Multi-particle azimuthal correlations in p-Pb and Pb-Pb collisions at the CERN Large Hadron Collider

Measurements of multi-particle azimuthal correlations (cumulants) for charged particles in p-Pb and Pb-Pb collisions are presented. They help address the question of whether there is evidence for global, flow-like, azimuthal correlations in the p-Pb system. Comparisons are made to measurements from the larger Pb-Pb system, where such evidence is established. In particular, the second harmonic two-particle cumulants are found to decrease with multiplicity, characteristic of a dominance of few-particle correlations in p-Pb collisions. However, when a $|\Delta \eta|$ gap is placed to suppress such correlations, the two-particle cumulants begin to rise at high-multiplicity, indicating the presence of global azimuthal correlations. The Pb-Pb values are higher than the p-Pb values at similar multiplicities. In both systems, the second harmonic four-particle cumulants exhibit a transition from positive to negative values when the multiplicity increases. The negative values allow for a measurement of $v_{2}\{4\}$ to be made, which is found to be higher in Pb-Pb collisions at similar multiplicities. The second harmonic six-particle cumulants are also found to be higher in Pb-Pb collisions. In Pb-Pb collisions, we generally find $v_{2}\{4\} \simeq v_{2}\{6\}\neq 0$ which is indicative of a Bessel-Gaussian function for the $v_{2}$ distribution. For very high-multiplicity Pb-Pb collisions, we observe that the four- and six-particle cumulants become consistent with 0. Finally, third harmonic two-particle cumulants in p-Pb and Pb-Pb are measured. These are found to be similar for overlapping multiplicities, when a $|\Delta\eta| > 1.4$ gap is placed.Comment: 25 pages, 11 captioned figures, 3 tables, authors from page 20, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/87

Multiplicity dependence of jet-like two-particle correlations in p-Pb collisions at sNN\sqrt{s_{NN}} = 5.02 TeV

Two-particle angular correlations between unidentified charged trigger and associated particles are measured by the ALICE detector in p-Pb collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV. The transverse-momentum range 0.7 $< p_{\rm{T}, assoc} < p_{\rm{T}, trig} <$ 5.0 GeV/$c$ is examined, to include correlations induced by jets originating from low momen\-tum-transfer scatterings (minijets). The correlations expressed as associated yield per trigger particle are obtained in the pseudorapidity range $|\eta|<0.9$. The near-side long-range pseudorapidity correlations observed in high-multiplicity p-Pb collisions are subtracted from both near-side short-range and away-side correlations in order to remove the non-jet-like components. The yields in the jet-like peaks are found to be invariant with event multiplicity with the exception of events with low multiplicity. This invariance is consistent with the particles being produced via the incoherent fragmentation of multiple parton--parton scatterings, while the yield related to the previously observed ridge structures is not jet-related. The number of uncorrelated sources of particle production is found to increase linearly with multiplicity, suggesting no saturation of the number of multi-parton interactions even in the highest multiplicity p-Pb collisions. Further, the number scales in the intermediate multiplicity region with the number of binary nucleon-nucleon collisions estimated with a Glauber Monte-Carlo simulation.Comment: 23 pages, 6 captioned figures, 1 table, authors from page 17, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/161

Anisotropic flow of charged hadrons, pions and (anti-)protons measured at high transverse momentum in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}}=2.76 TeV

The elliptic, $v_2$, triangular, $v_3$, and quadrangular, $v_4$, azimuthal anisotropic flow coefficients are measured for unidentified charged particles, pions and (anti-)protons in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV with the ALICE detector at the Large Hadron Collider. Results obtained with the event plane and four-particle cumulant methods are reported for the pseudo-rapidity range $|\eta|<0.8$ at different collision centralities and as a function of transverse momentum, $p_{\rm T}$, out to $p_{\rm T}=20$ GeV/$c$. The observed non-zero elliptic and triangular flow depends only weakly on transverse momentum for $p_{\rm T}>8$ GeV/$c$. The small $p_{\rm T}$ dependence of the difference between elliptic flow results obtained from the event plane and four-particle cumulant methods suggests a common origin of flow fluctuations up to $p_{\rm T}=8$ GeV/$c$. The magnitude of the (anti-)proton elliptic and triangular flow is larger than that of pions out to at least $p_{\rm T}=8$ GeV/$c$ indicating that the particle type dependence persists out to high $p_{\rm T}$.Comment: 16 pages, 5 captioned figures, authors from page 11, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/186

Charge separation relative to the reaction plane in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}}= 2.76 TeV

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.Comment: 12 pages, 3 captioned figures, authors from page 2 to 6, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/286

A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio

Particle-yield modification in jet-like azimuthal di-hadron correlations in Pb-Pb collisions at sNN\sqrt{s_{\rm NN}} = 2.76 TeV

The yield of charged particles associated with high-$p_{\rm T}$ trigger particles ($8 < p_{\rm T} < 15$ GeV/$c$) is measured with the ALICE detector in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV relative to proton-proton collisions at the same energy. The conditional per-trigger yields are extracted from the narrow jet-like correlation peaks in azimuthal di-hadron correlations. In the 5% most central collisions, we observe that the yield of associated charged particles with transverse momenta $p_{\rm T}> 3$ GeV/$c$ on the away-side drops to about 60% of that observed in pp collisions, while on the near-side a moderate enhancement of 20-30% is found.Comment: 15 pages, 2 captioned figures, 1 table, authors from page 10, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/350

Transverse sphericity of primary charged particles in minimum bias proton-proton collisions at s=0.9\sqrt{s}=0.9, 2.76 and 7 TeV

Measurements of the sphericity of primary charged particles in minimum bias proton--proton collisions at $\sqrt{s}=0.9$, 2.76 and 7 TeV with the ALICE detector at the LHC are presented. The observable is linearized to be collinear safe and is measured in the plane perpendicular to the beam direction using primary charged tracks with $p_{\rm T}\geq0.5$ GeV/c in $|\eta|\leq0.8$. The mean sphericity as a function of the charged particle multiplicity at mid-rapidity ($N_{\rm ch}$) is reported for events with different $p_{\rm T}$ scales ("soft" and "hard") defined by the transverse momentum of the leading particle. In addition, the mean charged particle transverse momentum versus multiplicity is presented for the different event classes, and the sphericity distributions in bins of multiplicity are presented. The data are compared with calculations of standard Monte Carlo event generators. The transverse sphericity is found to grow with multiplicity at all collision energies, with a steeper rise at low $N_{\rm ch}$, whereas the event generators show the opposite tendency. The combined study of the sphericity and the mean $p_{\rm T}$ with multiplicity indicates that most of the tested event generators produce events with higher multiplicity by generating more back-to-back jets resulting in decreased sphericity (and isotropy). The PYTHIA6 generator with tune PERUGIA-2011 exhibits a noticeable improvement in describing the data, compared to the other tested generators.Comment: 21 pages, 9 captioned figures, 3 tables, authors from page 16, published version, figures from http://aliceinfo.cern.ch/ArtSubmission/node/308

Azimuthal anisotropy of charged jet production in root s(NN)=2.76 TeV Pb-Pb collisions

We present measurements of the azimuthal dependence of charged jet production in central and semi-central root s(NN) = 2.76 TeV Pb-Pb collisions with respect to the second harmonic event plane, quantified as nu(ch)(2) (jet). Jet finding is performed employing the anti-k(T) algorithm with a resolution parameter R = 0.2 using charged tracks from the ALICE tracking system. The contribution of the azimuthal anisotropy of the underlying event is taken into account event-by-event. The remaining (statistical) region-to-region fluctuations are removed on an ensemble basis by unfolding the jet spectra for different event plane orientations independently. Significant non-zero nu(ch)(2) (jet) is observed in semi-central collisions (30-50% centrality) for 20 <p(T)(ch) (jet) <90 GeV/c. The azimuthal dependence of the charged jet production is similar to the dependence observed for jets comprising both charged and neutral fragments, and compatible with measurements of the nu(2) of single charged particles at high p(T). Good agreement between the data and predictions from JEWEL, an event generator simulating parton shower evolution in the presence of a dense QCD medium, is found in semi-central collisions. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Peer reviewe

Forward-central two-particle correlations in p-Pb collisions at root s(NN)=5.02 TeV

Two-particle angular correlations between trigger particles in the forward pseudorapidity range (2.5 2GeV/c. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B. V.Peer reviewe