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| CMS-PAS-HIN-24-004 | ||
| Characterizing the Initial State in XeXe and PbPb Collisions using Multiparticle Cumulants | ||
| CMS Collaboration | ||
| 27 February 2025 | ||
| Abstract: The nuclear shape and size dependences of Fourier flow harmonics ($ v_{n} $, $ n = $ 2, 3, 4) in XeXe collisions at $ \sqrt{s_{{\mathrm{NN}}}} = $ 5.44 TeV and PbPb collisions at $ \sqrt{s_{{\mathrm{NN}}}} = $ 5.36 TeV are studied using the CMS detector. For the first time, correlations between higher-power moments of two or three flow harmonics, as a function of collision centrality, are compared in XeXe and PbPb collisions. This is achieved by measuring multiparticle mixed harmonic cumulants (up to 8-particle cumulants) using charged particles in the pseudorapidity range $ |\eta| < $ 2.4 and transverse momentum range 0.5 $ < p_{T} < $ 3.0 GeV/$c $. The results are compared to theoretical models to investigate the non-linear hydrodynamic response by examining correlations between $ v_{2} $, $ v_{3} $, and $ v_{4} $ and their corresponding eccentricities $ \varepsilon_{2} $, $ \varepsilon_{3} $, and $ \varepsilon_{4} $. This work provides valuable insights into the deformation parameters of the Xe nucleus and constrains initial-state model parameters influencing the evolution of the quark-gluon plasma in heavy-ion collisions at the LHC. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
$ v_{n}\{2,|\Delta\eta| > 2\} $ (n = 2, 3) as a function of centrality in XeXe and PbPb, calculated from the 2-particle correlation method. The bars and the open boxes represent statistical and systematic uncertainties, respectively. The red solid lines show the prediction from TRENTo-IC in terms of the initial-state eccentricities $ \varepsilon_{n} $ for deformed Xe (Xe-(a)), and the black line is for spherical Xe (Xe-(b)) when taken in ratio with Pb. The shaded bands show the different hydrodynamic predictions for different sets of deformations from the IP-Glasma+MUSIC+UrQMD model. |
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Figure 1-a:
$ v_{n}\{2,|\Delta\eta| > 2\} $ (n = 2, 3) as a function of centrality in XeXe and PbPb, calculated from the 2-particle correlation method. The bars and the open boxes represent statistical and systematic uncertainties, respectively. The red solid lines show the prediction from TRENTo-IC in terms of the initial-state eccentricities $ \varepsilon_{n} $ for deformed Xe (Xe-(a)), and the black line is for spherical Xe (Xe-(b)) when taken in ratio with Pb. The shaded bands show the different hydrodynamic predictions for different sets of deformations from the IP-Glasma+MUSIC+UrQMD model. |
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Figure 1-b:
$ v_{n}\{2,|\Delta\eta| > 2\} $ (n = 2, 3) as a function of centrality in XeXe and PbPb, calculated from the 2-particle correlation method. The bars and the open boxes represent statistical and systematic uncertainties, respectively. The red solid lines show the prediction from TRENTo-IC in terms of the initial-state eccentricities $ \varepsilon_{n} $ for deformed Xe (Xe-(a)), and the black line is for spherical Xe (Xe-(b)) when taken in ratio with Pb. The shaded bands show the different hydrodynamic predictions for different sets of deformations from the IP-Glasma+MUSIC+UrQMD model. |
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Figure 2:
$ v_{n}\{4\}/v_{n}\{2,|\Delta\eta| > 2\} $ (n = 2, 3) as a function of centrality in XeXe and PbPb, calculated from multiparticle cumulants. The bars and the open boxes represent statistical and systematic uncertainties, respectively. The red and blue solid lines show the predictions from TRENTo-IC in terms of the initial-state eccentricities $ \varepsilon_{n} $ for deformed Xe (Xe-(a)), and Pb nuclei. The shaded band shows the hydrodynamic predictions for the IP-Glasma+MUSIC+UrQMD model parameters for Xe-(a). The cyan line shows the theoretical prediction for $ v_{3}\{4\}/v_{3}\{2,|\Delta\eta| > 2\} $ according to $ A^{-1/4} $ scaling. |
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Figure 2-a:
$ v_{n}\{4\}/v_{n}\{2,|\Delta\eta| > 2\} $ (n = 2, 3) as a function of centrality in XeXe and PbPb, calculated from multiparticle cumulants. The bars and the open boxes represent statistical and systematic uncertainties, respectively. The red and blue solid lines show the predictions from TRENTo-IC in terms of the initial-state eccentricities $ \varepsilon_{n} $ for deformed Xe (Xe-(a)), and Pb nuclei. The shaded band shows the hydrodynamic predictions for the IP-Glasma+MUSIC+UrQMD model parameters for Xe-(a). The cyan line shows the theoretical prediction for $ v_{3}\{4\}/v_{3}\{2,|\Delta\eta| > 2\} $ according to $ A^{-1/4} $ scaling. |
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Figure 2-b:
$ v_{n}\{4\}/v_{n}\{2,|\Delta\eta| > 2\} $ (n = 2, 3) as a function of centrality in XeXe and PbPb, calculated from multiparticle cumulants. The bars and the open boxes represent statistical and systematic uncertainties, respectively. The red and blue solid lines show the predictions from TRENTo-IC in terms of the initial-state eccentricities $ \varepsilon_{n} $ for deformed Xe (Xe-(a)), and Pb nuclei. The shaded band shows the hydrodynamic predictions for the IP-Glasma+MUSIC+UrQMD model parameters for Xe-(a). The cyan line shows the theoretical prediction for $ v_{3}\{4\}/v_{3}\{2,|\Delta\eta| > 2\} $ according to $ A^{-1/4} $ scaling. |
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Figure 3:
The top panel shows the normalized symmetric cumulants NSC(2,3) and NSC(2,4) as a function of centrality in XeXe and PbPb, calculated from multiparticle cumulants. The bars and the open boxes represent statistical and systematic uncertainties, respectively. The red and blue solid lines show the predictions from TRENTo-IC in terms of initial-state eccentricities $ \varepsilon_{n} $ for deformed Xe (Xe-(a)), and Pb nuclei. The solid lines show the prediction from IP-Glasma IC model having the same Xe and Pb nucleus parameters, while the shaded band shows the hydrodynamic predictions for the IP-Glasma+MUSIC+UrQMD model. The bottom panel shows the ratios of NSC(m,n) for XeXe/PbPb as a function of centrality. The red solid lines show the initial-state predictions from TRENTo-IC while the orange solid lines show those from IP-Glasma IC. The blue shaded band is the hydrodynamic prediction given by IP-Glasma+MUSIC+UrQMD. |
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Figure 3-a:
The top panel shows the normalized symmetric cumulants NSC(2,3) and NSC(2,4) as a function of centrality in XeXe and PbPb, calculated from multiparticle cumulants. The bars and the open boxes represent statistical and systematic uncertainties, respectively. The red and blue solid lines show the predictions from TRENTo-IC in terms of initial-state eccentricities $ \varepsilon_{n} $ for deformed Xe (Xe-(a)), and Pb nuclei. The solid lines show the prediction from IP-Glasma IC model having the same Xe and Pb nucleus parameters, while the shaded band shows the hydrodynamic predictions for the IP-Glasma+MUSIC+UrQMD model. The bottom panel shows the ratios of NSC(m,n) for XeXe/PbPb as a function of centrality. The red solid lines show the initial-state predictions from TRENTo-IC while the orange solid lines show those from IP-Glasma IC. The blue shaded band is the hydrodynamic prediction given by IP-Glasma+MUSIC+UrQMD. |
png |
Figure 3-b:
The top panel shows the normalized symmetric cumulants NSC(2,3) and NSC(2,4) as a function of centrality in XeXe and PbPb, calculated from multiparticle cumulants. The bars and the open boxes represent statistical and systematic uncertainties, respectively. The red and blue solid lines show the predictions from TRENTo-IC in terms of initial-state eccentricities $ \varepsilon_{n} $ for deformed Xe (Xe-(a)), and Pb nuclei. The solid lines show the prediction from IP-Glasma IC model having the same Xe and Pb nucleus parameters, while the shaded band shows the hydrodynamic predictions for the IP-Glasma+MUSIC+UrQMD model. The bottom panel shows the ratios of NSC(m,n) for XeXe/PbPb as a function of centrality. The red solid lines show the initial-state predictions from TRENTo-IC while the orange solid lines show those from IP-Glasma IC. The blue shaded band is the hydrodynamic prediction given by IP-Glasma+MUSIC+UrQMD. |
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Figure 4:
A selection of six-particle three-harmonic symmetric cumulants and normalized symmetric cumulants as a function of centrality in XeXe (left plot) and PbPb (right plot), calculated from multiparticle cumulants. The bars represent the statistical and negligible systematic uncertainties, added in quadrature. The shaded bands show the corresponding hydrodynamic predictions from the IP-Glasma+MUSIC+UrQMD model for deformed Xe (Xe-(a)), and Pb nuclei. |
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Figure 4-a:
A selection of six-particle three-harmonic symmetric cumulants and normalized symmetric cumulants as a function of centrality in XeXe (left plot) and PbPb (right plot), calculated from multiparticle cumulants. The bars represent the statistical and negligible systematic uncertainties, added in quadrature. The shaded bands show the corresponding hydrodynamic predictions from the IP-Glasma+MUSIC+UrQMD model for deformed Xe (Xe-(a)), and Pb nuclei. |
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Figure 4-b:
A selection of six-particle three-harmonic symmetric cumulants and normalized symmetric cumulants as a function of centrality in XeXe (left plot) and PbPb (right plot), calculated from multiparticle cumulants. The bars represent the statistical and negligible systematic uncertainties, added in quadrature. The shaded bands show the corresponding hydrodynamic predictions from the IP-Glasma+MUSIC+UrQMD model for deformed Xe (Xe-(a)), and Pb nuclei. |
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Figure 5:
Six-particle normalized mixed harmonic cumulants (nMHC) as a function of centrality in XeXe and PbPb, calculated from multiparticle cumulants. The bars represent the statistical and negligible systematic uncertainties, added in quadrature. The shaded bands show the corresponding hydrodynamic predictions from the IP-Glasma+MUSIC+UrQMD model for deformed Xe (Xe-(a)), and Pb nuclei. |
png |
Figure 5-a:
Six-particle normalized mixed harmonic cumulants (nMHC) as a function of centrality in XeXe and PbPb, calculated from multiparticle cumulants. The bars represent the statistical and negligible systematic uncertainties, added in quadrature. The shaded bands show the corresponding hydrodynamic predictions from the IP-Glasma+MUSIC+UrQMD model for deformed Xe (Xe-(a)), and Pb nuclei. |
png |
Figure 5-b:
Six-particle normalized mixed harmonic cumulants (nMHC) as a function of centrality in XeXe and PbPb, calculated from multiparticle cumulants. The bars represent the statistical and negligible systematic uncertainties, added in quadrature. The shaded bands show the corresponding hydrodynamic predictions from the IP-Glasma+MUSIC+UrQMD model for deformed Xe (Xe-(a)), and Pb nuclei. |
png pdf |
Figure 6:
Eight-particle normalized mixed harmonic cumulants (nMHC) as a function of centrality in XeXe and PbPb, calculated from multiparticle cumulants. The bars represent the statistical and negligible systematic uncertainties, added in quadrature. The shaded bands show the corresponding hydrodynamic predictions from the IP-Glasma+MUSIC+UrQMD model for deformed Xe (Xe-(a)), and Pb nuclei. The solid lines represent the initial-state model predictions. |
png |
Figure 6-a:
Eight-particle normalized mixed harmonic cumulants (nMHC) as a function of centrality in XeXe and PbPb, calculated from multiparticle cumulants. The bars represent the statistical and negligible systematic uncertainties, added in quadrature. The shaded bands show the corresponding hydrodynamic predictions from the IP-Glasma+MUSIC+UrQMD model for deformed Xe (Xe-(a)), and Pb nuclei. The solid lines represent the initial-state model predictions. |
png |
Figure 6-b:
Eight-particle normalized mixed harmonic cumulants (nMHC) as a function of centrality in XeXe and PbPb, calculated from multiparticle cumulants. The bars represent the statistical and negligible systematic uncertainties, added in quadrature. The shaded bands show the corresponding hydrodynamic predictions from the IP-Glasma+MUSIC+UrQMD model for deformed Xe (Xe-(a)), and Pb nuclei. The solid lines represent the initial-state model predictions. |
png pdf |
Figure 7:
$ v_{4}\{2,\left|\Delta\eta\right| > 2\} $ as a function of centrality in XeXe and PbPb, calculated from 2-particle correlation method. The bars and the open boxes represent statistical and systematic uncertainties, respectively. The red line shows the prediction from TRENTo-IC in terms in terms of $ \varepsilon_{4} $ for Xe-(a), while the shaded bands show the different hydrodynamic predictions for four different sets of deformations from the IP-Glasma+MUSIC+UrQMD model. |
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Figure 7-a:
$ v_{4}\{2,\left|\Delta\eta\right| > 2\} $ as a function of centrality in XeXe and PbPb, calculated from 2-particle correlation method. The bars and the open boxes represent statistical and systematic uncertainties, respectively. The red line shows the prediction from TRENTo-IC in terms in terms of $ \varepsilon_{4} $ for Xe-(a), while the shaded bands show the different hydrodynamic predictions for four different sets of deformations from the IP-Glasma+MUSIC+UrQMD model. |
png |
Figure 7-b:
$ v_{4}\{2,\left|\Delta\eta\right| > 2\} $ as a function of centrality in XeXe and PbPb, calculated from 2-particle correlation method. The bars and the open boxes represent statistical and systematic uncertainties, respectively. The red line shows the prediction from TRENTo-IC in terms in terms of $ \varepsilon_{4} $ for Xe-(a), while the shaded bands show the different hydrodynamic predictions for four different sets of deformations from the IP-Glasma+MUSIC+UrQMD model. |
png pdf |
Figure 8:
$ v_{n}\{4\} $ (n = 2, 3) as a function of centrality in XeXe and PbPb, calculated using 4-particle cumulants. The bars and the open boxes represent statistical and systematic uncertainties, respectively. |
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Figure 8-a:
$ v_{n}\{4\} $ (n = 2, 3) as a function of centrality in XeXe and PbPb, calculated using 4-particle cumulants. The bars and the open boxes represent statistical and systematic uncertainties, respectively. |
png |
Figure 8-b:
$ v_{n}\{4\} $ (n = 2, 3) as a function of centrality in XeXe and PbPb, calculated using 4-particle cumulants. The bars and the open boxes represent statistical and systematic uncertainties, respectively. |
| Tables | |
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Table 1:
Woods-Saxon deformation parameters for the four sets of Xe nucleus and the Pb nucleus. |
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Table 2:
Signs of correlations between different moments of $ v_{2} $ and $ v_{3}/v_{4} $. |
| Summary |
| For the first time, detailed comparisons of individual flow harmonics, two- and three-harmonic correlations, and higher-power mixed harmonic cumulants have been performed between XeXe collisions at $ \sqrt{s_{{\mathrm{NN}}}} = $ 5.44 TeV and PbPb collisions at $ \sqrt{s_{{\mathrm{NN}}}} = $ 5.36 TeV. The results have been compared with the theoretical predictions of the IP-Glasma+MUSIC+UrQMD hydrodynamic model and TRENTo-IC and IP-Glasma initial-state models, which were calculated with various sets of deformation parameters for the Xe nucleus. We find that the final-state IP-Glasma+MUSIC+UrQMD model calculation with $ R_{0} = $ 5.601, $ a_{0} = $ 0.492, $ \beta_{2} = $ 0.207, $ \beta_{4} = - $0.003 for Xe matches the data best. On the other hand, the difference in initial-state predictions from the TRENTo-IC and IP-Glasma IC models not only point to the sensitivity of these observables to the pre-equilibrium dynamics needed to model the experimental data, but also to the increasing non-linearity of the higher-power moments of the flow harmonics in peripheral collisions. The comparison of the higher-power moments in XeXe and PbPb collisions is a good way to study the impact of the system size on these observables, where it is seen that the observables containing higher-power moments of fluctuation-driven $ v_{3} $ and $ v_{4} $ have greater magnitude in XeXe, it being the smaller nucleus. Subtle differences exist between data and model calculations with the current sets of parameters. These differences highlight the importance of fine-tuning the model parameters, including not only the nuclear deformation parameters but also those intrinsic to hydrodynamic calculations such as transport coefficients and freeze-out criteria. Moreover, the degree of applicability of hydrodynamics to peripheral heavy-ion collisions remains an open question. Such analyses can significantly improve the overall understanding of initial conditions and transport properties of the Quark-Gluon Plasma (QGP) created at the LHC. |
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