Non-flow Contributions Research Articles

Benchmarking the non-flow contributions to the elliptic flow parameter (v2) in proton-proton collisions

Abstract This manuscript reports on the elliptic flow parameter, v 2 , in proton-proton (p–p) collisions using PYTHIA8 event generator simulations. The typical event plane (EP) method v 2 (EP) as the one used for the real data analysis has been adopted to measure the v 2 of particles composed of different quark flavors, and produced at mid-pseudorapidity ∣η∣≤1 at center-of-mass energy s = 200 GeV and s = 13 TeV. The event plane has been constructed using the soft-charged particles with transverse momentum ( p T < 2 GeV/c) produced in various η ranges. The pseudorapidity gap technique (Δη) between the particle of interest and the soft charged particles contributed to the event plane constructions has been utilized to benchmark the non-flow contributions. The v 2 π ± , π 0 , v 2 J ∕ ψ , ϒ , K , D , B , and the v 2 γ dir show similar pattern dependence on the transverse momentum for the same Δη, at both s = 200 GeV and s = 13 TeV. At each center-of-mass energy, the measured v 2 shows obvious dependence on the quark flavor contents where v 2 γ dir ≤ v 2 J ∕ ψ , ϒ , K , D , B ≤ v 2 π ± , π 0 for similar Δη gap. The measured v 2 shows slightly higher values at smaller s for particles of similar values of Δη gaps, particularly at small Δη gap. The measured v 2 for all particles shows systematic decreases with increasing the Δη gap as expected from the previous experimental results. Because PYTHIA8 simulations do not incorporate final state interactions, the v 2 ( EP ) values reported here primarily reflect the non-flow contributions and its dependence on the quark contents, pseudorapidity gap as a function on p T at each center of mass–energy. These contributions should be carefully subtracted from the signal in real data analysis that employs the same event plane determination algorithm.

Investigating nonflow contribution subtraction in d-Au collisions with AMPT model

Investigating nonflow contribution subtraction in d-Au collisions with AMPT model

Measurements of second-harmonic Fourier coefficients from azimuthal anisotropies in p+p, p+Au, d+Au, and He3+Au collisions at sNN=200 GeV

Recently, the PHENIX Collaboration has published second- and third-harmonic Fourier coefficients $v_2$ and $v_3$ for midrapidity ($|\eta|<0.35$) charged hadrons in 0\%--5\% central $p$$+$Au, $d$$+$Au, and $^3$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV utilizing three sets of two-particle correlations for two detector combinations with different pseudorapidity acceptance [Phys. Rev. C {\bf 105}, 024901 (2022)]. This paper extends these measurements of $v_2$ to all centralities in $p$$+$Au, $d$$+$Au, and $^3$He$+$Au collisions, as well as $p$$+$$p$ collisions, as a function of transverse momentum ($p_T$) and event multiplicity. The kinematic dependence of $v_2$ is quantified as the ratio $R$ of $v_2$ between the two detector combinations as a function of event multiplicity for $0.5$$<$$p_T$$<$$1$ and $2$$<$$p_T$$<$$2.5$ GeV/$c$. A multiphase-transport (AMPT) model can reproduce the observed $v_2$ in most-central to midcentral $d$$+$Au and $^3$He$+$Au collisions. However, the AMPT model systematically overestimates the measurements in $p$$+$$p$, $p$$+$Au, and peripheral $d$$+$Au and $^3$He$+$Au collisions, indicating a higher nonflow contribution in AMPT than in the experimental data. The AMPT model fails to describe the observed $R$ for $0.5$$<$$p_T$$<$$1$ GeV/$c$, but there is qualitative agreement with the measurements for $2$$<$$p_T$$<$$2.5$ GeV/$c$.

Estimate of a nonflow baseline for the chiral magnetic effect in isobar collisions at RHIC

Recently, STAR reported the isobar (4496Ru + 4496Ru, 4096Zr + 4096Zr) results for the chiral magnetic effect (CME) search. The Ru+Ru to Zr+Zr ratio of the CME-sensitive observable Δγ, normalized by elliptic anisotropy (υ2), is observed to be close to the inverse multiplicity (N) ratio. In other words, the ratio of the NΔγ/υ2 observable is close to the naive background baseline of unity. However, nonflow correlations are expected to cause the baseline to deviate from unity. To further understand the isobar results, we decompose the nonflow contributions to NΔγ/υ2 (isobar ratio) into three terms and quantify each term by using the nonflow in υ2 measurement, published STAR data, and HIJING simulation. From these studies, we estimate a nonflow baseline of the isobar ratio of NΔγ/υ2 for the CME and discuss its implications.

Study QGP through the Correlation Function with Pb-Pb Collisions at

This paper focuses on repeating and verifying the predecessor’s work. We briefly describe our dataset from CMS and then provide information about the Glauber Model built with python. Then, the correlation function of our data and different orders of its Fourier decomposition are presented to verify the former discussion. With the correlation function, we will show the fluctuation of the directed and elliptic flow caused by the non-flow, which comes from the intractable strong interaction during the evolution of the QGP. Based on the assumption that the non-flow contribution is ignorable in large relative pseudorapidity interval, (|Δη|), we separate the non-flow contribution from the elliptic flow. Finally, we provide a detailed derivation of the Fourier decomposition of correlation and discuss their physical meaning, absent in general paperwork.

Two- and three-particle nonflow contributions to the chiral magnetic effect measurement by spectator and participant planes in relativistic heavy ion collisions

Correlation measurements with respect to the spectator and participant planes in relativistic heavy ion collisions were proposed to extract the chiral magnetic effect (CME) from background dominated azimuthal correlators. This paper investigates the effects of two- and three-particle nonflow correlations on the extracted CME signal fraction, $f_{\text{CME}}$. It is found, guided by a multiphase transport (AMPT) model and the heavy ion jet interaction generator (HIJING) together with experimental data, that the nonflow effects amount to approximately $(4\pm5)$% and $(-5\pm3)$% without and with pseudorapidity gaps, respectively, in 20-50% centrality Au+Au collisions at $\sqrt{s_{\text{NN}}}= 200 \text{ GeV}$.

Multivariate cumulants in flow analyses: The next generation

We reconcile for the first time the strict mathematical formalism of multivariate cumulants with the use of cumulants in anisotropic flow analyses in high-energy nuclear collisions. This reconciliation yields to the next generation of estimators to be used in flow analyses. We review all fundamental properties of multivariate cumulants and use them as a foundation to establish two simple necessary conditions to determine whether some multivariate random variable is a multivariate cumulant in the basis they are expressed in. We argue that properties of cumulants are preserved only for the stochastic variables on which the cumulant expansion has been performed directly, and if there are no underlying symmetries due to which some terms in the cumulant expansion are identically zero. We illustrate one possibility of new multivariate cumulants of azimuthal angles by defining them event-by-event and by keeping all nonisotropic terms in the cumulant expansion. Furthermore, we introduce new cumulants of flow amplitudes named asymmetric cumulants, which generalize recently introduced symmetric cumulants for the case when flow amplitudes are raised to different powers. Finally, we present the new concept of cumulants of symmetry plane correlations and provide the first realization for the lowest orders. The new estimators can be used directly to constrain the multivariate probability density function of flow fluctuations, since its functional form can be reconstructed only from its true moments or cumulants. The new definition for cumulants of azimuthal angles enables separation of nonflow and flow contributions and offers first insights into how the combinatorial background contributes for small multiplicities to flow measurements with correlation techniques. All the presented results are supported by Monte Carlo studies using state-of-the-art models.

Two-particle azimuthal correlations in photonuclear ultraperipheral Pb+Pb collisions at 5.02 TeV with ATLAS

Two-particle long-range azimuthal correlations are measured in photonuclear collisions using 1.7 nb$^{-1}$ of 5.02 TeV Pb+Pb collision data collected by the ATLAS experiment at the LHC. Candidate events are selected using a dedicated high-multiplicity photonuclear event trigger, a combination of information from the zero-degree calorimeters and forward calorimeters, and from pseudorapidity gaps constructed using calorimeter energy clusters and charged-particle tracks. Distributions of event properties are compared between data and Monte Carlo simulations of photonuclear processes. Two-particle correlation functions are formed using charged-particle tracks in the selected events, and a template-fitting method is employed to subtract the non-flow contribution to the correlation. Significant nonzero values of the second- and third-order flow coefficients are observed and presented as a function of charged-particle multiplicity and transverse momentum. The results are compared with flow coefficients obtained in proton-proton and proton-lead collisions in similar multiplicity ranges, and with theoretical expectations. The unique initial conditions present in this measurement provide a new way to probe the origin of the collective signatures previously observed only in hadronic collisions.

Exploring origins for correlations between flow harmonics and transverse momentum in small collision systems

High statistics data sets from experiments at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) with small and large collision species have enabled a wealth of new flow measurements, including the event-by-event correlation between observables. One exciting such observable $\rho(v^{2}_{n},[p_{T}])$ gauges the correlation between the mean transverse momentum of particles in an event and the various flow coefficients ($v_n$) in the same event [1]. Recently it has been proposed that very low multiplicity events may be sensitive to initial-state glasma correlations [2] rather than flow-related dynamics. We find utilizing the IP-JAZMA framework that the color domain explanation for the glasma results are incomplete. We then explore predictions from PYTHIA-8, and the version for including nuclear collisions called PYTHIA-ANGANTYR, which have only non-flow correlations and the AMPT model which has both non-flow and flow-type correlations. We find that PYTHIA-ANGANTYR has non-flow contributions to $\rho(v^{2}_{n},[p_{T}])$ in p+O, p+Pb, O+O collisions that are positive at low multiplicity and comparable to the glasma correlations. It is striking that in PYTHIA-8 in p+p collisions there is actually a sign-change from positive to negative $\rho(v^{2}_{n},[p_{T}])$ as a function of multiplicity. The AMPT results match the experimental data general trends in Pb+Pb collisions at the LHC, except at low multiplicity where AMPT has the opposite sign. In p+Pb collisions, AMPT has the opposite sign from experimental data and we explore this within the context of parton geometry. Predictions for p+O, O+O, and Xe+Xe are also presented.

Signatures of collectivity and flow in small systems observed by PHENIX

A wide variety of recent measurements from small systems indicate that there are collective flow phenomena in these systems, which are well described by hydrodynamics. However, it is widely understood that all flow measurements are affected by nonflow correlations. In order to disentangle the genuine hydrodynamical flow from the nonflow contributions, we have systematically studied the v2 as a function of pT and η in p+Au and d+Au collisions at sNN=200GeV by comparing several nonflow subtraction methods and by combining different detectors. We have also measured 4-particle cumulants in p+Au at sNN=200GeV with subevents, which kinematically suppress nonflow via removal of short-range correlations.

ATLAS measurements of collective flow of heavy-flavor hadrons in small collision systems

Azimuthal anisotropy of heavy-flavor mesons in small systems has been studied with the ATLAS detector at the LHC. A template fit method is used to subtract non-flow contributions using a simultaneous fit of samples with low and high charged-particle multiplicities. The heavy-flavor flow in p+Pb is studied using multiple probes, including prompt D0 mesons, J/ψ, and muons from semi-leptonic decays of heavy-flavor hadrons. In pp collisions, flow coefficients for muons from heavy-flavor hadron decays, separated into charm- and bottom-hadron origins, are measured. The observed heavy-flavor azimuthal anisotropies in p+Pb and pp collisions are found to be qualitatively similar to those of light hadrons indicating a similar origin for both types of particles.

Long-range collectivity in small collision-systems with two- and four-particle correlations @ STAR

New STAR differential and integral v2,3 measurements that explicitly account for non-flow contributions, are reported for p/d/3He+Au, collisions at sNN=200GeV. The measurements, which leverage the two-particle correlators for p/d/3He+Au and minimum-bias p+p collisions in tandem with three well established methods of non-flow subtraction, are observed to be method-independent. For comparable multiplicities, they further indicate system-independent v2{2} and v3{2} values that are consistent with the critical role of both “size” (Nch) and the subnucleonic-fluctuations-driven eccentricities ε2,3, but are inconsistent with the notion of shape engineering in p/d/3He+Au collisions. The scaling function derived from the measurements, confirm the important role of final-state effects across a broad spectrum of collision-system sizes and energies, and suggests an increase in η/s(T,μB) for small collision-systems.

Two-particle differential transverse momentum and number density correlations in p−Pb collisions at 5.02 TeV and Pb-Pb collisions at 2.76 TeV at the CERN Large Hadron Collider

We present measurements of two-particle differential number correlation functions $R_{2}$ and transverse momentum correlation functions $P_{2}$, obtained from p-Pb collisions at 5.02 TeV and Pb-Pb collisions at 2.76 TeV. The results are obtained using charged particles in the pseudorapidity range $|\eta| <$ 1.0, and transverse momentum range $0.2 < p_{\rm T} < 2.0$ GeV/$c$ as a function of pair separation in pseudorapidity, $|\Delta\eta|$, azimuthal angle, $\Delta\varphi$, and for several charged-particle multiplicity classes. Measurements are carried out for like-sign and unlike-sign charged-particle pairs separately and combined to obtain charge-independent and charge-dependent correlation functions. We study the evolution of the width of the near-side peak of these correlation functions with collision centrality. Additionally, we study Fourier decompositions of the correlators in $\Delta\varphi$ as a function of the pair separation $|\Delta\eta|$. Significant differences in the dependence of their harmonic coefficients on multiplicity classes are found. These differences can be exploited, in theoretical models, to obtain further insight into charged-particle production and transport in heavy-ion collisions. Moreover, an upper limit of non-flow contributions to flow coefficients $v_{n}$ measured in Pb-Pb collisions based on the relative strength of Fourier coefficients measured in p-Pb interactions is estimated.

Examination of flow and nonflow factorization methods in small collision systems

Two particle correlations have been used extensively to study hydrodynamic flow patterns in heavy-ion collisions. In small collision systems, such as $p$$+$$p$ and $p$$+$$A$, where particle multiplicities are much smaller than in $A$$+$$A$ collisions, non-flow effects from jet correlations, momentum conservation, particle decays, etc. can be significant, even when imposing a large pseudorapidity gap between the particles. A number of techniques to subtract the non-flow contribution in two particle correlations have been developed by experiments at the Large Hadron Collider (LHC) and then used to measure particle flow in $p$$+$$p$ and $p$$+$Pb collisions. Recently, experiments at the Relativistic Heavy Ion Collider (RHIC) have explored the possibility of adopting these techniques for small collision systems at lower energies. In this paper, we test these techniques using Monte Carlo generators PYTHIA and HIJING, which do not include any collective flow, and AMPT, which does. We find that it is crucial to examine the results of such tests both for correlations integrated over particle transverse momentum $p_T$ and differentially as a function of $p_T$. Our results indicate reasonable non-flow subtraction for $p$$+$$p$ collisions at the highest LHC energies, while failing if applied to $p$$+$$p$ collisions at RHIC. In the case of $p$$+$Au collisions at RHIC, both HIJING and AMPT results indicate a substantial over-subtraction of non-flow for $p_{T}\gtrsim1~{\rm GeV}/c$ and hence an underestimate of elliptic flow.

Long-range collectivity in small collision systems with two- and four-particle correlations at STAR

New STAR measurements of two- and four-particle (c2{4}) azimuthal angle correlations are reported for p+Au collisions at 200 GeV and d+Au collisions from 19.6 to 200 GeV. A negative c2{4}, consistent with collective anisotropic flow, is observed in high multiplicity d+Au events at 62.4 and 200 GeV where the statistical significance of the data allows an analysis. A template fitting method, employed to subtract non-flow contributions to the two-particle correlations, allows the extraction of the anisotropy coefficients (ν2) for these systems at their respective energies. The ν2 results for different energies show a common dependence on the charged particle multiplicity density (〈dNch/dη〉), which provide important insight on the nature of collective behavior in small collision systems.

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.

Effect of an anisotropic escape mechanism on elliptic flow in relativistic heavy-ion collisions

We study the effect of anisotropic escape mechanism on elliptic flow in relativistic heavy-ion collisions. We use Glauber model to generate initial conditions and ignore hydrodynamic expansion in the transverse direction. We employ Beer-Lambert law to allow for the transmittance of produced hadrons in the medium and calculate the anisotropy generated due to the suppression of particles traversing through the medium. In order to separate non-flow contribution due to surface bias effects, we ignore hydrodynamic expansion in the transverse direction and consider purely longitudinal boost-invariant expansion. We calculate the transverse momentum dependence of elliptic flow, generated from anisotropic escape mechanism due to surface bias effects, for various centralities in $\sqrt{s_{NN}}=200$ GeV Au$+$Au collisions at RHIC and $\sqrt{s_{NN}}=2.76$ TeV Pb$+$Pb collisions at LHC. We find that the surface bias effects have a sizable contribution to the total elliptic flow observed in heavy-ion collisions indicating that the viscosity of the QCD matter extracted from hydrodynamic simulations may be underestimated.

Estimates of the collision symmetry planes in HADES experiment at GSI

Estimate of the collision symmetry planes is a crucial part of the anisotropic flow analysis in heavy-ion collisions. HADES experiment at GSI has different possibilities for symmetry plane estimation. In this letter different methods of the symmetry plane resolution calculation are compared and the differences are explained in terms of non-flow contribution.

Event-plane decorrelation over pseudorapidity and its effect on azimuthal anisotropy measurements in relativistic heavy-ion collisions

Within A Multi-Phase Transport model, we investigate decorrelation of event planes over pseudorapidity and its effect on azimuthal anisotropy measurements in relativistic heavy-ion collisions. The decorrelation increases with increasing {\eta} gap between particles used to reconstruct the event planes. The third harmonic event planes are found even anticorrelated between forward and backward rapidities, the source of which may root in the opposite orientation of the collision geometry triangularities. The decorrelation may call into question the anisotropic flow measurements with pseudorapidity gap designed to reduce nonflow contributions, hence the hydrodynamic properties of the quark-gluon plasma extracted from those measurements.

Forward-Backward Flow Correlations in Relativistic Heavy-Ion Collisions

We discuss the torque effect in the initial fireball formed in relativistic heavy-ion collisions, manifesting itself, on the event-by-event basis, in a relative angle between the principal axes of the transverse momentum distributions in the forward and backward rapidity regions. The torque follows from two natural features: 1) the sources of particles (e.g. wounded nucleons) emit predominantly in their forward hemispheres, and 2) there exist fluctuations in the transverse distribution of sources from the two colliding nuclei. On the average, the standard event-by-event deviation of the relative torque angle is about 20 degrees for the central and 10 degrees for the mid-peripheral collisions. The hydrodynamic expansion of a torqued fireball leads to a torqued collective flow of the fluid, which, in turn, yields torqued principal axes of the transverse-momentumdistributions at different rapidities. We discuss experimental measures based on cumulants involving particles in different rapidity regions, which allow for a quantitative extraction of the effect from the experimental data. We estimate the non-flow contributions from resonance decays with the help of THERMINATOR.