Four-particle Cumulants Research Articles

Recent ATLAS measurements of azimuthal anisotropies in pp and p+Pb collisions

The azimuthal anisotropies of particle yields observed in relativistic heavy-ion collisions are considered as an evidence of the formation on a deconfined Quark-Gluon Plasma produced in these collisions. Interestingly, recent measurements in pp and p+Pb systems from ATLAS and other experiments show similar features as those observed in A+A collisions, indicating the possibility of the production of such a deconfined medium in smaller collision systems. This report presents a summary of the recent ATLAS results on azimuthal anisotropies in pp collisions at 5.02 TeV and 13 TeV, p+Pb collisions at 5.02 TeV and 8.16 TeV as well as in peripheral 2.76 TeV Pb+Pb interactions. It includes measurements of two-particle correlations of charged particles as well as correlations of heavy flavor muons and charged particles in Δϕ and Δη, with a template fitting procedure used to subtract the dijet contributions. Additionally, measurements of cumulants of multi-particle correlations, cn{2-8} are presented. The two-particle correlations and cumulants confirm a presence of collective phenomena in these collision systems, but the results on four-particle cumulants for pp collisions do not demonstrate a similar collective behaviour. However, the cumulant measurements in small collision systems can be biased by non-flow correlations. A novel subevent cumulant method that suppresses the contribution of non-flow effects was proposed recently by ATLAS allowing to measure significant azimuthal anisotropies in both pp and p+Pb collisions.

Two- and Multi-particle Azimuthal Correlations in Small Collision Systems with the ATLAS Detector

The recent ATLAS results on two- and multi-particle azimuthal correlations of charged particles are presented for s=5.02 TeV and 13 TeV pp, sNN=5.02 TeV p+Pb and sNN=2.76 TeV low-multiplicity Pb+Pb collisions. To suppress the “non-flow” contribution from the correlations, a template fitting procedure is used in the two-particle correlations (2PC) measurements, while for multi-particle correlations the cumulant method is applied. The correlations are expressed in the form of Fourier harmonics vn(n=2,3,4) measuring the global azimuthal anisotropy of produced particles. The measurements presented hereafter confirm the evidence for collective phenomena in high-multiplicity p+Pb and low-multiplicity Pb+Pb collisions. For pp collisions the results on four-particle cumulants do not demonstrate a similar collective behaviour.

New insights of multi-particle azimuthal correlations with symmetric cumulants in p-p, p-Pb, and Pb-Pb collisions

The first comparison of anisotropy harmonics (vn, n = 2–4) and event-by-event correlations of different orders between p–p (13 TeV), p–Pb (5.02 and 8.16 TeV) and Pb–Pb (5.02 TeV) as a function of multiplicity is presented. The vn coefficients are extracted via long-range (|Δη|>2) two-particle correlations reaching a very-high-multiplicity region. Event-by-event correlations among v2, v3 and v4 are measured using the four-particle symmetric cumulant (SC(n,m), n = 2, m = 3, 4). For high-multiplicity (more than 100 tracks) events, v2 is found to have a negative correlation with the v3, while the v2 and v4 are positively correlated. Normalized by the two-particle vn, the SC(2,3) are quantitatively similar for p–Pb and Pb–Pb data, while a strong system size dependence is observed for SC(2,4). These new data provide important insights to the origin of collectivity observed in small collision systems.

Measurement of multi-particle azimuthal correlations with the subevent cumulant method in pp and p+Pb collisions with the ATLAS detector

The measurement of four-particle cumulant and anisotropic elliptic flow coefficient for the second harmonic, c2{4} and v2{4}, are presented using pp data at s=5.02 and s=13 TeV and p+Pb data at sNN=5.02 TeV. The values of c2{4} are calculated using the standard cumulant method and recently proposed two and three subevent methods. The three subevent method gives a negative c2{4}, and thus a well-defined v2{4} (which equals (−c2{4})1/4), in these collision systems. v2{4} is found to be smaller than v2 measured using the two-particle correlation method (denoted as v2{2}), as expected for a collective behavior. Following a recent model framework, the measured values of v2{4} and v2{2} are used to probe the number of sources in the initial state collision geometry.

Measurement of multi-particle azimuthal correlations in pp, p\xa0+\xa0Pb and low-multiplicity Pb\xa0+\xa0Pb collisions with the ATLAS detector

Multi-particle cumulants and corresponding Fourier harmonics are measured for azimuthal angle distributions of charged particles in pp collisions at sqrt{s} = 5.02 and 13 TeV and in p + Pb collisions at sqrt{s_{_text {NN}}} = 5.02 TeV, and compared to the results obtained for low-multiplicity mathrm{Pb}~+~mathrm{Pb} collisions at sqrt{s_{_text {NN}}} = 2.76 TeV. These measurements aim to assess the collective nature of particle production. The measurements of multi-particle cumulants confirm the evidence for collective phenomena in p + Pb and low-multiplicity mathrm{Pb}~+~mathrm{Pb} collisions. On the other hand, the pp results for four-particle cumulants do not demonstrate collective behaviour, indicating that they may be biased by contributions from non-flow correlations. A comparison of multi-particle cumulants and derived Fourier harmonics across different collision systems is presented as a function of the charged-particle multiplicity. For a given multiplicity, the measured Fourier harmonics are largest in mathrm{Pb}~+~mathrm{Pb}, smaller in p + Pb and smallest in pp collisions. The pp results show no dependence on the collision energy, nor on the multiplicity.

Fluctuations of Flow Harmonics in Pb+Pb Collisions at $\sqrt {s_{NN}}=2.76$ TeV from the Glauber Model

In the framework of the Glauber model as implemented in GLISSANDO 2, we study the fluctuations of flow harmonics in Pb+Pb collisions at the LHC centre-of-mass energy of 2.76 TeV. The model with wounded nucleons and the admixture of binary collisions leads to reasonable agreement for the ellipticity and triangularity fluctuations with the experimental data from the ATLAS, ALICE, and CMS collaborations, verifying the assumption that the initial eccentricity is approximately proportional to the harmonic flow of charged particles. While the agreement, in particular at the level of event-by-event distributions of eccentricities/flow coefficients in not perfect, it leads to a fair (at the level of a few percent for all centralities except the most peripheral collisions) description of the scaled standard deviation and the F measure which involve the four-particle cumulants. We also discuss the case of quadrangular flow. Computer scripts that generate our results from the GLISSANDO 2 simulations are provided.

Azimuthal Anisotropy in U+U and Au+Au Collisions at RHIC.

Collisions between prolate uranium nuclei are used to study how particle production and azimuthal anisotropies depend on initial geometry in heavy-ion collisions. We report the two- and four-particle cumulants, v_{2}{2} and v_{2}{4}, for charged hadrons from U+U collisions at sqrt[s_{NN}]=193 GeV and Au+Au collisions at sqrt[s_{NN}]=200 GeV. Nearly fully overlapping collisions are selected based on the energy deposited by spectators in zero degree calorimeters (ZDCs). Within this sample, the observed dependence of v_{2}{2} on multiplicity demonstrates that ZDC information combined with multiplicity can preferentially select different overlap configurations in U+U collisions. We also show that v_{2} vs multiplicity can be better described by models, such as gluon saturation or quark participant models, that eliminate the dependence of the multiplicity on the number of binary nucleon-nucleon collisions.

Investigation of possible hadronic flow insNN=5.02TeVp−Pbcollisions

Using the ultrarelativistic quantum molecular dynamics (UrQMD) model, we investigate azimuthal correlations in $p\ensuremath{-}\mathrm{Pb}$ collisions at $\sqrt{{s}_{\mathit{NN}}}=5.02\phantom{\rule{0.28em}{0ex}}\mathrm{TeV}$. Comparison with the experimental data shows that UrQMD cannot reproduce the multiplicity dependence of two- and four-particle cumulants, especially the transition from positive to negative values of ${c}_{2}{4}$ in high-multiplicity events, which has been taken as experimental evidence of collectivity in $p\ensuremath{-}\mathrm{Pb}$ collisions. Meanwhile, UrQMD cannot describe the differential elliptic flow ${v}_{2}({p}_{\mathrm{T}})$ of all charged hadrons at various multiplicity classes. These discrepancies show that the simulated hadronic $p\ensuremath{-}\mathrm{Pb}$ systems cannot generate enough collective flow as observed in experiment, the associated hadron emissions are largely influenced by nonflow effects. However, the characteristic ${v}_{2}({p}_{\mathrm{T}})$ mass ordering of pions, kaons, and protons is observed in UrQMD, which is the consequence of hadronic interactions and not necessarily associated with strong fluid-like expansions.

Isolation of flow and nonflow correlations by two- and four-particle cumulant measurements of azimuthal harmonics in [formula omitted] Au+Au collisions

A data-driven method was applied to Au+Au collisions at sNN=200 GeV made with the STAR detector at RHIC to isolate pseudorapidity distance Δη-dependent and Δη-independent correlations by using two- and four-particle azimuthal cumulant measurements. We identified a Δη-independent component of the correlation, which is dominated by anisotropic flow and flow fluctuations. It was also found to be independent of η within the measured range of pseudorapidity |η|<1. In 20–30% central Au+Au collisions, the relative flow fluctuation was found to be 34%±2%(stat.)±3%(sys.) for particles with transverse momentum pT less than 2 GeV/c. The Δη-dependent part, attributed to nonflow correlations, is found to be 5%±2%(sys.) relative to the flow of the measured second harmonic cumulant at |Δη|>0.7.

Azimuthal asymmetries and the emergence of “collectivity” from multi-particle correlations in high-energy pA collisions

We show how angular asymmetries ∼cos⁡2ϕ can arise in dipole scattering at high energies. We illustrate the effects due to anisotropic fluctuations of the saturation momentum of the target with a finite correlation length in the transverse impact parameter plane, i.e. from a domain-like structure. We compute the two-particle azimuthal cumulant in this model including both one-particle factorizable as well as genuine two-particle non-factorizable contributions to the two-particle cross section. We also compute the full BBGKY hierarchy for the four-particle azimuthal cumulant and find that only the fully factorizable contribution to c2{4} is negative while all contributions from genuine two, three and four-particle correlations are positive. Our results may provide some qualitative insight into the origin of azimuthal asymmetries in p+Pb collisions at the LHC which reveal a change of sign of c2{4} in high-multiplicity events.

Multiparticle azimuthal correlations inp-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.

Measurement of flow harmonics with multi-particle cumulants in Pb+Pb collisions at [Formula: see text]TeV with the ATLAS detector.

ATLAS measurements of the azimuthal anisotropy in lead–lead collisions at sqrt{s_{mathrm {NN}}}=2.76 TeV are shown using a dataset of approximately 7 upmu b^{-1} collected at the LHC in 2010. The measurements are performed for charged particles with transverse momenta 0.5<p_{mathrm {T}}<20 GeV and in the pseudorapidity range |eta |<2.5. The anisotropy is characterized by the Fourier coefficients, mathrm {v}_n, of the charged-particle azimuthal angle distribution for n = 2–4. The Fourier coefficients are evaluated using multi-particle cumulants calculated with the generating function method. Results on the transverse momentum, pseudorapidity and centrality dependence of the mathrm {v}_n coefficients are presented. The elliptic flow, mathrm {v}_2, is obtained from the two-, four-, six- and eight-particle cumulants while higher-order coefficients, mathrm {v}_3 and mathrm {v}_4, are determined with two- and four-particle cumulants. Flow harmonics mathrm {v}_n measured with four-particle cumulants are significantly reduced compared to the measurement involving two-particle cumulants. A comparison to mathrm {v}_n measurements obtained using different analysis methods and previously reported by the LHC experiments is also shown. Results of measurements of flow fluctuations evaluated with multi-particle cumulants are shown as a function of transverse momentum and the collision centrality. Models of the initial spatial geometry and its fluctuations fail to describe the flow fluctuations measurements.

Flow measurements and selection of body–body and tip–tip enhanced samples in U + U collisions at STAR

Abstract The azimuthal anisotropy of particle production is commonly used in high-energy nuclear collisions to study the early evolution of the expanding system. The prolate shape of uranium nuclei provides the possibility to study how the initial geometry of the nuclei affects the azimuthal distributions. In this paper, the two- and four-particle cumulants, v 2 { 2 } and v 2 { 4 } , from U + U collisions at s NN = 193 GeV and Au + Au collisions at s NN = 200 GeV for inclusive charged hadrons will be presented. The STAR Zero Degree Calorimeter is used to subdivide the 0–1% centrality bin into even finer centralities. Differences were observed between the multiplicity dependence of v 2 { 2 } for most central Au + Au and U + U collisions. It has also been demonstrated that ZDC and multiplicity in combination provide a way to select body–body or tip–tip enhanced samples of central U + U collisions. Comparisons to models show that an IP-Glasma model based on gluon saturation for the initial state better describes the slope of v 2 { 2 } vs. multiplicity than the Glauber model with a standard two-component model for multiplicity.

Flow harmonics in Pb + Pb collisions at SNN=2.76 TeV with the ATLAS detector

The measurement of the azimuthal anisotropy of charged particles produced in lead–lead collisions at SNN=2.76TeV is reported. The Fourier coefficients vn of the azimuthal angle distribution are obtained using multi-particle cumulants. The results on the transverse momentum and centrality dependence of the elliptic flow (v2) obtained from two-, four-, six- and eight-particle cumulants are presented. Higher-order harmonics, v3 and v4, are also derived using two- and four-particle cumulants and shown as a function of centrality and transverse momentum. A reduction of contributions from correlations not related to the collective flow are discussed. Event-by-event fluctuations of the flow harmonics are also presented as a function of transverse momentum and the collision centrality.

Anisotropic flow and flow fluctuations for Au + Au atsNN=200GeV in a multiphase transport model

Anisotropic flow coefficients and their fluctuations are investigated for Au+Au collisions at center of mass energy $\sqrt{s_{NN}}$ = 200 GeV by using a multi-phase transport model with string melting scenario. Experimental results of azimuthal anisotropies by means of the two- and four-particle cumulants are generally well reproduced by the model including both parton cascade and hadronic rescatterings. Event-by-event treatments of the harmonic flow coefficients $v_n$ (for n = 2, 3 and 4) are performed, in which event distributions of $v_n$ for different orders are consistent with Gaussian shapes over all centrality bins. Systematic studies on centrality, transverse momentum ($p_{T}$) and pseudo-rapidity ($\eta$) dependencies of anisotropic flows and quantitative estimations of the flow fluctuations are presented. The $p_{T}$ and $\eta$ dependencies of absolute fluctuations for both $v_2$ and $v_3$ follow similar trends as their flow coefficients. Relative fluctuation of triangular flow $v_3$ is slightly centrality-dependent, which is quite different from that of elliptic flow $v_2$. It is observed that parton cascade has a large effect on the flow fluctuations, but hadronic scatterings make little contribution to the flow fluctuations, which indicates flow fluctuations are mainly modified during partonic evolution stage.

Azimuthal anisotropy measurements by STAR

The recent study of centrality and transverse momentum ($p_{T}$) dependence of inclusive charged hardron elliptic anisotropy ($v_{2}$) at midrapidity ($|\eta|<1.0$) in Au+Au collision at $\sqrt{s_{NN}} =$ 7.7, 11.5, 19.6, 27, and 39 GeV in STAR Beam Energy Scan program is presented. We show that the observed increase of inclusive $v_{2}$ is mainly due to the average $p_{T}$ increase with energy. In Au+Au 200 GeV collisions, the triangular anisotropy ($v_{3}$) measurements highly depend on measurment methods; $v_{3}$ is strongly dependent on $\Delta\eta$. The difference between two- and four-particle cumulants $v_{2}\lbrace{2}\rbrace$ and $v_{2}\lbrace{4}\rbrace$ for Au+Au and Cu+Cu collision at $\sqrt{s_{NN}} = $ 62.4 and 200 GeV is used to explore flow fluctuations. Furthermore, by exploiting the symmetry of average flow in pseudorapidity $\eta$ about mid-rapidty, the $\Delta\eta$-dependent and independent components are seperated using $v_{2}\lbrace2\rbrace$ and $v_{2}\lbrace{4}\rbrace$.

Flow and Correlations in PbPb and pPb Collisions from CMS Experiment

Measurements of two- and four-particle angular correlations for inclusive charged particles in pPb collisions at p sNN = 5:02 TeV are presented over a wide pseu- dorapidity range, | | < 2.5 and full azimuth from the CMS experiment. Results from 31 nb 1 of pPb data, collected during the 2013 LHC running are compared to 2.76 TeV semi peripheral PbPb collision data, from 2011 PbPb run, having similar range of particle multiplicities. The second-order (v2) and third-order (v3) anisotropy harmonics are ex- tracted using the two-particle azimuthal correlation technique. v2 is also extracted using a four-particle cumulant method to further explore the multi-particle nature of correlations in pPb collisions. We observe a remarkable similarity in the v3 signal as a function of multiplicity between pPb and PbPb systems.

Production anisotropy of h±, π± and p/p¯ at high-pT in Pb–Pb collisions at sNN=2.76TeV

Abstract The high- P T particle production anisotropy in Pb–Pb collisions at s N N = 2.76 TeV studied by the ALICE experiment is presented. The event plane and the four-particle cumulant method are used to extract the ν 2 and ν 3 flow coefficients of unidentified charged hadrons, pions and protons out to p T = 20 GeV / c . The observed non-zero values of the elliptic flow in the high- p T region where the collective phenomena are negligible are discussed.

Collective dynamics in high-energy proton-nucleus collisions

We analyze the proton-lead collisions at the LHC energy of 5.02TeV in the three-stage approach, previously used to successfully describe the relativistic A-A collisions. The approach consists of the early phase, modeled with the Glauber model, the event-by-event viscous 3+1 dimensional (3+1 D) relativistic hydrodynamics, and the statistical hadronization at freeze-out. We show that features typical of collective dynamics, such as the harmonic flow and the ridge structures in the two-particle correlations in relative azimuth and pseudorapidity, may be naturally explained in our framework. In the proton-nucleus system the harmonic flow is generated from an initially event-by-event deformed system and is entirely due to these initial fluctuations. Notably, fluctuations of strength of the initial Glauber sources which yield the observed distribution of hadron multiplicities and, at the same time, lead to correct values of the elliptic flow coefficients both from the two- and four-particle cumulant method, as measured by the ATLAS collaboration. The azimuthally asymmetric flow is not modified significantly when changing the viscosity coefficient, the initial time for the collective expansion, or the initial size of the fireball. The results present an estimate of the collective component in the two-particle correlations measured experimentally. We demonstrate that the harmonic flow coefficients can be experimentally measured with methods based on large rapidity gaps which reduce some of the other sources of correlations.

Measurement with the ATLAS detector of multi-particle azimuthal correlations in [formula omitted] collisions at [formula omitted

In order to study further the long-range correlations (“ridge”) observed recently in p+Pb collisions at sNN=5.02 TeV, the second-order azimuthal anisotropy parameter of charged particles, v2, has been measured with the cumulant method using the ATLAS detector at the LHC. In a data sample corresponding to an integrated luminosity of approximately 1 μb−1, the parameter v2 has been obtained using two- and four-particle cumulants over the pseudorapidity range |η|<2.5. The results are presented as a function of transverse momentum and the event activity, defined in terms of the transverse energy summed over 3.1<η<4.9 in the direction of the Pb beam. They show features characteristic of collective anisotropic flow, similar to that observed in Pb+Pb collisions. A comparison is made to results obtained using two-particle correlation methods, and to predictions from hydrodynamic models of p+Pb collisions. Despite the small transverse spatial extent of the p+Pb collision system, the large magnitude of v2 and its similarity to hydrodynamic predictions provide additional evidence for the importance of final-state effects in p+Pb reactions.