High precision measurements of flow coefficients $v_{n}$ ($n = 1 - 4$) for protons, deuterons and tritons relative to the first-order spectator plane have been performed in Au+Au collisions at $\sqrt{s_{NN}} = 2.4$ GeV with the High-Acceptance Di-Electron Spectrometer (HADES) at the SIS18/GSI. Flow coefficients are studied as a function of transverse momentum $p_{t}$ and rapidity $y_{cm}$ over a large region of phase space and for several classes of collision centrality. A clear mass hierarchy is found for the slope of $v_{1}$, $d v_{1}/d y^{\prime}|_{y^{\prime} = 0}$ where $y^{\prime}$ is the scaled rapidity, and for $v_{2}$ at mid-rapidity. Scaling with the number of nucleons is observed for the $p_{t}$ dependence of $v_{2}$ and $v_{4}$ at mid-rapidity, which is indicative for nuclear coalescence as the main process responsible for light nuclei formation. $v_{2}$ is found to scale with the initial eccentricity $\langle \epsilon_{2} \rangle$, while $v_{4}$ scales with $\langle \epsilon_{2} \rangle^{2}$ and $\langle \epsilon_{4} \rangle$. The multi-differential high-precision data on $v_{1}$, $v_{2}$, $v_{3}$, and $v_{4}$ provides important constraints on the equation-of-state of compressed baryonic matter.
The resolution $\Re_{n}$ of the first-order spectator event plane for flow coefficients of different orders $n$ as a function of the event centrality (Adamczewski-Musch:2020iio). The circles correspond to centrality intervals of $5 \%$ width and the squares to $10 \%$ width (curves are meant to guide the eye).
The resolution $\Re_{n}$ of the first-order spectator event plane for flow coefficients of different orders $n$ as a function of the event centrality (Adamczewski-Musch:2020iio). The circles correspond to centrality intervals of $5 \%$ width and the squares to $10 \%$ width (curves are meant to guide the eye).
The flow coefficients $v_{1}$, $v_{2}$, $v_{3}$, and $v_{4}$ (from top to bottom panels) of protons, deuterons and tritons (from left to right panels) in semi-central ($20 - 30 \%$) Au+Au collisions at $\sqrt{s_{NN}} = 2.4$ GeV as a function of the centre-of-mass rapidity $y_{cm}$ in transverse momentum intervals of $50$ MeV$/c$ width. Systematic uncertainties are displayed as boxes. Lines are to guide the eye.
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/$c$.
Azimuthal anisotropy $v_2\{BB\}$ as a function of transverse momentum $p_T$ in $p$+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.
Azimuthal anisotropy $v_2\{BF\}$ as a function of transverse momentum $p_T$ in $p$+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.
Azimuthal anisotropy $v_2\{BB\}$ as a function of transverse momentum $p_T$ in $d$+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.
Flow coefficients $v_{n}$ of the orders $n = 1 - 6$ are measured with the High-Acceptance DiElectron Spectrometer (HADES) at GSI for protons, deuterons and tritons as a function of centrality, transverse momentum and rapidity in Au+Au collisions at $\sqrt{s_{NN}} = 2.4$ GeV. Combining the information from the flow coefficients of all orders allows to construct for the first time, at collision energies of a few GeV, a multi-differential picture of the angular emission pattern of these particles. It reflects the complicated interplay between the effect of the central fireball pressure on the emission of particles and their subsequent interaction with spectator matter. The high precision information on higher order flow coefficients is a major step forward in constraining the equation-of-state of dense baryonic matter.
The $p_{t}$ dependence of $v_{1}$ for protons, deuterons and tritons in the rapidity interval $-0.25 < y_{cm} < -0.15$ in semi-central ($20 - 30$ %) $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}=2.4$ GeV.
The $p_{t}$ dependence of $v_{3}$ for protons, deuterons and tritons in the rapidity interval $-0.25 < y_{cm} < -0.15$ in semi-central ($20 - 30$ %) $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}=2.4$ GeV.
The $p_{t}$ dependence of $v_{5}$ for protons, deuterons and tritons in the rapidity interval $-0.25 < y_{cm} < -0.15$ in semi-central ($20 - 30$ %) $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}=2.4$ GeV.
Flow harmonics ($v_n$) 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 $\sqrt{s_{NN}}$ = 39 and 200 GeV from data collected by the STAR experiment at RHIC. We observe that $v_{2}$ and $v_{3}$ 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 $v_{2}$-$v_{4}$ 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 $v_{2}$ and $v_{3}$. The best description of $v_{2}$-$v_{4}$ correlations at $\sqrt{s_{NN}}$ = 200 GeV is obtained with inclusion of the system's nonlinear response to initial eccentricities accompanied by the viscous effect with $\eta/s$ $>$ 0.08. Theoretical calculations using different initial conditions, equations of state and viscous coefficients need to be further explored to extract $\eta/s$ of the medium created at RHIC.
Symmetric cumulant SC(2,3) and SC(2,4) as a function of average number of participant nucleons in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.
Symmetric cumulant SC(2,3) as a function of average number of participant nucleons in Au+Au collisions at $\sqrt{s_{NN}}$ = 39 GeV.
Symmetric cumulant SC(2,4) as a function of average number of participant nucleons in Au+Au collisions at $\sqrt{s_{NN}}$ = 39 GeV.
Elliptic flow ($v_{2}$) values for identified particles at mid-rapidity in Au+Au collisions, measured by the STAR experiment in the Beam Energy Scan at RHIC at $\sqrt{s_{NN}}=$ 7.7--62.4 GeV, are presented. A beam-energy dependent difference of the values of $v_{2}$ between particles and corresponding anti-particles was observed. The difference increases with decreasing beam energy and is larger for baryons compared to mesons. This implies that, at lower energies, particles and anti-particles are not consistent with the universal number-of-constituent-quark (NCQ) scaling of $v_{2}$ that was observed at $\sqrt{s_{NN}}=$ 200 GeV.
The elliptic flow $v_{2}$ of protons and anti-protons as a function of the transverse momentum, $p_{T}$, for 0–80$\%$ central Au+Au collisions. The lower panels show the difference in $v_{2}(p_{T})$ between the particles and anti-particles. The solid curves are fits with a horizontal line. The shaded areas depict the magnitude of the systematic errors.
The elliptic flow $v_{2}$ of protons and anti-protons as a function of the transverse momentum, $p_{T}$, for 0–80$\%$ central Au+Au collisions. The lower panels show the difference in $v_{2}(p_{T})$ between the particles and anti-particles. The solid curves are fits with a horizontal line. The shaded areas depict the magnitude of the systematic errors.
The elliptic flow $v_{2}$ of protons and anti-protons as a function of the transverse momentum, $p_{T}$, for 0–80$\%$ central Au+Au collisions. The lower panels show the difference in $v_{2}(p_{T})$ between the particles and anti-particles. The solid curves are fits with a horizontal line. The shaded areas depict the magnitude of the systematic errors.
A systematic study is presented for centrality, transverse momentum ($p_T$) and pseudorapidity ($\eta$) dependence of the inclusive charged hadron elliptic flow ($v_2$) at midrapidity($|\eta| < 1.0$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7, 11.5, 19.6, 27 and 39 GeV. The results obtained with different methods, including correlations with the event plane reconstructed in a region separated by a large pseudorapidity gap and 4-particle cumulants ($v_2{4}$), are presented in order to investigate non-flow correlations and $v_2$ fluctuations. We observe that the difference between $v_2{2}$ and $v_2{4}$ is smaller at the lower collision energies. Values of $v_2$, scaled by the initial coordinate space eccentricity, $v_{2}/\varepsilon$, as a function of $p_T$ are larger in more central collisions, suggesting stronger collective flow develops in more central collisions, similar to the results at higher collision energies. These results are compared to measurements at higher energies at the Relativistic Heavy Ion Collider ($\sqrt{s_{NN}}$ = 62.4 and 200 GeV) and at the Large Hadron Collider (Pb + Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV). The $v_2(p_T)$ values for fixed $p_T$ rise with increasing collision energy within the $p_T$ range studied ($< 2 {\rm GeV}/c$). A comparison to viscous hydrodynamic simulations is made to potentially help understand the energy dependence of $v_{2}(p_{T})$. We also compare the $v_2$ results to UrQMD and AMPT transport model calculations, and physics implications on the dominance of partonic versus hadronic phases in the system created at Beam Energy Scan (BES) energies are discussed.
The event plane resolutions for Au + Au collisions at $\sqrt{s_{NN}}$ = 7.7, 11.5, 19.6, 27 and 39 GeV as a function of collision centrality.
The comparison of $v_2$ as a function of $p_T$ between GF-cumulant and Q-cumulant methods in Au+Au collisions at $\sqrt{s_{NN}}$ = 39 GeV.
The $p_T$ (> 0.2 GeV/c) and $\eta$ ($∣\eta∣$ < 1) integrated $v_2$ as a function of collision centrality for Au + Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV, 11.5 GeV, 19.6 GeV, 27 GeV and 39 GeV.
The results from the STAR Collaboration on directed flow (v_1), elliptic flow (v_2), and the fourth harmonic (v_4) in the anisotropic azimuthal distribution of particles from Au+Au collisions at sqrtsNN = 200 GeV are summarized and compared with results from other experiments and theoretical models. Results for identified particles are presented and fit with a Blast Wave model. Different anisotropic flow analysis methods are compared and nonflow effects are extracted from the data. For v_2, scaling with the number of constituent quarks and parton coalescence is discussed. For v_4, scaling with v_2^2 and quark coalescence is discussed.
Directed flow of charged hadrons v1{3} as a function of pseudorapidity for 10–70% centrality.
Directed flow of charged hadrons v1 {EP1,EP2} as a function of pseudorapidity for 20–60% centrality.
Charged hadron v2 for the centrality bins 5 to 10% and in steps of 10% starting at 10, 20, 30, 40, 50, 60, and 70 up to 80% along with min. bias as a function of p_T.
We report first results on elliptic flow of identified particles at mid-rapidity in Au+Au collisions at $\sqrt{s_{_{NN}}}=130$ GeV using the STAR TPC at RHIC. The elliptic flow as a function of transverse momentum and centrality differs significantly for particles of different masses. This dependence can be accounted for in hydrodynamic models, indicating that the system created shows a behavior consistent with collective hydrodynamical flow. The fit to the data with a simple model gives information on the temperature and flow velocities at freeze-out.
Differential elliptic flow for pions for minimum-bias events, the systematic uncertainty for minimum-bias data is 13%.
Differential elliptic flow for protons + antiprotons for minimum-bias events, the systematic uncertainty for minimum-bias data is 13%.
Differential elliptic flow for kaons for minimum-bias events, the systematic uncertainty for minimum-bias data is 13%.
Elliptic flow from nuclear collisions is a hadronic observable sensitive to the early stages of system evolution. We report first results on elliptic flow of charged particles at midrapidity in Au+Au collisions at sqrt(s_NN)=130 GeV using the STAR TPC at RHIC. The elliptic flow signal, v_2, averaged over transverse momentum, reaches values of about 6% for relatively peripheral collisions and decreases for the more central collisions. This can be interpreted as the observation of a higher degree of thermalization than at lower collision energies. Pseudorapidity and transverse momentum dependence of elliptic flow are also presented.
Elliptic flow as a function of centrality defined as nch/nmax. Also given is epsilon, the initial space eccentricity of the overlap region, as well as the cumulative fraction of events starting with the most central. From the results of the study of non-flow contributions by different subevent selections and the maximum magnitudes of the first and higher-order harmonics, we estimate a systematic error for v2 of about 0.007, with somewhat smaller uncertainty for the mid-centralities where the resolution of the event plane is high.
Elliptic flow as a function of transverse momen-tum for minimum bias events
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