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Register a new userAzimuthal anisotropy: the higher harmonics
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Arthur M. Poskanzer
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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.
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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.
The LHC data on azimuthal anisotropy harmonics from PbPb collisions at center-of-mass energy 2.76 TeV per nucleon pair are analyzed and interpreted in the framework of the HYDJET++ model. The cross-talk of elliptic $v_2$ and triangular $v_3$ flow in the model generates both even and odd harmonics of higher order. Comparison with the experimental data shows that this mechanism is able to reproduce the $p_{rm T}$ and centrality dependencies of quadrangular flow $v_4$, and also the basic trends for pentagonal $v_5$ and hexagonal $v_6$ flows.
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.
Measured 2nd and 4th azimuthal anisotropy coefficients v_{2,4}(N_{part}), p_T) are scaled with the initial eccentricity varepsilon_{2,4}(N_{part}) of the collision zone and studied as a function of the number of participants N_{part} and the transverse momenta p_T. Scaling violations are observed for $p_T alt 3$ GeV/c, consistent with a $p_T^2$ dependence of viscous corrections and a linear increase of the relaxation time with $p_T$. These empirical viscous corrections to flow and the thermal distribution function at freeze-out constrain estimates of the specific viscosity and the freeze-out temperature for two different models for the initial collision geometry. The apparent viscous corrections exhibit a sharp maximum for $p_T agt 3$ GeV/c, suggesting a breakdown of the hydrodynamic ansatz and the onset of a change from flow-driven to suppression-driven anisotropy.
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.
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