CMS-HIN-21-010

CMS-HIN-21-010 ; CERN-EP-2023-158
Higher-order moments of the elliptic flow distribution in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV
CMS Collaboration
19 November 2023
JHEP 02 (2024) 106
Abstract: The hydrodynamic flow-like behavior of charged hadrons in high-energy lead-lead collisions is studied through multiparticle correlations. The elliptic anisotropy values based on different orders of multiparticle cumulants, $ v_{2}\{2k\} $, are measured up to the tenth order ($ k = $ 5) as functions of the collision centrality at a nucleon-nucleon center-of-mass energy of $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The data were recorded by the CMS experiment at the LHC and correspond to an integrated luminosity of 0.607 nb$^{-1}$. A hierarchy is observed between the coefficients, with $ v_{2}\{2\} > v_{2}\{4\} \gtrsim v_{2}\{6\} \gtrsim v_{2}\{8\} \gtrsim v_{2}\{10\} $. Based on these results, centrality-dependent moments for the fluctuation-driven event-by-event $ v_{2} $ distribution are determined, including the skewness, kurtosis and, for the first time, superskewness. Assuming a hydrodynamic expansion of the produced medium, these moments directly probe the initial-state geometry in high-energy nucleus-nucleus collisions.
Links: e-print arXiv:2311.11370 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures	Summary	References	CMS Publications

Figures
png pdf	Figure 1: A schematic view of a non-central nucleus-nucleus collision in the transverse plane.
png pdf	Figure 2: The $ v_{2}\{2k\} $ ($ k = $ 1, ..., 5) values as functions of centrality in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The vertical sizes of the open boxes denote the systematic uncertainties. Statistical uncertainties are negligible compared to the marker size. Points are plotted at the center of the respective centrality ranges. The markers are displaced horizontally for better visibility.
png pdf	Figure 3: The relative differences $ (v_{2}\{2k\}-v_{2}\{10\})/v_{2}\{10\} $ ($ k = $ 1, ..., 4) as functions of centrality in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The vertical sizes of the open boxes denote the systematic uncertainties. Statistical uncertainties are negligible compared to the marker size. Points are plotted at the center of the respective centrality ranges.
png pdf	Figure 4: The $ h_{1}=(v_{2}\{6\}-v_{2}\{8\})/({v}_{2}\{4\}-v_{2}\{6\}) $ (closed blue circles) and the $ h_{2}=(v_{2}\{8\}-v_{2}\{10\})/({v}_{2}\{6\}-v_{2}\{8\}) $ (closed red squares) hydrodynamic probes as functions 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 by $ h_{1}^{\text{Taylor}} $ and $ h_{2}^{\text{Taylor}} $, respectively. The horizontal blue (red) line represents a constant value of 1/11 (3/19). The bars (the vertical sizes of the open boxes) denote the statistical (systematic) uncertainties. Points are plotted at the center of the respective centrality ranges.
png pdf	Figure 5: The ratios between the hydrodynamic probes and their Taylor expansions. The ratios are plotted as functions of centrality in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The vertical sizes of the open boxes denote systematic uncertainties. Statistical uncertainties are negligible compared to the marker size. Points are plotted at the center of the respective centrality ranges.
png pdf	Figure 6: The magnitudes of the measured (closed circles) standardized skewness $ \gamma^{\text{exp}}_{1} $ (upper), standardized kurtosis $ \gamma^{\text{exp}}_{2} $ (middle), and standardized superskewness $ \gamma^{\text{exp}}_{3} $ (lower) as functions of centrality in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The magnitudes of the corrected skewness $ \gamma^{\text{exp}}_{1\text{,corr}} $ (upper), corrected kurtosis $ \gamma^{\text{exp}}_{2\text{, corr}} $ (middle), and corrected superskewness $ \gamma^{\text{exp}}_{3\text{, corr}} $ (lower) are presented with the open circles. The bars (the vertical sizes of the open boxes) denote statistical (systematic) uncertainties. Points are plotted at the center of the respective centrality ranges.

Summary

The elliptic anisotropy values based on different orders of multiparticle cumulants, $ v_{2}\{2k\} $ (1 $ \le k \le $ 5), are determined as functions of centrality in lead-lead collisions at a center-of-mass energy per nucleon pair of $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV, with an integrated luminosity of 0.607 nb$^{-1}$. The $ v_{2}\{10\} $ value is determined for the first time. A fine splitting is observed between the harmonic values based on different cumulant orders, with $ v_{2}\{4\} \gtrsim v_{2}\{6\} \gtrsim v_{2}\{8\} \gtrsim v_{2}\{10\} $. The ordering of the $ v_{2}\{2k\} $ values is consistent with a hydrodynamic evolution of the quark-gluon plasma (QGP). This splitting is attributed to a non-Gaussian behavior in the event-by-event fluctuations of the $ v_{2} $ distribution, leading to nonzero values of the skewness, kurtosis, and superskewness. The splitting becomes finer as the $ k $ value increases, with the difference between the adjacent $ v_{2}\{2k\} $ values decreasing by about an order of magnitude for each increment. The standardized magnitude of the $ v_{2} $ moments are presented, together with their corrected values, where contributions from higher-order moments (up to the 5th moment) are removed. The large data set of lead-lead collisions collected by the CMS experiment enables a precise measurement of the hydrodynamic 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 hydrodynamic expectation that had taken the skewness of the initial-state geometry as the main source of non-Gaussian fluctuations. In that case, the ratio was not expected to depend on centrality. Based on the first $ 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 QGP. The new probe, $ h_{2} $, defined as $ h_{2}=(v_{2}\{8\}-v_{2}\{10\})/({v}_{2}\{6\}-v_{2}\{8\}) $, is also found to have a centrality dependence, with a shape similar to the $ h_{1} $ results. The centrality dependence of both ratios can be understood in terms of the evolving shape of the interaction region with centrality. Based on these results, centrality-dependent moments for the fluctuation-driven event-by-event $ v_{2} $ distribution are determined, including the skewness, kurtosis and, for the first time, superskewness. The results provide basic input for a precision test of models that assume a hydrodynamic expansion of the QGP.

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