Pseudorapidity dependence of the anisotropic flow of charged particles in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV

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.

Figures

Figure 1

Measurements of the pseudorapidity dependence of $\mathrm{v}_2$, $\mathrm{v}_3$ and $\mathrm{v}_4$ in each centrality bin. The vertical lines represent the statistical uncertainties and the boxes represent the systematic uncertainties. The statistical uncertainties are usually smaller than the marker size.
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Figure 2

Elliptic flow for the $25$-$50\%$ centrality range. Boxes represent systematic uncertainties and errors bars represent statistical uncertainties. The results for $\mathrm{v}_2\{2\}$ from this analysis are compared to measurements using the event plane method from CMS and ATLAS at the same energy and lower energy results from PHOBOS . For the comparable LHC energy, the $p_\text{T}$ range for ALICE is $p_\text{T} > 0 $ GeV/c, for CMS is $0.3 < p_\text{T} < 3 $ GeV/c, and for ATLAS is $p_\text{T} > 0.07 $ GeV/c.
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Figure 3

The elliptic flow as observed in the rest frame of one of the projectiles by using the variable $|\eta|-y_{beam}$ ($y_{beam}=7.99$) for the event averaged $0$-$40\%$ centrality range. The results from $\mathrm{v}_2\{2\}$ from this analysis are compared to lower energy results from PHOBOS . The vertical lines represent the statistical uncertainties and the boxes represent the systematic uncertainties. For the PHOBOS results only statistical errors are shown.
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Figure 4

Ratio of $\mathrm{v}_n\{2\}$ between central ($0$-$5\%$) and peripheral ($50$-$60\%$) events for $\mathrm{v}_2$, $\mathrm{v}_3$ and $\mathrm{v}_4$. The vertical lines represent the statistical uncertainties and the boxes represent the systematic uncertainties. The $\mathrm{v}_2$ results are multiplied by 3 to fit on the same scale as $\mathrm{v}_3$ and $\mathrm{v}_4$.
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Figure 5

Ratios between different harmonics for the $30$-$40\%$ centrality range. The vertical lines represent the statistical uncertainties and the boxes represent the common systematic uncertainties. In the bottom panel the ratios are rescaled to $1$ at mid-rapidity and the common systematic uncertainties are shown as the thick bars on the left.
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Figure 6

Ratios between $\mathrm{v}_{n}$ coefficients and $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$ values for different centralities. Measurements of $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$ are taken from a previous ALICE publication . Only systematic uncertainties are shown, as the statistical uncertainties are smaller than the symbols.
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Figure 7

Comparisons to hydrodynamics predictions , where input parameters (temperature dependence of $\eta/s$) have been tuned to RHIC data for the Pb-Pb 20-30% (top) and 40-50% (bottom) centralities. The predictions are for Pb-Pb $\sqrt{s_{\text{NN}}} = 2.76$ TeV collisions.
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Figure 8

Comparison to AMPT for the centrality ranges $5$-$10\%$ and (top) and $40$-$50\%$ (bottom). The AMPT predictions are for Pb-Pb $\sqrt{s_{\text{NN}}} = 2.76$ TeV collisions.
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