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| CMS-PAS-HIN-21-010 | ||
| Probing hydrodynamics and the moments of the elliptic flow distribution in ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}}= $ 5.02 TeV lead-lead collisions using higher-order cumulants | ||
| CMS Collaboration | ||
| April 2022 | ||
| Abstract: The $v_{2}$ cumulant values for the elliptic anisotropy harmonic, $v_{2}\{2k\}$, are determined up to the tenth order ($k = 5$) as a function of the collision centrality in ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}}= $ 5.02 TeV lead-lead collisions. The data were obtained by the CMS experiment at the LHC. A fine splitting is observed for the coefficients, with $v_{2}\{2\} > v_{2}\{4\} \gtrsim v_{2}\{6\} \gtrsim v_{2}\{8\} \gtrsim v_{2}\{10\}$. The subtle differences in the higher order harmonics allow for a precise determination of the underlying hydrodynamics. Based on these results, centrality-dependent moments for the fluctuation-driven $v_{2}$ distribution are determined, including the skewness, the kurtosis and, for the first time, the superskewness. Assuming a hydrodynamic expansion of the produced medium, these moments directly probe the initial state geometry in high energy nuclear collisions. | ||
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These preliminary results are superseded in this paper, Submitted to JHEP. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
The $v_{2}\{2k\}$ ($k = $ 1,..., 5) magnitudes as a function of centrality in PbPb collisions at$ {\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 5.02 TeV. The measurement is performed for $|\eta | < $ 2.4 and 0.5 $ < {p_{\mathrm {T}}} < $ 3.0 GeV/$c$. The bars (open boxes) denote statistical (systematic) uncertainties. Statistical uncertainties are negligible compared to the marker size. |
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Figure 2:
The $h_{1}$ (closed blue circles) and the new $h_{2}$ (closed red squares) hydrodynamics probe as function of centrality in PbPb collisions at ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} =$ 5.02 TeV. The distributions depicted with the open circles and squares represent the corresponding Taylor expansions given with $h_{1}^{\mathrm {Taylor}}$ and $h_{2}^{\mathrm {Taylor}}$ respectively. The horizontal blue (red) line represents a constant value of 1/11 (3/19). The measurement is performed for $|\eta | < $ 2.4 and 0.5 $ < {p_{\mathrm {T}}} < $ 3.0 GeV/$c$. The bars (boxes) denote statistical (systematic) uncertainties. |
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Figure 3:
The ratios between the hydrodynamics probes and their Taylor expansions. The ratios are plotted as a function of centrality in PbPb collisions at ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 5.02 TeV. The bars (open boxes) denote statistical (systematic) uncertainties. Statistical uncertainties are negligible compared to the marker size. |
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Figure 3-a:
The ratios between the hydrodynamics probes and their Taylor expansions. The ratios are plotted as a function of centrality in PbPb collisions at ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 5.02 TeV. The bars (open boxes) denote statistical (systematic) uncertainties. Statistical uncertainties are negligible compared to the marker size. |
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Figure 3-b:
The ratios between the hydrodynamics probes and their Taylor expansions. The ratios are plotted as a function of centrality in PbPb collisions at ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 5.02 TeV. The bars (open boxes) denote statistical (systematic) uncertainties. Statistical uncertainties are negligible compared to the marker size. |
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Figure 4:
The magnitudes of the experimentally measured (closed circles) skewness $\gamma ^{exp}_{1}$ (top), kurtosis $\gamma ^{exp}_{2}$ (middle) and the superskewness $\gamma ^{exp}_{3}$ (bottom) as a function of centrality in PbPb collisions at ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} =$ 5.02 TeV. The magnitudes of the 'cleaned' skewness $\gamma ^{exp}_{1,corr}$ (top), kurtosis $\gamma ^{exp}_{2,corr}$ (middle) and the superskewness $\gamma ^{exp}_{3,corr}$ (bottom) are presented with the open circles. The measurement is performed for $|\eta | < $ 2.4 and 0.5 $ < {p_{\mathrm {T}}} < $ 3.0 GeV/$c$. The bars (open boxes) denote statistical (systematic) uncertainties. |
| Summary |
| The cumulants of the elliptic flow distribution $v_{2}\{2k\}$ (1 $ \le k \le $ 5) are determined as a function of centrality for PbPb collisions at ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 5.02 TeV. For the first time, the $v_{2}\{10\}$ cumulant is determined. A fine splitting is observed between the cumulants, with $v_{2}\{4\} \gtrsim v_{2}\{6\} \gtrsim v_{2}\{8\} \gtrsim v_{2}\{10\}$. This splitting is attributed to a non-Gaussian behavior in the event-by-event fluctuations of the $v_{2}$ distribution leading to non-zero values of the skewness $\gamma^{exp}_{1}$, kurtosis $\gamma^{exp}_{2}$ and the superskewness $\gamma^{exp}_{3}$ of this distribution. The standardized magnitude of these moments are presented, together with their "cleaned'' values, where contributions from higher-order moments (up to the 5th moment) are removed. The splitting becomes finer with an increase of $k$, and the difference between unity and the ratios between the neighboring $v_{2}\{2k\}$ decrease from about 0.01 for $k=$ 2 to 1$\times$10$^{-4}$ for $k=$ 5. The large data set collected by the CMS Collaboration for PbPb collisions enable a precise measurement of the hydrodynamics probe $h_{1}$ as a function of centrality, where $h_{1}=(v_{2}\{6\}-v_{2}\{8\})/({v}_{2}\{4\}-v_{2}\{6\})$. A strong centrality dependence is observed, with values slowly increasing going to more peripheral collisions. This contrasts with an earlier hydrodynamics expectation that had taken the skewness of the initial-state geometry as the main source of the of non-Gaussian fluctuations. In this case the ratio was not expected to depend on centrality. Based on the new $v_{2}\{10\}$ measurements, a new hydrodynamic probe is introduced that gives an even more precise measure of the initial state geometry assuming a hydrodynamic evolution of the medium. The new probe $h_{2}$, given as $h_{2}=(v_{2}\{8\}-v_{2}\{10\})/({v}_{2}\{6\}-v_{2}\{8\})$, is found to have a centrality dependence with a shape similar to the earlier $h_{1}$ results. The centrality dependence of both ratios can be understood in terms of the evolving shape of the interaction region with centrality. This is shown by performing a Taylor expansion of the $v_{2}$ cumulant generating function up to the 4th (5th) moment, as expressed through the measured $v_{2}\{2k\}$ cumulants, for both hydrodynamics probes. These results place further constraints on the initial state geometry assumed in hydrodynamics calculations of the medium expansion in high energy nuclear collisions. |
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