CMSHIN21010 ; CERNEP2023158  
Higherorder 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 flowlike behavior of charged hadrons in highenergy leadlead 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 nucleonnucleon centerofmass 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, centralitydependent moments for the fluctuationdriven eventbyevent $ 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 initialstate geometry in highenergy nucleusnucleus collisions.  
Links: eprint arXiv:2311.11370 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; 
Figures  
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Figure 1:
A schematic view of a noncentral nucleusnucleus collision in the transverse plane. 
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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. 
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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. 
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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. 
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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. 
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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 leadlead collisions at a centerofmass 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 quarkgluon plasma (QGP). This splitting is attributed to a nonGaussian behavior in the eventbyevent 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 higherorder moments (up to the 5th moment) are removed. The large data set of leadlead 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 initialstate geometry as the main source of nonGaussian 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 initialstate 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, centralitydependent moments for the fluctuationdriven eventbyevent $ 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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