Azimuthal Anisotropy Coefficients Research Articles

Azimuthal anisotropy of jet particles in p-Pb and Pb-Pb collisions at sNN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{{\ extrm{s}}_{\ extrm{NN}}} $$\\end{document} = 5.02 TeV

The azimuthal anisotropy of particles associated with jets (jet particles) at midrapidity is measured for the first time in p-Pb and Pb-Pb collisions at sNN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{{\ extrm{s}}_{\ extrm{NN}}} $$\\end{document} = 5.02 TeV down to transverse momentum (pT) of 0.5 GeV/c and 2 GeV/c, respectively, with ALICE. The results obtained in p-Pb collisions are based on a novel three-particle correlation technique. The azimuthal anisotropy coefficient v2 in high-multiplicity p-Pb collisions is positive, with a significance reaching 6.8σ at low pT, and its magnitude is smaller than in semicentral Pb-Pb collisions. In contrast to the measurements in Pb-Pb collisions, the v2 coefficient is also found independent of pT within uncertainties. Comparisons with the inclusive charged-particle v2 and with AMPT calculations are discussed. The predictions suggest that parton interactions play an important role in generating a non-zero jet-particle v2 in p-Pb collisions, even though they overestimate the reported measurement. These observations shed new insights on the understanding of the origin of the collective behaviour of jet particles in small systems such as p-Pb collisions, and provide significant stringent new constraints to models.

Elliptic anisotropy of open-charm hadrons from parton scatterings in p -Pb collisions at energies available at the CERN Large Hadron Collider

The elliptic azimuthal anisotropy coefficient (v2) of open-charm hadrons at midrapidity (|η<1|) was studied in p-Pb collisions at sNN=8.16 TeV using a multiphase transport () model including an additional charm quark–antiquark pair production trigger. The model provides a simultaneous description of the measured pT spectrum and v2 of the D0 meson, as well as the v2 of light flavor meson Ks0. We found that the D0 and Ks0 v2 are both significantly affected by different parton scatterings among charm and light quarks. In addition, the predictions for the v2 of other charm hadrons including D+, Ds+, and Λc+ in p-Pb collisions are given for the first time. The v2 of open-charm hadrons reasonably follows the number-of-constituent-quark (NCQ) scaling up to 2.5 GeV, strongly indicating the importance of partonic degrees of freedom for the collectivity of heavy flavors in high-multiplicity p-Pb collisions. These findings may hint at the formation of deconfined matter in small collision systems, and provide referential value for future measurements of azimuthal anisotropy at energies available at the CERN Large Hadron Collider. Published by the American Physical Society 2024

Probing the path-length dependence of parton energy loss via scaling properties in heavy ion collisions

The scaling property of large-p⊥ hadron suppression, RAA(p⊥), measured in heavy ion collisions at the relativistic heavy ion collider and at the large hadron collider (LHC) leads to the determination of the average parton energy loss ⟨ε⟩ in quark-gluon plasma produced in a variety of collision systems and centrality classes. Relating ⟨ε⟩ to the particle multiplicity and collision geometry allows for probing the dependence of parton energy loss on the path length L. We find that ⟨ε⟩∝Lβ with β=1.02−0.06+0.09, which is consistent with the perturbative quantum chromodynamics expectation of parton energy loss in a longitudinally expanding quark-gluon plasma. We then demonstrate that the azimuthal anisotropy coefficient divided by the collision eccentricity, v2/e, follows the same scaling property as RAA. This scaling is observed in data, which are reproduced by the model at large p⊥. Finally, a linear relationship between v2/e and the logarithmic derivative of RAA is found and confirmed in data, offering an additional way to probe the L dependence of parton energy loss using coming measurements from LHC run 3. Published by the American Physical Society 2024

Measurements of azimuthal anisotropy of nonprompt D0 mesons in PbPb collisions at [formula omitted

Measurements of the elliptic (v2) and triangular (v3) azimuthal anisotropy coefficients are presented for ▪ mesons produced in ▪ hadron decays (nonprompt ▪ mesons) in lead-lead collisions at sNN=5.02TeV. The results are compared with previously published charm meson anisotropies measured using prompt ▪ mesons. The data were collected with the CMS detector in 2018 with an integrated luminosity of 0.58nb−1. Azimuthal anisotropy is sensitive to the interactions of quarks with the hot and dense medium created in heavy ion collisions. Comparing results for prompt and nonprompt ▪ mesons can assist in understanding the mass dependence of these interactions. The nonprompt results show lower magnitudes of v2 and v3 and weaker dependences on the meson transverse momentum and collision centrality than those found for prompt ▪ mesons. The results are in agreement with theoretical predictions that include a mass dependence in the interactions of quarks with the medium.

Measurements of the Elliptic and Triangular Azimuthal Anisotropies in Central ^{3}He+Au, d+Au and p+Au Collisions at sqrt[s_{NN}]=200 GeV.

The elliptic (v_{2}) and triangular (v_{3}) azimuthal anisotropy coefficients in central ^{3}He+Au, d+Au, and p+Au collisions at sqrt[s_{NN}]=200 GeV are measured as a function of transverse momentum (p_{T}) at midrapidity (|η|<0.9), via the azimuthal angular correlation between two particles both at |η|<0.9. While the v_{2}(p_{T}) values depend on the colliding systems, the v_{3}(p_{T}) values are system independent within the uncertainties, suggesting an influence on eccentricity from subnucleonic fluctuations in these small-sized systems. These results also provide stringent constraints for the hydrodynamic modeling of these systems.

Measurements of azimuthal anisotropies of jet production in Pb+Pb collisions at sNN=5.02 TeV with the ATLAS detector

The azimuthal variation of jet yields in heavy-ion collisions provides information about the path-length dependence of the energy loss experienced by partons passing through the hot, dense nuclear matter known as the quark-gluon plasma. This paper presents the azimuthal anisotropy coefficients $v_2$, $v_3$, and $v_4$ measured for jets in Pb+Pb collisions at $\sqrt{s_{NN}} =$ 5.02 TeV using the ATLAS detector at the LHC. The measurement uses data collected in 2015 and 2018, corresponding to an integrated luminosity of 2.2 nb$^{-1}$. The $v_n$ values are measured as a function of the transverse momentum of the jets between 71 GeV and 398 GeV and the event centrality. A nonzero value of $v_2$ is observed in all but the most central collisions. The value of $v_2$ is largest for jets with lower transverse momentum, with values up to 0.05 in mid-central collisions. A smaller, nonzero value of $v_3$ of approximately 0.01 is measured with no significant dependence on jet $p_T$ or centrality, suggesting that fluctuations in the initial state play a small but distinct role in jet energy loss. No significant deviation of $v_4$ from zero is observed in the measured kinematic region.

Influence of Collective Nuclear Vibrations on Initial State Eccentricities in Pb + Pb Collisions

We study within the Monte Carlo Glauber model the influence of collective quantum effects in the Pb nucleus on the azimuthal anisotropy coefficients $\epsilon_{2,3}$ in Pb+Pb collisions at the LHC energies. To account for the quantum effects, we modify the sampling of the nucleon positions by applying suitable filters that guarantee that the colliding nuclei have the mean squared quadrupole and octupole moments consistent with the ones extracted from the experimental quadrupole and octupole strength functions for the Pb nucleus with the help of the energy weighted sum rule. Our Monte Carlo Glauber model with the modified sampling of the nucleon positions leads to $\epsilon_2\{2\}/\epsilon_3\{2\}\approx 0.8$ at centrality $\lesssim 1$\%, which allows to resolve the $v_2$-to-$v_3$ puzzle.

Measurement of prompt [formula omitted]-meson production and azimuthal anisotropy in Pb–Pb collisions at [formula omitted

The production yield and angular anisotropy of prompt Ds+ mesons were measured as a function of transverse momentum (pT) in Pb–Pb collisions at a centre-of-mass energy per nucleon pair sNN=5.02TeV collected with the ALICE detector at the LHC. Ds+ mesons and their charge conjugates were reconstructed at midrapidity (|y|<0.5) from their hadronic decay channel Ds+→ϕπ+, with ϕ→K−K+, in the pT intervals 2<pT<50GeV/c and 2<pT<36GeV/c for the 0–10% and 30–50% centrality intervals. For pT>10GeV/c, the measured Ds+-meson nuclear modification factor RAA is consistent with the one of non-strange D mesons within uncertainties, while at lower pT a hint for a Ds+-meson RAA larger than that of non-strange D mesons is seen. The enhanced production of Ds+ relative to non-strange D mesons is also studied by comparing the pT-dependent Ds+/D0 production yield ratios in Pb–Pb and in pp collisions. The ratio measured in Pb–Pb collisions is found to be on average higher than that in pp collisions in the interval 2<pT<8GeV/c with a significance of 2.3σ and 2.4σ for the 0–10% and 30–50% centrality intervals. The azimuthal anisotropy coefficient v2 of prompt Ds+ mesons was measured in Pb–Pb collisions in the 30–50% centrality interval and is found to be compatible with that of non-strange D mesons. The main features of the measured RAA, Ds+/D0 ratio, and v2 as a function of pT are described by theoretical calculations of charm-quark transport in a hydrodynamically expanding quark–gluon plasma including hadronisation via charm-quark recombination with light quarks from the medium. The pT-integrated production yield of Ds+ mesons is compatible with the prediction of the statistical hadronisation model.

Checking nonflow assumptions and results via PHENIX published correlations in p+p , p+Au , d+Au , and He3+Au at sNN=200 GeV

Recently the PHENIX Collaboration has made available two-particle correlation Fourier coefficients for multiple detector combinations in minimum bias p+p and 0-5% central p+Au, d+Au, 3He+Au collisions at 200 GeV [1]. Using these coefficients for three sets of two-particle correlations, azimuthal anisotropy coefficients $v_2$ and $v_3$ are extracted for midrapidity charged hadrons as a function of transverse momentum. In this paper, we use the available coefficients to explore various non-flow hypotheses as well as compare the results with theoretical model calculations. The non-flow methods fail basic closure tests with AMPT and PYTHIA/ANGANTYR, particularly when including correlations with particles in the low multiplicity light-projectile going direction. In data, the non-flow adjusted $v_2$ results are modestly lower in p+Au and the adjusted $v_3$ results are more significantly higher in p+Au and d+Au. However, the resulting higher values for the ratio $v_3/v_2$ in p+Au at RHIC compared to p+Pb at the LHC is additional evidence for a significant over-correction. Incorporating these additional checks, the conclusion that these flow coefficients are dominated by initial geometry coupled with final-state interactions (e.g.~hydrodynamic expansion of quark-gluon plasma) remains true, and explanations based on initial-state glasma are ruled out. The detailed balance between intrinsic and fluctuation-driven geometry and the exact role of weakly versus strongly-coupled pre-hydrodynamic evolution remains an open question for triangular flow, requiring further theoretical and experimental investigation.

Elliptic flow for φ mesons measured by PHENIX

The systematic study of hadronic elliptic flow in various relativistic heavy ion collisions is important for the investigation of the initial geometry influence on the quark gluon plasma characteristics. The φ meson consists of strange and antistrange quarks and has a small interaction cross section with non-strange hadrons. Therefore, φ mesons are barely affected by late hadronic stage and reflect detailed information about hot and dense matter properties. Additionally, the comparison of elliptic flow for φ mesons to those of charged hadrons will provide additional information on the flavor dependence of flow. PHENIX has measured second order azimuthal anisotropy coefficients for φ mesons in Cu+Au collisions at √SNN = 200 GeV and in U+U collisions at √SNN = 193 GeV at midrapidity (| η | &lt; 0.35). The obtained data suggest scaling of elliptic flow for φ mesons with eccentricity of participant nucleons in Cu+Au, U+U, and Au+Au collisions. Viscous hydrodynamic model iEBE-VISHNU provides a simultaneous description of the obtained data.

Constraints on the Initial State of Pb-Pb Collisions via Measurements of Z-Boson Yields and Azimuthal Anisotropy at sqrt[s_{NN}]=5.02 TeV.

The CMS experiment at the LHC has measured the differential cross sections of Z bosons decaying to pairs of leptons, as functions of transverse momentum and rapidity, in lead-lead collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The measured Z boson elliptic azimuthal anisotropy coefficient is compatible with zero, showing that Z bosons do not experience significant final-state interactions in the medium produced in the collision. Yields of Z bosons are compared to Glauber model predictions and are found to deviate from these expectations in peripheral collisions, indicating the presence of initial collision geometry and centrality selection effects. The precision of the measurement allows, for the first time, for a data-driven determination of the nucleon-nucleon integrated luminosity as a function of lead-lead centrality, thereby eliminating the need for its estimation based on a Glauber model.

Coupled Boltzmann transport equations of heavy quarks and quarkonia in quark-gluon plasma

We develop a framework of coupled transport equations for open heavy flavor and quarkonium states, in order to describe their transport inside the quark-gluon plasma. Our framework is capable of studying simultaneously both open and hidden heavy flavor observables in heavy-ion collision experiments and can account for both, uncorrelated and correlated recombination. Our recombination implementation depends on real-time open heavy quark and antiquark distributions. We carry out consistency tests to show how the interplay among open heavy flavor transport, quarkonium dissociation and recombination drives the system to equilibrium. We then apply our framework to study bottomonium production in heavy-ion collisions. We include ϒ(1S), ϒ(2S), ϒ(3S), χb(1P) and χb(2P) in the framework and take feed-down contributions during the hadronic gas stage into account. Cold nuclear matter effects are included by using nuclear parton distribution functions for the initial primordial heavy flavor production. A calibrated 2 + 1 dimensional viscous hydrodynamics is used to describe the bulk QCD medium. We calculate both the nuclear modification factor RAA of all bottomonia states and the azimuthal angular anisotropy coefficient v2 of the ϒ(1S) state and find that our results agree reasonably with experimental measurements. Our calculations indicate that correlated cross-talk recombination is an important production mechanism of bottomonium in current heavy-ion experiments. The importance of correlated recombination can be tested experimentally by measuring the ratio of RAA(χb(1P)) and RAA(ϒ(2S)).

Relativistic Langevin dynamics: charm versus beauty

The production of heavy quarks (charm and beauty) provides unique insights into the transport properties of the Quark–Gluon Plasma (QGP) in heavy-ion collisions. Experimentally, the nuclear modification factor R_{mathrm{AA}} and the azimuthal anisotropy coefficient v_{mathrm{2}} of heavy-flavor mesons are powerful observables to study the medium-related effects, such as energy loss and collectivity, on the heavy quark propagation through the QGP evolution. The latest measurements of the prompt and non-prompt open heavy-flavor hadrons allow a systematic comparison of the transport behaviors probed by charm and beauty quarks. In this work we make such an attempt utilizing our recently developed framework. By performing a quantitative investigation of R_{mathrm{AA}} and v_{mathrm{2}}, it is found that both charm and beauty quarks are efficient probes to capture the dynamical features of QGP, in particular the resulting mass hierarchy for the energy loss and azimuthal anisotropy, which are well inherited by the various D/B-meson species. Moreover, our calculations can describe simultaneously R_{mathrm{AA}} and v_{mathrm{2}} data for the prompt and non-prompt D^{0} mesons in central (0-10%) and semi-central (30-50%) Pb–Pb collisions at sqrt{s_{mathrm{NN}}}=5.02~{mathrm{TeV}}. The predictions for B-meson observables for upcoming experimental tests are also made down to the low momentum region.

Collective Nuclear Vibrations and Initial State Shape Fluctuations in Central Pb + Pb Collisions: Resolving the v2 to v3 Puzzle

We have studied, for the first time, the influence of the collective quantum effects in the nuclear wave functions on the azimuthal anisotropy coefficients $\epsilon_{2,3}$ in the central Pb+Pb collisions at the LHC energies. With the help of the energy weighted sum rule we demonstrate that the classical treatment with the Woods-Saxon nuclear density overestimates the mean square quadrupole moment of the $^{208}$Pb nucleus by a factor of $\sim 2.2$. The Monte-Carlo Glauber simulation of the central Pb+Pb collisions accounting for the restriction on the quadrupole moment leads to $\epsilon_2/\epsilon_3\approx 0.8$ which allows to resolve the $v_2$-to-$v_3$ puzzle.

COLLECTIVE NUCLEAR VIBRATIONS AND INITIAL STATE SHAPE flUCTUATIONS IN CENTRAL PB + PB COLLISIONS: RESOLVING THE V2 TO V3 PUZZLE

We have studied, for the first time, the influence of the collective quantum effects in the nuclear wavefunctions on the azimuthal anisotropy coefficients ∈2,3 in the central Pb + Pb collisions at the LHC energies. With the help of the energy weighted sum rule, we demonstrate that the classical treatment with the Woods—Saxon nuclear density overestimates the mean square quadrupole moment of the 208Pb nucleus by a factor of ~2.2. The Monte Carlo Glauber simulation of the central Pb + Pb collisions accounting for the restriction on the quadrupole moment leads to ∈2/∈3 ≈ 0.8 which allows to resolve the v2-to-v3 puzzle.

Transverse momentum and process dependent azimuthal anisotropies in sqrt{s_{mathrm {NN}}}=8.16\xa0TeV p+Pb collisions with the ATLAS detector

The azimuthal anisotropy of charged particles produced in sqrt{s_{mathrm {NN}}}=8.16 TeV p+Pb collisions is measured with the ATLAS detector at the LHC. The data correspond to an integrated luminosity of 165 mathrm {nb}^{-1} that was collected in 2016. Azimuthal anisotropy coefficients, elliptic v_2 and triangular v_3, extracted using two-particle correlations with a non-flow template fit procedure, are presented as a function of particle transverse momentum (p_mathrm {T}) between 0.5 and 50 GeV. The v_2 results are also reported as a function of centrality in three different particle p_mathrm {T} intervals. The results are reported from minimum-bias events and jet-triggered events, where two jet p_mathrm {T} thresholds are used. The anisotropies for particles with p_mathrm {T} less than about 2 GeV are consistent with hydrodynamic flow expectations, while the significant non-zero anisotropies for p_mathrm {T} in the range 9–50 GeV are not explained within current theoretical frameworks. In the p_mathrm {T} range 2–9 GeV, the anisotropies are larger in minimum-bias than in jet-triggered events. Possible origins of these effects, such as the changing admixture of particles from hard scattering and the underlying event, are discussed.

Charged-particle angular correlations in XeXe collisions at sNN=5.44 TeV

Azimuthal correlations of charged particles in xenon-xenon collisions at a center-of-mass energy per nucleon pair of $ \sqrt{s_{_\mathrm{NN}}} =$ 5.44 TeV are studied. The data were collected by the CMS experiment at the LHC with a total integrated luminosity of 3.42 $\mu$b$^{-1}$. The collective motion of the system formed in the collision is parameterized by a Fourier expansion of the azimuthal particle density distribution. The azimuthal anisotropy coefficients $v_{2}$, $v_{3}$, and $v_{4}$ are obtained by the scalar-product, two-particle correlation, and multiparticle correlation methods. Within a hydrodynamic picture, these methods have different sensitivities to non-collective and fluctuation effects. The dependence of the Fourier coefficients on the size of the colliding system is explored by comparing the xenon-xenon results with equivalent lead-lead data. Model calculations that include initial-state fluctuation effects are also compared to the experimental results. The observed angular correlations provide new constraints on the hydrodynamic description of heavy ion collisions.

Elliptic Flow of Charm and Strange Hadrons in High-Multiplicity p+Pb Collisions at sqrt[s_{NN}]=8.16 TeV.

The elliptic azimuthal anisotropy coefficient (v_{2}) is measured for charm (D^{0}) and strange (K_{S}^{0}, Λ, Ξ^{-}, and Ω^{-}) hadrons, using a data sample of p+Pb collisions collected by the CMS experiment, at a nucleon-nucleon center-of-mass energy of sqrt[s_{NN}]=8.16 TeV. A significant positive v_{2} signal from long-range azimuthal correlations is observed for all particle species in high-multiplicity p+Pb collisions. The measurement represents the first observation of possible long-range collectivity for open heavy flavor hadrons in small systems. The results suggest that charm quarks have a smaller v_{2} than the lighter quarks, probably reflecting a weaker collective behavior. This effect is not seen in the larger PbPb collision system at sqrt[s_{NN}]=5.02 TeV, also presented.

Measurement of Prompt D^{0} Meson Azimuthal Anisotropy in Pb-Pb Collisions at sqrt[s_{NN}]=5.02 TeV.

The prompt D^{0} meson azimuthal anisotropy coefficients, v_{2} and v_{3}, are measured at midrapidity (|y|<1.0) in Pb-Pb collisions at a center-of-mass energy sqrt[s_{NN}]=5.02 TeV per nucleon pair with data collected by the CMS experiment. The measurement is performed in the transverse momentum (p_{T}) range of 1 to 40 GeV/c, for central and midcentral collisions. The v_{2} coefficient is found to be positive throughout the p_{T} range studied. The first measurement of the prompt D^{0} meson v_{3} coefficient is performed, and values up to 0.07 are observed for p_{T} around 4 GeV/c. Compared to measurements of charged particles, a similar p_{T} dependence, but smaller magnitude for p_{T}<6 GeV/c, is found for prompt D^{0} meson v_{2} and v_{3} coefficients. The results are consistent with the presence of collective motion of charm quarks at low p_{T} and a path length dependence of charm quark energy loss at high p_{T}, thereby providing new constraints on the theoretical description of the interactions between charm quarks and the quark-gluon plasma.

Enhancement of cyanobacterial control by fungi degraded palm oil trunk

The elliptic azimuthal anisotropy coefficient (v2) is measured for charm (D0) and strange (K0 S, Λ, Ξ−, and Ω−) hadrons, using a data sample of p þ Pb collisions collected by the CMS experiment, at a nucleonnucleon center-of-mass energy of ffiffiffiffiffiffiffi sNN p ¼ 8.16 TeV. A significant positive v2 signal from long-range azimuthal correlations is observed for all particle species in high-multiplicity p þ Pb collisions. The measurement represents the first observation of possible long-range collectivity for open heavy flavor hadrons in small systems. The results suggest that charm quarks have a smaller v2 than the lighter quarks, probably reflecting a weaker collective behavior. This effect is not seen in the larger PbPb collision system at ffiffiffiffiffiffiffi sNN p ¼ 5.02 TeV, also presented.