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.
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.
We present the first measurement of the two-particle transverse momentum differential correlation function, $P_2\equiv\langle \Delta p_{\rm T} \Delta p_{\rm T} \rangle /\langle p_{\rm T} \rangle^2$, in Pb-Pb collisions at $\sqrt{s_{_{\rm NN}}} =$ 2.76 TeV. Results for $P_2$ are reported as a function of relative pseudorapidity ($\Delta \eta$) and azimuthal angle ($\Delta \varphi$) between two particles for different collision centralities. The $\Delta \phi$ dependence is found to be largely independent of $\Delta \eta$ for $|\Delta \eta| \geq$ 0.9. In 5% most central Pb-Pb collisions, the two-particle transverse momentum correlation function exhibits a clear double-hump structure around $\Delta \varphi = \pi$ (i.e., on the away side), which is not observed in number correlations in the same centrality range, and thus provides an indication of the dominance of triangular flow in this collision centrality. Fourier decompositions of $P_2$, studied as a function of collision centrality, show that correlations at $|\Delta \eta| \geq$ 0.9 can be well reproduced by a flow ansatz based on the notion that measured momentum correlations are strictly determined by the collective motion of the system.
Projection of $P_{2}$ along $\Delta\varphi$ in 0-5% centrality in the range $|\Delta \eta| \geq$ 0.9
$v_{2}$ coefficients measured from $P_2$ for particle pairs in the range $0.2 \leq |\Delta\eta| \leq 0.9$.
$v_{2}$ coefficients measured from $P_2$ for particle pairs in the range $0.9 \leq |\Delta\eta| \leq 1.9$.
We present measurements of the elliptic ($\mathrm{v}_2$), triangular ($\mathrm{v}_3$) and quadrangular ($\mathrm{v}_4$) anisotropic azimuthal flow over a wide range of pseudorapidities ($-3.5< \eta < 5$). The measurements are performed with Pb-Pb collisions at $\sqrt{s_{\text{NN}}} = 2.76$ TeV using the ALICE detector at the Large Hadron Collider (LHC). The flow harmonics are obtained using two- and four-particle correlations from nine different centrality intervals covering central to peripheral collisions. We find that the shape of $\mathrm{v}_n(\eta)$ is largely independent of centrality for the flow harmonics $n=2-4$, however the higher harmonics fall off more steeply with increasing $|\eta|$. We assess the validity of extended longitudinal scaling of $\mathrm{v}_2$ by comparing to lower energy measurements, and find that the higher harmonic flow coefficients are proportional to the charged particle densities at larger pseudorapidities. Finally, we compare our measurements to both hydrodynamical and transport models, and find they both have challenges when it comes to describing our data.
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We report the first results of elliptic ($v_2$), triangular ($v_3$) and quadrangular flow ($v_4$) of charged particles in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV with the ALICE detector at the CERN Large Hadron Collider. The measurements are performed in the central pseudorapidity region $|\eta|<0.8$ and for the transverse momentum range $0.2<p_{\rm T}<5$ GeV/$c$. The anisotropic flow is measured using two-particle correlations with a pseudorapidity gap greater than one unit and with the multi-particle cumulant method. Compared to results from Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV, the anisotropic flow coefficients $v_{2}$, $v_{3}$ and $v_{4}$ are found to increase by ($3.0\pm0.6$)%, ($4.3\pm1.4$)% and ($10.2\pm3.8$)%, respectively, in the centrality range 0-50%. This increase can be attributed mostly to an increase of the average transverse momentum between the two energies. The measurements are found to be compatible with hydrodynamic model calculations. This comparison provides a unique opportunity to test the validity of the hydrodynamic picture and the power to further discriminate between various possibilities for the temperature dependence of shear viscosity to entropy density ratio of the produced matter in heavy-ion collisions at the highest energies.
Centrality dependence of $v_2$, with two- and multi-particle correlations, integrated over the $p_{\rm T}$ range 0.2 < $p_{\rm T}$ < 5.0 GeV/$c$, at $\sqrt{s_{\rm NN}}$ = 5.02 TeV.
Centrality dependence of $v_3$ and $v_4$, with two-particle correlations, integrated over the $p_{\rm T}$ range 0.2 < $p_{\rm T}$ < 5.0 GeV/c, at $\sqrt{s_{\rm NN}}$ = 5.02 TeV.
Centrality dependence of $v_2$, with two- and multi-particle correlations, integrated over the $p_{\rm T}$ range 0.2 < $p_{\rm T}$ < 5.0 GeV/c, at $\sqrt{s_{\rm NN}}$ = 2.76 TeV.
New PHENIX measurements of the anisotropic flow coefficients $v_2\{\Psi_2\}$, $v_3\{\Psi_3\}$, $v_4\{\Psi_4\}$ and $v_4\{\Psi_2\}$ for identified particles ($\pi^{\pm}$, $K^{\pm}$, and $p+\bar{p}$) obtained relative to the event planes $\Psi_n$ in Au$+$Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV are presented as functions of collision centrality and particle transverse momenta $p_T$. The $v_n$ coefficients show characteristic patterns consistent with hydrodynamical expansion of the matter produced in the collisions. For each harmonic $n$, a modified valence quark number $n_q$ scaling plotting $v_n/(n_q)^{n/2}$ versus ${\rm KE}_T/n_q$ is observed to yield a single curve for all the measured particle species for a broad range of transverse kinetic energies ${\rm KE}_T$. A simultaneous blast wave model fit to the observed particle spectra and $v_n(p_T)$ coefficients identifies spatial eccentricities $s_n$ at freeze-out, which are much smaller than the initial-state geometric values.
Azimuthal anisotropy $v_n$ via the event-plane method for charge-combined $\pi^{\pm}$ in 0%–50% central Au+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.
Azimuthal anisotropy $v_2$ and $v_3$ via the two-particle correlation method for charge-combined $\pi^{\pm}$ in 0%–50% central Au+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.
Azimuthal anisotropy $v_4$ via the two-particle correlation method for charge-combined $\pi^{\pm}$ in 0%–50% central Au+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.
Flow coefficients v_n for n = 2, 3, 4, characterizing the anisotropic collective flow in Au+Au collisions at sqrt(s_NN) = 200 GeV, are measured relative to event planes Ψ_n determined at large rapidity. We report v_n as a function of transverse momentum and collision centrality, and study the correlations among the event planes of different order n. The v_n are well described by hydrodynamic models which employ a Glauber Monte Carlo initial state geometry with fluctuations, providing additional constraining power on the interplay between initial conditions and the effects of viscosity as the system evolves. This new constraint improves precision of the extracted viscosity to entropy density ratio eta/s.
Charged hadron azimuthal anisotropy $v_2$, $v_3$, and $v_4$ vs $p_T$ in 0-10% central Au+Au collisions at 200 GeV. The mean $<p_T>$ in each $p_T$ bins used for the $v_n$ measurement is shown in Fig.2.6.
Charged hadron azimuthal anisotropy $v_2$, $v_3$, and $v_4$ vs $p_T$ in 10-20% central Au+Au collisions at 200 GeV. The mean $<p_T>$ in each $p_T$ bins used for the $v_n$ measurement is shown in Fig.2.6.
Charged hadron azimuthal anisotropy $v_2$, $v_3$, and $v_4$ vs $p_T$ in 20-30% central Au+Au collisions at 200 GeV. The mean $<p_T>$ in each $p_T$ bins used for the $v_n$ measurement is shown in Fig.2.6.
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