Four-particle Cumulants Research Articles

Disentangling the development of collective flow in high energy proton proton collisions with a multiphase transport model

In this work, we investigate the collective flow development in high energy proton proton (pp) collisions with a multiphase transport model (AMPT) based on PYTHIA8 initial conditions with a sub-nucleon structure. It is found that the PYTHIA8 based AMPT model can reasonably describe both the charged hadron productions and elliptic flow experimental data measured in pp collisions at s=13 TeV. By turning on the parton and hadron rescatterings in AMPT separately, we find that the observed collective flow in pp collisions is largely developed during the parton evolution, while no significant flow effect can be generated with the pure hadronic rescatterings. It is also shown that the parton escape mechanism is important for describing both the magnitude of the two-particle cumulant and the sign of the four-particle cumulants. We emphasize that the strong mass ordering of the elliptic flow results from the coalescence process in the transport model and can thus be regarded as unique evidence related to the creation of deconfined parton matter in high energy pp collisions.

Symmetric cumulant sc2,4{4} and asymmetric cumulant ac2{3} from transverse momentum conservation and flow

Multiparticle cumulants method can be used to reveal long-range collectivity in small and large colliding systems. The four-particle symmetric cumulant sc2,4{4}, three-particle asymmetric cumulant ac2{3}, and the normalized cumulants nsc2,4{4} and nac2{3} from the transverse momentum conservation and flow are calculated. The interplay between the two effects is also investigated. Our results are in a good agreement with the recent ATLAS measurements of multiparticle azimuthal correlations with the subevent cumulant method, which provides insight into the origin of collective flow in small systems. Published by the American Physical Society 2024

Anisotropic flow and flow fluctuations of identified hadrons in Pb–Pb collisions at sqrt{s_{textrm{NN}}} = 5.02 TeV

The first measurements of elliptic flow of π±, K±, textrm{p}+overline{textrm{p}} , {textrm{K}}_{textrm{S}}^0 , Lambda +overline{Lambda} , ϕ, {Xi}^{-}+{overline{Xi}}^{+} , and {varOmega}^{-}+{overline{varOmega}}^{+} using multiparticle cumulants in Pb–Pb collisions at sqrt{s_{textrm{NN}}} = 5.02 TeV are resented. Results obtained with two- (v2{2}) and four-particle cumulants (v2{4}) are shown as a function of transverse momentum, pT, for various collision centrality intervals. Combining the data for both v2{2} and v2{4} also allows us to report the first measurements of the mean elliptic flow, elliptic flow fluctuations, and relative elliptic flow fluctuations for various hadron species. These observables probe the event-by-event eccentricity fluctuations in the initial state and the contributions from the dynamic evolution of the expanding quark–gluon plasma. The characteristic features observed in previous pT-differential anisotropic flow measurements for identified hadrons with two-particle correlations, namely the mass ordering at low pT and the approximate scaling with the number of constituent quarks at intermediate pT, are similarly present in the four-particle correlations and the combinations of v2{2} and v2{4}. In addition, a particle species dependence of flow fluctuations is observed that could indicate a significant contribution from final state hadronic interactions. The comparison between experimental measurements and CoLBT model calculations, which combine the various physics processes of hydrodynamics, quark coalescence, and jet fragmentation, illustrates their importance over a wide pT range.

Nonequilibrium components in the region of very low transverse momentum in high-energy nuclear collisions

We analyze Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV with a novel framework based on the dynamical core--corona picture that describes particle productions from both equilibrium and non-equilibrium components. We remark the possibility of the contribution from non-equilibrium components at very low transverse momentum ($p_{T}$) region and show that such contributions significantly affect $p_{T}$-integrated four-particle cumulants. These results strongly suggest the necessity of non-equilibrium components when one extracts properties of the quark-gluon plasma from experimental data using sophisticated dynamical models based on relativistic hydrodynamics.

Probing Charm Quark Dynamics via Multiparticle Correlations in Pb-Pb Collisions at sqrt[s_{NN}]=5.02 TeV.

Multiparticle azimuthal correlations of prompt D^{0} mesons are measured in Pb-Pb collisions at a nucleon-nucleon center-of-mass energy of sqrt[s_{NN}]=5.02 TeV. For the first time, a four-particle cumulant method is used to extract the second Fourier coefficient of the azimuthal distribution (v_{2}) of D^{0} mesons as a function of event centrality and the D^{0} transverse momentum. The ratios of the four-particle v_{2} values to previously measured two-particle cumulant results provide direct experimental access to event-by-event fluctuations of charm quark azimuthal anisotropies. These ratios are also found to be comparable to those of inclusive charged particles in the event. However, hints of deviations are seen in the most central and peripheral collisions. To investigate the origin of flow fluctuations in the charm sector, these measurements are compared to a model implementing fluctuations of charm quark energy loss via collisional or radiative processes in the quark-gluon plasma. These models cannot quantitatively describe the data over the full transverse momentum and centrality ranges, although the calculations with collisional energy loss provide a better description of the data.

Correlations of azimuthal anisotropy Fourier harmonics with subevent cumulants in pPb collisions at sNN=8.16TeV

Event-by-event correlations of azimuthal anisotropy Fourier coefficients ($v_n$) in 8.16 TeV pPb collision data, collected by the CMS experiment at the LHC, are extracted using a subevent four-particle cumulant technique. Each combination of four charged particles are selected from either two, three, or four distinct subevent regions of a pseudorapidity range from $-$2.4 to 2.4 of the CMS tracker, and with transverse momentum between 0.3 and 3.0 GeV. Using the subevent cumulant technique, correlations between $v_n$ of different orders are measured as functions of particle multiplicity and compared to the standard cumulant method without subevents over a wide event multiplicity range. At high multiplicity, the $v_2$ and $v_3$ coefficients exhibit an anticorrelation; this behavior is observed consistently using various methods. The $v_2$ and $v_4$ correlation strength is found to depend on the number of subevents used in the calculation. As the event multiplicity decreases, the results from different subevent methods diverge because of different contributions of non-collective or few-particle correlations. Correlations extracted with the four-subevent method exhibit a tendency to diminish monotonically toward the lowest multiplicity region (about 20 charged tracks) investigated. These findings extend previous studies to a significantly lower event multiplicity range and establish the evidence for the onset of long-range collective multiparticle correlations in small system collisions.

Searching for small droplets of hydrodynamic fluid in proton\u2013proton collisions at the LHC

In this paper, we investigate the hydrodynamic collectivity in proton-proton collisions at sqrt{s}= 13 TeV, using iEBE-VISHNU with three different initial conditions, namely, HIJING, super-MC and TRENTo. With properly tuned parameters, hydrodynamics gives reasonable descriptions of the measured two-particle correlations, including the integrated and p_mathrm{T}-differential flow. However, the hydrodynamic simulations fail to describe the negative four-particle cumulant c_2^v{4} as measured in experiments. The four-particle cumulant c_2^v{4} is always positive after hydrodynamic evolutions. Further investigations show that the non-linear response between the final v_2 and the initial varepsilon _2 becomes significant in p-p systems. This leads to a large deviation from linear eccentricity scaling and generates additional flow fluctuations, which results in a positive c_2^v{4} even with a negative c_2^varepsilon {4} from the initial state. We also presented the first hydrodynamic calculations of mixed harmonic azimuthal correlations in p-p collisions. Although many qualitative features are reproduced by the hydrodynamic simulations, the measured negative normalized Symmetric-Cumulant nsc_{2,3}{4} cannot be reproduced. Obviously hydrodynamic calculations have a general difficulty to describe the data. It triggers that whether hydrodynamics with a new initial state could solve this puzzle, or hydrodynamics itself is not the appreciated mechanism of the observed collectivity, and the non-hydrodynamic modes become important in p-p collisions at the LHC.

Fluctuations of anisotropic flow in Pb+Pb collisions at sqrt{{mathrm{s}}_{mathrm{NN}}} = 5.02 TeV with the ATLAS detector

Multi-particle azimuthal cumulants are measured as a function of centrality and transverse momentum using 470 μb−1 of Pb+Pb collisions at sqrt{s_{mathrm{NN}}} = 5.02 TeV with the ATLAS detector at the LHC. These cumulants provide information on the event-by-event fluctuations of harmonic flow coefficients vn and correlated fluctuations between two harmonics vn and vm. For the first time, a non-zero four-particle cumulant is observed for dipolar flow, v1. The four-particle cumulants for elliptic flow, v2, and triangular flow, v3, exhibit a strong centrality dependence and change sign in ultra-central collisions. This sign change is consistent with significant non-Gaussian fluctuations in v2 and v3. The four-particle cumulant for quadrangular flow, v4, is found to change sign in mid-central collisions. Correlations between two harmonics are studied with three- and four-particle mixed-harmonic cumulants, which indicate an anti-correlation between v2 and v3, and a positive correlation between v2 and v4. These correlations decrease in strength towards central collisions and either approach zero or change sign in ultra-central collisions. To investigate the possible flow fluctuations arising from intrinsic centrality or volume fluctuations, the results are compared between two different event classes used for centrality definitions. In peripheral and mid-central collisions where the cumulant signals are large, only small differences are observed. In ultra-central collisions, the differences are much larger and transverse momentum dependent. These results provide new information to disentangle flow fluctuations from the initial and final states, as well as new insights on the influence of centrality fluctuations.

Investigations of Anisotropic Flow Using Multiparticle Azimuthal Correlations in pp, p-Pb, Xe-Xe, and Pb-Pb Collisions at the LHC.

Measurements of anisotropic flow coefficients (v_{n}) and their cross-correlations using two- and multiparticle cumulant methods are reported in collisions of pp at sqrt[s]=13 TeV, p-Pb at a center-of-mass energy per nucleon pair sqrt[s_{NN}]=5.02 TeV, Xe-Xe at sqrt[s_{NN}]=5.44 TeV, and Pb-Pb at sqrt[s_{NN}]=5.02 TeV recorded with the ALICE detector. The multiplicity dependence of v_{n} is studied in a very wide range from 20 to 3000 particles produced in the midrapidity region |η|<0.8 for the transverse momentum range 0.2<p_{T}<3.0 GeV/c. An ordering of the coefficients v_{2}>v_{3}>v_{4} is found in pp and p-Pb collisions, similar to that seen in large collision systems, while a weak v_{2} multiplicity dependence is observed relative to nucleus-nucleus collisions in the same multiplicity range. Using a novel subevent method, v_{2} measured with four-particle cumulants is found to be compatible with that from six-particle cumulants in pp and p-Pb collisions. The magnitude of the correlation between v_{n}^{2} and v_{m}^{2}, evaluated with the symmetric cumulants SC(m,n) is observed to be positive at all multiplicities for v_{2} and v_{4}, while for v_{2} and v_{3} it is negative and changes sign for multiplicities below 100, which may indicate a different v_{n} fluctuation pattern in this multiplicity range. The observed long-range multiparticle azimuthal correlations in high multiplicity pp and p-Pb collisions can neither be described by pythia 8 nor by impact-parameter-Glasma, music, and ultrarelativistic quantum molecular dynamics model calculations, and hence, provide new insights into the understanding of collective effects in small collision systems.

Measurement of the flow harmonic correlations in pp, p+Pb and low multiplicity Pb+Pb collisions with the ATLAS detector at the LHC

Recent measurements of the correlations between flow harmonics obtained using four-particle symmetric cumulants and three-particle asymmetric cumulants with the ATLAS detector at the LHC are described. The data sets of pp, p+Pb and peripheral Pb+Pb collisions at various energies are analyzed, aiming to probe the long-range collective nature of multi-particle production in small systems. The sensitivity of the standard cumulant method to non-flow correlations is investigated by introducing the subevents method. A systematic reduction of non-flow effects is observed when using the two-subevent method. Further reduction is observed with the three-subevent method that is consistent with the results obtained with the four-subevent one. A negative correlation between ν2 and ν3 and a positive correlation between ν2 and ν4, for all studied collision systems and over full multiplicity range, is observed. The correlation strength computed as symmetric cumulants normalized by the 〈νn2〉 is similar for all collision systems and weakly depends on multiplicity. These measurements provide new evidence for long-range multi-particle collectivity in small collision systems and quantify the nature of its event-by-event fluctuations.

Flow fluctuations in Pb+Pb collisions at [formula omitted] with the ATLAS detector

Measurements of four-particle cumulants cn{4} for n=1,2,3,4 are presented using 470μb−1 of Pb+Pb collisions at sNN=5.02TeV with the ATLAS detector at the LHC. These cumulants provide information on the event-by-event fluctuations of single harmonics p(vn). For the first time, a negative c1{4} is observed. The c4{4} is found to be negative in central collisions but changes sign around 20–25% centrality. This behavior is consistent with a nonlinear contribution to v4 that is proportional to v22. c2{4} and c3{4} are calculated using two reference event classes in order to investigate the influence of volume fluctuations. Over most of the centrality range, c2{4} and c3{4} are found to be negative, while in the ultra-central collisions, c2{4} changes sign and becomes positive, suggesting a deviation from Gaussian behavior in the event-by-event fluctuation of v2. The magnitudes of the sign change are also found to be dependent of the event class definition.

Correlated long-range mixed-harmonic fluctuations measured in pp, p+Pb and low-multiplicity Pb+Pb collisions with the ATLAS detector

Correlations of two flow harmonics vn and vm via three- and four-particle cumulants are measured in 13 TeV pp, 5.02 TeV p+Pb, and 2.76 TeV peripheral Pb+Pb collisions with the ATLAS detector at the LHC. The goal is to understand the multi-particle nature of the long-range collective phenomenon in these collision systems. The large non-flow background from dijet production present in the standard cumulant method is suppressed using a method of subevent cumulants involving two, three and four subevents separated in pseudorapidity. The results show a negative correlation between v2 and v3 and a positive correlation between v2 and v4 for all collision systems and over the full multiplicity range. However, the magnitudes of the correlations are found to depend on the event multiplicity, the choice of transverse momentum range and collision system. The relative correlation strength, obtained by normalisation of the cumulants with the 〈vn2〉 from a two-particle correlation analysis, is similar in the three collision systems and depends weakly on the event multiplicity and transverse momentum. These results based on the subevent methods provide strong evidence of a similar long-range multi-particle collectivity in pp, p+Pb and peripheral Pb+Pb collisions.

Multiparticle azimuthal cumulants in p+Pb collisions from a multiphase transport model

A new subevent cumulant method was recently developed, which can significantly reduce the non-flow contributions in long-range correlations for small systems compared to the standard cumulant method. In this work, we study multi-particle cumulants in $p$+Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV with a multiphase transport model (AMPT), including two- and four-particle cumulants ($c_{2}\{2\}$ and $c_{2}\{4\}$) and symmetric cumulants [SC(2, 3) and SC(2, 4)]. Our numerical results show that $v_{2}\{2\}$ is consistent with the experimental data, while the magnitude of $c_{2}\{4\}$ is smaller than the experimental data, which may indicate either the collectivity is underestimated or some dynamical fluctuations are absent in the AMPT model. For the symmetric cumulants, we find that the results from the standard cumulant method are consistent with the experimental data, but those from the subevent cumulant method show different behaviors. The results indicate that the measurements from the standard cumulant method are contaminated by non-flow effects, especially when the number of produced particles is small. The subevent cumulant method is a better tool to explore the $real$ collectivity in small systems.

Correlation measurements between flow harmonics in Au+Au collisions at RHIC

Flow harmonics (vn) in the Fourier expansion of the azimuthal distribution of particles are widely used to quantify the anisotropy in particle emission in high-energy heavy-ion collisions. The symmetric cumulants, SC(m,n), are used to measure the correlations between different orders of flow harmonics. These correlations are used to constrain the initial conditions and the transport properties of the medium in theoretical models. In this Letter, we present the first measurements of the four-particle symmetric cumulants in Au+Au collisions at sNN=39 and 200 GeV from data collected by the STAR experiment at RHIC. We observe that v2 and v3 are anti-correlated in all centrality intervals with similar correlation strengths from 39 GeV Au+Au to 2.76 TeV Pb+Pb (measured by the ALICE experiment). The v2–v4 correlation seems to be stronger at 39 GeV than at higher collision energies. The initial-stage anti-correlations between second and third order eccentricities are sufficient to describe the measured correlations between v2 and v3. The best description of v2–v4 correlations at sNN=200GeV is obtained with inclusion of the system's nonlinear response to initial eccentricities accompanied by the viscous effect with η/s>0.08. Theoretical calculations using different initial conditions, equations of state and viscous coefficients need to be further explored to extract η/s of the medium created at RHIC.

A remark on the sign change of the four-particle azimuthal cumulant in small systems

The azimuthal cumulants, c2{2} and c2{4}, originating from the global conservation of transverse momentum in the presence of hydro-like elliptic flow are calculated. We observe the sign change of c2{4} for small number of produced particles. This is in a qualitative agreement with the recent ATLAS measurement of multi-particle azimuthal correlations with the subevent cumulant method.

Observation of Correlated Azimuthal Anisotropy Fourier Harmonics in pp and p+Pb Collisions at the LHC.

The azimuthal anisotropy Fourier coefficients (v_{n}) in 8.16TeV p+Pb data are extracted via long-range two-particle correlations as a function of the event multiplicity and compared to corresponding results in pp and PbPb collisions. Using a four-particle cumulant technique, v_{n} correlations are measured for the first time in pp and p+Pb collisions. The v_{2} and v_{4} coefficients are found to be positively correlated in all collision systems. For high-multiplicity p+Pb collisions, an anticorrelation of v_{2} and v_{3} is observed, with a similar correlation strength as in PbPb data at the same multiplicity. The new correlation results strengthen the case for a common origin of the collectivity seen in p+Pb and PbPb collisions in the measured multiplicity range.

Measurement of long-range multiparticle azimuthal correlations with the subevent cumulant method in pp and p +Pb collisions with the ATLAS detector at the CERN Large Hadron Collider

A detailed study of multi-particle azimuthal correlations is presented using $pp$ data at $\sqrt{s}=5.02$ and 13 TeV, and $p$+Pb data at $\sqrt{s_{\rm{NN}}}=5.02$ TeV, recorded with the ATLAS detector at the LHC. The azimuthal correlations are probed using four-particle cumulants $c_{n}\{4\}$ and flow coefficients $v_n\{4\}=(-c_{n}\{4\})^{1/4}$ for $n=2$ and 3, with the goal of extracting long-range multi-particle azimuthal correlation signals and suppressing the short-range correlations. The values of $c_{n}\{4\}$ are obtained as a function of the average number of charged particles per event, $\left\langle N_{\rm{ch}} \right\rangle$, using the recently proposed two-subevent and three-subevent cumulant methods, and compared with results obtained with the standard cumulant method. The three-subevent method is found to be least sensitive to short-range correlations, which originate mostly from jets with a positive contribution to $c_{n}\{4\}$. The three-subevent method gives a negative $c_{2}\{4\}$, and therefore a well-defined $v_2\{4\}$, nearly independent of $\left\langle N_{\rm{ch}} \right\rangle$, which provides direct evidence that the long-range multi-particle azimuthal correlations persist to events with low multiplicity. Furthermore, $v_2\{4\}$ is found to be smaller than the $v_2\{2\}$ measured using the two-particle correlation method, as expected for long-range collective behavior. Finally, the measured values of $v_2\{4\}$ and $v_2\{2\}$ are used to estimate the number of sources relevant for the initial eccentricity in the collision geometry.

Measurements of Multiparticle Correlations in d+Au Collisions at 200, 62.4, 39, and 19.6GeV and p+Au Collisions at 200GeV and Implications for Collective Behavior.

Recently, multiparticle-correlation measurements of relativistic p/d/^{3}He+Au, p+Pb, and even p+p collisions show surprising collective signatures. Here, we present beam-energy-scan measurements of two-, four-, and six-particle angular correlations in d+Au collisions at sqrt[s_{NN}]=200, 62.4, 39, and 19.6GeV. We also present measurements of two- and four-particle angular correlations in p+Au collisions at sqrt[s_{NN}]=200 GeV. We find the four-particle cumulant to be real valued for d+Au collisions at all four energies. We also find that the four-particle cumulant in p+Au has the opposite sign as that in d+Au. Further, we find that the six-particle cumulant agrees with the four-particle cumulant in d+Au collisions at 200GeV, indicating that nonflow effects are subdominant. These observations provide strong evidence that the correlations originate from the initial geometric configuration, which is then translated into the momentum distribution for all particles, commonly referred to as collectivity.

Multiparticle Collectivity from Initial State Correlations in High Energy Proton-Nucleus Collisions

Qualitative features of multiparticle correlations in light-heavy ion (p+A) collisions at RHIC and LHC are reproduced in a simple initial state model of partons in the projectile coherently scattering off localized domains of color charge in the heavy nuclear target. These include (i)the ordering of the magnitudes of the azimuthal angle nth Fourier harmonics of two-particle correlations v_{n}{2}, (ii)the energy and transverse momentum dependence of the four-particle Fourier harmonic v_{2}{4}, and (iii)the energy dependence of four-particle symmetric cumulants measuring correlations between different Fourier harmonics. Similar patterns are seen in an Abelian version of the model, where we observe v_{2}{2}>v_{2}{4}≈v_{2}{6}≈v_{2}{8} of two, four, six, and eight particle correlations. While such patterns are often interpreted as signatures of collectivity arising from hydrodynamic flow, our results provide an alternative description of the multiparticle correlations seen in p+A collisions.

Parton model description of multiparticle azimuthal correlations in pA collisions

In arXiv:1705.00745, an initial state "parton model" of quarks scattering off a dense nuclear target was shown to qualitatively reproduce the systematics of multiparticle azimuthal anisotropy cumulants measured in proton/deuteron-nucleus ($pA$) collisions at RHIC and the LHC. The systematics included i) the behavior of the four-particle cumulant $c_2\{4\}$, which generates a real four-particle second Fourier harmonic $v_2\{4\}$, ii) the ordering $v_2\{2\}>v_2\{4\}\approx v_2\{6\}\approx v_2\{8\}$ for two-, four-, six-, and eight-particle Fourier harmonics, iii) the behavior of so-called symmetric cumulants $\text{SC}(2,3)$ and $\text{SC}(2,4)$. These features of azimuthal multiparticle cumulants were previously interpreted as a signature of hydrodynamic flow; our results challenge this interpretation. We expand here upon our previous study and present further details and novel results on the saturation scale and transverse momentum ($p_\perp$) dependence of multiparticle azimuthal correlations. We find that the dependence of $v_2\{2\}$ and $v_2\{4\}$ on the number of color domains in the target varies with the $p_\perp$ window explored. We extend our prior discussion of symmetric cumulants and compute as yet unmeasured symmetric cumulants. We investigate the $N_c$ dependence of $v_2\{2\}$ and $v_2\{4\}$. We contrast our results, which include multiple scatterings of each quark off the target, to the Glasma graph approximation, where each quark suffers at most two gluon exchanges with the target. We find that coherent multiple scattering is essential to obtain a positive definite $v_2\{4\}$. We provide an algorithm to compute expectation values of arbitrary products of the "dipole" lightlike Wilson line correlators.