of $\Delta\varphi=\varphi_{\mathrm{pair}}-\Psi_{\mathrm EP,2}$ for the centrality 20--30% and different $k_{\mathrm{T}}$ ranges.
In high-energy heavy-ion collisions, the correlations between the emitted particles can be used as a probe to gain insight into the charge creation mechanisms. In this Letter, we report the first results of such studies using the electric charge balance function in the relative pseudorapidity ($\Delta\eta$) and azimuthal angle ($\Delta\varphi$) in Pb--Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV with the ALICE detector at the Large Hadron Collider. The width of the balance function decreases with growing centrality (i.e. for more central collisions) in both projections. This centrality dependence is not reproduced by HIJING, while AMPT, a model which incorporates strings and parton rescattering, exhibits qualitative agreement with the measured correlations in $\Delta\varphi$ but fails to describe the correlations in $\Delta\eta$. A thermal blast-wave model incorporating local charge conservation and tuned to describe the $p_{\rm T}$ spectra and v$_2$ measurements reported by ALICE, is used to fit the centrality dependence of the width of the balance function and to extract the average separation of balancing charges at freeze-out. The comparison of our results with measurements at lower energies reveals an ordering with $\sqrt{s_{\rm NN}}$: the balance functions become narrower with increasing energy for all centralities. This is consistent with the effect of larger radial flow at the LHC energies but also with the late stage creation scenario of balancing charges. However, the relative decrease of the balance function widths in $\Delta\eta$ and $\Delta\varphi$ with centrality from the highest SPS to the LHC energy exhibits only small differences. This observation cannot be interpreted solely within the framework where the majority of the charge is produced at a later stage in the evolution of the heavy--ion collision.
The Balance Function as a function of the relative pseudorapidity of two charged particles for the centrality class 0-5%. Also shown in the second column is the result from the mixed data set.
The Balance Function as a function of the relative pseudorapidity of two charged particles for the centrality class 30-40%.
The Balance Function as a function of the relative pseudorapidity of two charged particles for the centrality class 70-80%.
Measurements of charge dependent azimuthal correlations with the ALICE detector at the LHC are reported for Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV. Two- and three-particle charge-dependent azimuthal correlations in the pseudo-rapidity range $|\eta| < 0.8$ are presented as a function of the collision centrality, particle separation in pseudo-rapidity, and transverse momentum. A clear signal compatible with a charge-dependent separation relative to the reaction plane is observed, which shows little or no collision energy dependence when compared to measurements at RHIC energies. This provides a new insight for understanding the nature of the charge dependent azimuthal correlations observed at RHIC and LHC energies.
The centrality dependence of the three-particle charge-dependent correlator MEAN(COS(PHI(A)+COS(PHI(B)-2*PHI(RP)) measured with the cumulant method.
The centrality dependence of the correlator three-particle charge-dependent MEAN(COS(PHI(A)+COS(PHI(B)-2*PHI(RP)) measured from correlations with the reaction plane (RP) estimated using the TPC detector.
The centrality dependence of the correlator three-particle charge-dependent MEAN(COS(PHI(A)+COS(PHI(B)-2*PHI(RP)) measured from correlations with the reaction plane (RP) estimated using the VZERO detector.
The directed flow of charged particles at mid-rapidity is measured in Pb-Pb collisions at $\sqrt{s_\rm{NN}}=2.76$ TeV relative to the collision symmetry plane defined by the spectator nucleons. A negative slope of the rapidity-odd directed flow component with approximately 3 times smaller magnitude than found at the highest RHIC energy is observed. This suggests a smaller longitudinal tilt of the initial system and disfavors the strong fireball rotation predicted for the LHC energies. The rapidity-even directed flow component is measured for the first time with spectators and found to be independent of pseudorapidity with a sign change at transverse momenta $p_{\rm T}$ between $1.2$ and $1.7$ GeV/$c$. Combined with the observation of a vanishing rapidity-even $p_{\rm T}$ shift along the spectator deflection this is strong evidence for dipole-like initial density fluctuations in the overlap zone of the nuclei. Similar trends in the rapidity-even directed flow and the estimate from two-particle correlations at mid-rapidity, which is larger by about a factor of 40, indicate a weak correlation between fluctuating participant and spectator symmetry planes. These observations open new possibilities for investigation of the initial conditions in heavy-ion collisions with spectator nucleons.
Correlation between x components of the Q-vector of projectile (Qpx) and target (Qtx) spectators, MEAN(QpxQtx).
Correlation between y components of the Q-vector of projectile (Qpy) and target (Qty) spectators, MEAN(QpyQty).
Correlation between x and y components of the Q-vector of projectile (Qpx) and target (Qty) spectators, MEAN(QpxQty).
Event-by-event fluctuations of the mean transverse momentum of charged particles produced in pp collisions at $\sqrt{s}$ = 0.9, 2.76 and 7 TeV, and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV are studied as a function of the charged-particle multiplicity using the ALICE detector at the LHC. Dynamical fluctuations indicative of correlated particle emission are observed in all systems. The results in pp collisions show little dependence on collision energy. The Monte Carlo event generators PYTHIA and PHOJET are in qualitative agreement with the data. Peripheral Pb-Pb data exhibit a similar multiplicity dependence as that observed in pp. In central Pb-Pb, the results deviate from this trend, featuring a significant reduction of the fluctuation strength. The results in Pb--Pb are in qualitative agreement with previous measurements in Au-Au at lower collision energies and with expectations from models that incorporate collective phenomena.
Relative fluctuation $\sqrt{C_m}/M(p_{\rm T})_m$ as a function of $\langle {\rm d}N_{\rm ch}/{\rm d}\eta \rangle$ in pp collisions at $\sqrt{s}$ = 0.9 TeV.
Relative fluctuation $\sqrt{C_m}/M(p_{\rm T})_m$ as a function of $\langle {\rm d}N_{\rm ch}/{\rm d}\eta \rangle$ in pp collisions at $\sqrt{s}$ = 2.76 TeV.
Relative fluctuation $\sqrt{C_m}/M(p_{\rm T})_m$ as a function of $\langle {\rm d}N_{\rm ch}/{\rm d}\eta \rangle$ in pp collisions at $\sqrt{s}$ = 7 TeV.
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at $\sqrt{s}=0.9$, 2.76 and 7 TeV. The measurement is performed in the central pseudorapidity region ($|\eta| < 0.8$) for the transverse momentum $p_{\rm T}>0.3$ GeV/$c$. Two separate pseudorapidity windows of width ($\delta \eta$) ranging from 0.2 to 0.8 are chosen symmetrically around $\eta=0$. The multiplicity correlation strength ($b_{\rm cor}$) is studied as a function of the pseudorapidity gap ($\eta_{\rm gap}$) between the two windows as well as the width of these windows. The correlation strength is found to decrease with increasing $\eta_{\rm gap}$ and shows a non-linear increase with $\delta\eta$. A sizable increase of the correlation strength with the collision energy, which cannot be explained exclusively by the increase of the mean multiplicity inside the windows, is observed. The correlation coefficient is also measured for multiplicities in different configurations of two azimuthal sectors selected within the symmetric FB $\eta$-windows. Two different contributions, the short-range (SR) and the long-range (LR), are observed. The energy dependence of $b_{\rm cor}$ is found to be weak for the SR component while it is strong for the LR component. Moreover, the correlation coefficient is studied for particles belonging to various transverse momentum intervals chosen to have the same mean multiplicity. Both SR and LR contributions to $b_{\rm cor}$ are found to increase with $p_{\rm T}$ in this case. Results are compared to PYTHIA and PHOJET event generators and to a string-based phenomenological model. The observed dependencies of $b_{\rm cor}$ add new constraints on phenomenological models.
Correlation strength $b_{\rm corr}$ for $\eta$-windows in $p_{\rm T}$ range $0.3-1.5$ (GeV/c) at $\sqrt{s}=0.9$ TeV.
Correlation strength $b_{\rm corr}$ for $\eta$-windows in $p_{\rm T}$ range $0.3-1.5$ (GeV/c) at $\sqrt{s}=2.76$ TeV.
Correlation strength $b_{\rm corr}$ for $\eta$-windows in $p_{\rm T}$ range $0.3-1.5$ (GeV/c) at $\sqrt{s}=7$ TeV.
Angular correlations between unidentified charged trigger ($t$) and associated ($a$) particles are measured by the ALICE experiment in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV for transverse momenta $0.25 < p_{T}^{t,\, a} < 15$ GeV/$c$, where $p_{T}^t > p_{T}^a$. The shapes of the pair correlation distributions are studied in a variety of collision centrality classes between 0 and 50% of the total hadronic cross section for particles in the pseudorapidity interval $|\eta| < 1.0$. Distributions in relative azimuth $\Delta\phi \equiv \phi^t - \phi^a$ are analyzed for $|\Delta\eta| \equiv |\eta^t - \eta^a| > 0.8$, and are referred to as "long-range correlations". Fourier components $V_{n\Delta} \equiv \langle \cos(n\Delta\phi)\rangle$ are extracted from the long-range azimuthal correlation functions. If particle pairs are correlated to one another through their individual correlation to a common symmetry plane, then the pair anisotropy $V_{n\Delta}(p_{T}^t, p_{T}^a)$ is fully described in terms of single-particle anisotropies $v_n (p_{T})$ as $V_{n\Delta}(p_{T}^t, p_{T}^a) = v_n(p_{T}^t) \, v_n(p_{T}^a)$. This expectation is tested for $1 \leq n \leq 5$ by applying a global fit of all $V_{n\Delta} (p_{T}^t, p_{T}^a)$ to obtain the best values $v_{n}\{GF\} (p_{T})$. It is found that for $2 \leq n \leq 5$, the fit agrees well with data up to $p_T^a \sim 3$-4 GeV/$c$, with a trend of increasing deviation as $p_{T}^t$ and $p_{T}^a$ are increased or as collisions become more peripheral. This suggests that no pair correlation harmonic can be described over the full $0.25 < p_{T} < 15$ GeV/$c$ range using a single $v_n(p_T)$ curve; such a description is however approximately possible for $2 \leq n \leq 5$ when $p_T^a < 4$ GeV/$c$. For the $n=1$ harmonic, however, a single $v_1(p_T$ curve is not obtained even within the reduced range $p_T^a < 4$ GeV/$c$.
Amplitudes of the VnDelta harmonics versus n for events with trigger particles having transverse momenta in the range 2-2.5 GeV and associated particles in the range 1.5-2.0 GeV for two centrality classes 0-2% and 2-10%. Note that in the paper the data are plotted multiplied by 100.
Amplitudes of the VnDelta harmonics versus n for events with trigger particles having transverse momenta in the range 2-2.5 GeV and associated particles in the range 1.5-2.0 GeV for three centrality classes 10-20%, 20-30% and 40-50%. Note that in the paper the data are plotted multiplied by 100.
Amplitudes of the VnDelta harmonics versus n for events with trigger particles having transverse momenta in the range 8-15 GeV and associated particles in the range 6-8 GeV for two centrality classes 40-50% and 0-20%. Note that in the paper the data are plotted multiplied by 100.
Two-particle angular correlations were measured in pp collisions at $\sqrt{s} = 7$ TeV for pions, kaons, protons, and lambdas, for all particle/anti-particle combinations in the pair. Data for mesons exhibit an expected peak dominated by effects associated with mini-jets and are well reproduced by general purpose Monte Carlo generators. However, for baryon-baryon and anti-baryon--anti-baryon pairs, where both particles have the same baryon number, a near-side anti-correlation structure is observed instead of a peak. This effect is interpreted in the context of baryon production mechanisms in the fragmentation process. It currently presents a challenge to Monte Carlo models and its origin remains an open question.
$\Delta\eta$ integrated projections of correlation functions for combined pairs of $\rm pp+\overline{p}\overline{p}$, $\rm p\Lambda+\overline{p}\overline{\Lambda}$, and $\Lambda\Lambda+\overline{\Lambda}\overline{\Lambda}$.
$\Delta\eta$ integrated projections of correlation functions for combined pairs of $\rm p\overline{p}$, $\rm p\overline{\Lambda}+\overline{p}\Lambda$, and $\Lambda\overline{\Lambda}$.
$\Delta\eta$ integrated projections of correlation functions for combined pairs of $\rm pp+\overline{p}\overline{p}$ for two transverse momentum intervals (a) $0.5 < p_{\rm T} < 1.25$ GeV/$c$ and (b) $1.25 < p_{\rm T} < 2.5$ GeV/$c$.
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to measure the space-time characteristics of particle production from the effects of quantum statistics and final-state interactions in two-particle correlations. Kaon femtoscopy is an important supplement to that of pions because it allows one to distinguish between different model scenarios working equally well for pions. In particular, we compare the measured 3D kaon radii with a purely hydrodynamical calculation and a model where the hydrodynamic phase is followed by a hadronic rescattering stage. The former predicts an approximate transverse mass ($m_{\mathrm{T}}$) scaling of source radii obtained from pion and kaon correlations. This $m_{\mathrm{T}}$ scaling appears to be broken in our data, which indicates the importance of the hadronic rescattering phase at LHC energies. A $k_{\mathrm{T}}$ scaling of pion and kaon source radii is observed instead. The time of maximal emission of the system is estimated using the three-dimensional femtoscopic analysis for kaons. The measured emission time is larger than that of pions. Our observation is well supported by the hydrokinetic model predictions.
Out projection of raw 3D LCMS K+- K+- correlation function for 0.2 < kT < 0.4 GeV/c bin.
Side projection of raw 3D LCMS K+- K+- correlation function for 0.2 < kT < 0.4 GeV/c bin
Long projection of raw 3D LCMS K+- K+- correlation function for 0.2 < kT < 0.4 GeV/c bin
Angular correlations between unidentified charged trigger particles and various species of charged associated particles (unidentified particles, pions, kaons, protons and antiprotons) are measured by the ALICE detector in p-Pb collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV in the transverse-momentum range $0.3 < p_{\rm T} < 4$ GeV/$c$. The correlations expressed as associated yield per trigger particle are obtained in the pseudorapidity range $|\eta_{\rm lab}|<0.8$. Fourier coefficients are extracted from the long-range correlations projected onto the azimuthal angle difference and studied as a function of $p_{\rm T}$ and in intervals of event multiplicity. In high-multiplicity events, the second-order coefficient for protons, $v_2^p$, is observed to be smaller than that for pions, $v_2^\pi$, up to about $p_{\rm T} = 2$ GeV/$c$. To reduce correlations due to jets, the per-trigger yield measured in low-multiplicity events is subtracted from that in high-multiplicity events. A two-ridge structure is obtained for all particle species. The Fourier decomposition of this structure shows that the second-order coefficients for pions and kaons are similar. The $v_2^p$ is found to be smaller at low $p_{\rm T}$ and larger at higher $p_{\rm T}$ than $v_2^pi$, with a crossing occurring at about 2 GeV. This is qualitatively similar to the elliptic-flow pattern observed in heavy-ion collisions. A mass ordering effect at low transverse momenta is consistent with expectations from hydrodynamic model calculations assuming a collectively expanding system.
The Fourier coefficients V2(2PC,sub) extracted for all charged particles as a function of PT from the correlation in the 0-20% multiplicity class after subraction of the correlation from the 60-100% event class.
The Fourier coefficients V2(2PC,sub) extracted for charged pions as a function of PT from the correlation in the 0-20% multiplicity class after subraction of the correlation from the 60-100% event class.
The Fourier coefficients V2(2PC,sub) extracted for charged kaons as a function of PT from the correlation in the 0-20% multiplicity class after subraction of the correlation from the 60-100% event class.
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