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star focus: Azimuthal harmonics in small and large collision systems at RHIC top energies

The STAR Collaboration has recently published, Azimuthal Harmonics in Small and Large Collision Systems at RHIC Top Energies, in Physical Review Letter, 122, 172301(2019).

This publication reports and compares recent integral and differential measurements (obtained with the STAR TPC), of the flow harmonics ($v_n, n=1-3$) for charged hadrons produced in U+U collisions ($\sqrt{s_{{NN}}}$ = 193 GeV) and Au+Au, Cu+Au, Cu+Cu, d+Au, and p+Au collisions ($\sqrt{s_{{NN}}}$ = 200 GeV). The measurements for these disparate collision-systems, allow systematic variations of the initial-state eccentricity and its fluctuations, as well as the size of the produced fireball at approximately the same collision energy. All are expected to influence the magnitude of $v_n$. The comparisons between the measurements for these small, medium and large collision systems, give unique insights into the role of final-state interactions as the collision-system size is varied. Similarly, the measurements provide more discerning constraints which can aid extraction of the temperature-dependent specific shear viscosity of the hot and dense media created in the collisions.


Two-particle azimuthal correlation functions (a-f) and four-particle cumulants (g) for pT-integrated track pairs. Results are shown for U+U (a) collisions (193 GeV) and Au+Au (b), Cu+Au (c), Cu+Cu (d), d+Au (e) and p+Au (f) collisions (200 GeV) for the same charged particle multiplicity $N_{ch}$. Panel (g) shows the four-particle second-order cumulant vs. $N_{ch}$, obtained with the three sub-events method from the same data sets.

The measurements exploit both the two- and multi-particle correlation techniques to extract $v_n$ as a function of the transverse momentum ($p_T$) and mean charged particle multiplicity $N_{ch}$. The first figure shows representative correlation functions (a-f) and four particle cumulants (g) which accentuate the qualitative similarity between the charged particle azimuthal distributions obtained for the full range of collision-system sizes. Further quantitative study reveals that for a fixed value of $N_{ch}$, the $v^{even}_{1}$ and $v_{3}$ coefficients are essentially independent of the colliding species, indicating that for a given $N_{ch}$, the fluctuation-driven initial-state eccentricities, $\varepsilon_{1}$ and $\varepsilon_{3}$, are system independent. By contrast, the $v_{2}$ coefficients indicate sizeable variations [for fixed $N_{ch}$] with the colliding species, showing the strong collision-system dependence of the shape-driven eccentricity $\varepsilon_{2}$.


$v_{2}/\varepsilon_{2}$ vs. $N_{ch}^{-1/3}$ for U+U, Au+Au, Cu+Au, Cu+Cu, d+Au and p+Au collisions as indicated. The open boxes indicate systematic uncertainties. The dotted line represents an exponential fit to the data. The inset shows the respective ratios of the slopes extracted for each system relative to the slope extracted from a fit to the combined data sets (Slope = 0.82 $\pm$ 0.02).

The second figure shows the $N_{ch}$ dependence of the eccentricity-scaled second harmonic $v_{2}/\varepsilon_{2}$, for the respective collision systems. Since such patterns reflect the influence of viscous attenuation in the hot and dense media created in the collisions, they suggest a collision-system-independent viscous attenuation coefficient. That is, the implied specific shear viscosity coefficient is independent of the collision-system and consequently, the initial-state eccentricity spectrum. Note that this pattern of viscous attenuation suggests a strong dependence on the dimensionless size of the produced media, where $N_{ch}$ is proportional to this size.

The detailed comparisons of the reported measurements highlight the sensitivity of vn to the magnitude of the initial-state eccentricity, system size and the final-state interactions in the expanding matter. Thus, they lend essential insight into the role of final-state interactions in the system studied and provide significant constraints for model calculations with an eye toward extraction of the temperature-dependent specific shear viscosity.

Posted May 31, 2018

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