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CMS-HIN-16-019 ; CERN-EP-2017-268
Non-Gaussian elliptic-flow fluctuations in PbPb collisions at $\sqrt{\smash[b]{s_{_\mathrm{NN}}}} = $ 5.02 TeV
Phys. Lett. B 789 (2019) 643
Abstract: Event-by-event fluctuations in the elliptic-flow coefficient $v_2$ are studied in PbPb collisions at $\sqrt{\smash[b]{s_{_\mathrm{NN}}}} = $ 5.02 TeV using the CMS detector at the CERN LHC. Elliptic-flow probability distributions ${p}(v_2)$ for charged particles with transverse momentum 0.3 $ < {p_{\mathrm{T}}} < $ 3.0 GeV/$c$ and pseudorapidity $ | \eta | < $ 1.0 are determined for different collision centrality classes. The moments of the ${p}(v_2)$ distributions are used to calculate the $v_{2}$ coefficients based on cumulant orders 2, 4, 6, and 8. A rank ordering of the higher-order cumulant results and nonzero standardized skewness values obtained for the ${p}(v_2)$ distributions indicate non-Gaussian initial-state fluctuation behavior. Bessel-Gaussian and elliptic power fits to the flow distributions are studied to characterize the initial-state spatial anisotropy.
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Figure 1:
Representative final unfolded $p(v_2)$ distributions (closed black circles) in three centrality bins (15-20%, 30-35%, and 55-60%) obtained using D'Agostini iteration unfolding. Respective observed $p(v_2^\mathrm {obs})$ distributions (open black squares) are shown to illustrate the statistical resolution present in each centrality bin prior to unfolding. Systematic uncertainties from the unfolding procedure are presented as shaded bands. Distributions are fitted with Bessel-Gaussian (dashed blue lines) and elliptic power (solid red lines) functions to infer information on the underlying $p(\varepsilon _2)$ distributions.

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Figure 2:
Elliptic-flow cumulant harmonics with values obtained from the moments of the unfolded $p(v_2)$ distributions. Statistical uncertainties are smaller than the symbol size. Systematic uncertainties are shown as gray bands.

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Figure 3:
Ratios of higher order cumulant elliptic-flow harmonics with values obtained from the moments of the unfolded $p(v_2)$ distributions. Both statistical (lines) and systematic (gray bands) uncertainties are shown. Hydrodynamic predictions for 2.76 TeV collisions from Ref. [27] are presented as a dark color band and are compared to the measured $v_{2}\{6\}/v_2\{4\}$ ratio. In addition, higher order cumulant ratios reported by the ATLAS Collaboration for 2.76 TeV collisions [14] with 0.5 $ < {p_{\mathrm {T}}} < $ 20.0 GeV/$c$ and $ | \eta | < $ 2.5 are compared to the 5.02 TeV measurement. The error bars on the ATLAS measurement represent the quadratic sum of statistical and systematic uncertainties and points are offset horizontally for clarity.

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Figure 4:
The skewness estimate with respect to the reaction plane determined using the elliptic-flow harmonic based on different cumulant orders. Both statistical and systematic uncertainties are shown, where statistical uncertainties are smaller than the data points. Hydrodynamic model predictions for 2.76 TeV PbPb collisions from Ref. [27] are shown as a colored band.

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Figure 5:
Centrality dependence of the parameters extracted from elliptic power function fits to the unfolded $p(v_2)$ distributions. Both statistical (error bars) and systematic (shaded boxes) uncertainties are shown. The solid lines represent theoretical calculations from Ref. [11] using viscous hydrodynamics with Glauber initial conditions and an $\eta /s$ value of 0.19 to determine the response coefficient $k_2$. Glauber (blue shaded band) and IP-Glasma (red shaded band) model calculations from Ref. [11] are shown for the $\alpha $ and $\varepsilon _0$ parameters.
In summary, a non-Gaussian behavior is observed in the event-by-event fluctuations of the elliptic flow $v_2$ coefficients in PbPb collisions recorded by the CMS detector at $\sqrt{\smash[b]{s_{_\mathrm{NN}}}} = $ 5.02 TeV. The probability distributions $p(v_2)$ for 5%-centrality bins between 5% and 60% centrality are found by unfolding statistical resolution effects from measured flow distributions. The $v_2$ coefficients corresponding to different cumulant orders are calculated from the moments of the unfolded $p(v_2)$ distributions. A rank ordering of $v_2\{4\} > v_2\{6\} > v_2\{8\}$, with differences on the order of a few percent, is observed for noncentral events with centralities greater than ${\approx}15%$. The standardized skewness of each $p(v_2)$ distribution is calculated using the cumulant results. In cases where there is a splitting of the cumulant values, the standardized skewness is found to be negative with an increasing magnitude as collisions become less central. Bessel-Gaussian and elliptic power functions are fitted to the unfolded $p(v_2)$ distributions. The two distributions are similar for central collisions, though the elliptic power function provides a better description for noncentral collisions.

Based on the elliptic power function fits, the centrality dependence of the flow response coefficient, which relates the final state geometry to the initial state energy density distribution, is found to be consistent with model calculations. However, the observed eccentricities are smaller than predictions based on either the Glauber model or the IP-Glasma model initial conditions with an assumed linear flow response. The current results illustrate that LHC experiments now have the precision to explore the details of the initial-state fluctuation behavior.
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