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Register a new userAzimuthal anisotropy at RHIC: the first and fourth harmonics
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We report the first observations of the first harmonic (directed flow, v_1), and the fourth harmonic (v_4), in the azimuthal distribution of particles with respect to the reaction plane in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC). Both measurements were done taking advantage of the large elliptic flow (v_2) generated at RHIC. From the correlation of v_2 with v_1 it is determined that v_2 is positive, or {it in-plane}. The integrated v_4 is about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8) harmonics upper limits on the magnitudes are reported.
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We report the first observations of the fourth harmonic (v_4) in the azimuthal distribution of particles at RHIC. The measurement was done taking advantage of the large elliptic flow generated at RHIC. The integrated v_4 is about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8) harmonics upper limits on the magnitudes are reported.
The first ($v_1^{text{even}}$), second ($v_2$) and third ($v_3$) harmonic coefficients of the azimuthal particle distribution at mid-rapidity, are extracted for charged hadrons and studied as a function of transverse momentum ($p_T$) and mean charged particle multiplicity density $langle mathrm{N_{ch}} rangle$ in U+U ($roots =193$~GeV), Au+Au, Cu+Au, Cu+Cu, $d$+Au and $p$+Au collisions at $roots = 200$~GeV with the STAR Detector. For the same $langle mathrm{N_{ch}} rangle$, the $v_1^{text{even}}$ and $v_3$ coefficients are observed to be independent of collision system, while $v_2$ exhibits such a scaling only when normalized by the initial-state eccentricity ($varepsilon_2$). The data also show that $ln(v_2/varepsilon_2)$ scales linearly with $langle mathrm{N_{ch}} rangle^{-1/3}$. These measurements provide insight into initial-geometry fluctuations and the role of viscous hydrodynamic attenuation on $v_n$ from small to large collision systems.
Collisions between prolate uranium nuclei are used to study how particle production and azimuthal anisotropies depend on initial geometry in heavy-ion collisions. We report the two- and four-particle cumulants, $v_2{2}$ and $v_2{4}$, for charged hadrons from U+U collisions at $sqrt{s_{rm NN}}$ = 193 GeV and Au+Au collisions at $sqrt{s_{rm NN}}$ = 200 GeV. Nearly fully overlapping collisions are selected based on the amount of energy deposited by spectators in the STAR Zero Degree Calorimeters (ZDCs). Within this sample, the observed dependence of $v_2{2}$ on multiplicity demonstrates that ZDC information combined with multiplicity can preferentially select different overlap configurations in U+U collisions. An initial-state model with gluon saturation describes the slope of $v_2{2}$ as a function of multiplicity in central collisions better than one based on Glauber with a two-component multiplicity model.
We present measurements of three-particle correlations for various harmonics in Au+Au collisions at energies ranging from $sqrt{s_{{rm NN}}}=7.7$ to 200 GeV using the STAR detector. The quantity $langlecos(mphi_1+nphi_2-(m+n)phi_3)rangle$ is evaluated as a function of $sqrt{s_{{rm NN}}}$, collision centrality, transverse momentum, $p_T$, pseudo-rapidity difference, $Deltaeta$, and harmonics ($m$ and $n$). These data provide detailed information on global event properties like the three-dimensional structure of the initial overlap region, the expansion dynamics of the matter produced in the collisions, and the transport properties of the medium. A strong dependence on $Deltaeta$ is observed for most harmonic combinations consistent with breaking of longitudinal boost invariance. Data reveal changes with energy in the two-particle correlation functions relative to the second-harmonic event-plane and provide ways to constrain models of heavy-ion collisions over a wide range of collision energies.
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 systems 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.
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