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| CMS-HIN-24-015 ; CERN-EP-2026-155 | ||
| Exploring the origin of $ \mathrm{D^0} $ meson elliptic flow in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV using event shape engineering | ||
| CMS Collaboration | ||
| 10 July 2026 | ||
| Submitted to Physics Letters B | ||
| Abstract: The influence of the initial-state geometry on the elliptic flow of prompt $ \mathrm{D^0} $ mesons in high-energy heavy ion collisions is explored. A lead-lead (PbPb) data sample at a center-of-mass energy per nucleon pair of 5.02 TeV and with an integrated luminosity of 0.607$ \text{nb}^{-1}$ was collected in 2018 with the CMS detector at the CERN LHC. Based on these data, an event-shape engineering technique is used to isolate collisions with similar geometrical properties. An asymmetry parameter, $ q_2 $, is first determined from the distribution of transverse energy in the forward region of the detector. This parameter is shown to be linearly correlated with the elliptic anisotropy of inclusive charged particles measured near mid-rapidity, as characterized by the second-order Fourier coefficients, $ v_2 $. Taking the charged particle $ v_2 $ coefficients as proxies for the initial-state eccentricity, the correlation of $ \mathrm{D^0} $ meson $ v_2 $ values near mid-rapidity with those of inclusive charged particles is then studied. For $ \mathrm{D^0} $ mesons with transverse momenta in the range of 2--30 GeV and for different degrees of collision overlap, the $ v_2 $ values are found strongly correlated with those for charged particles when selected based on similar $ q_2 $ intervals. This correlation suggests that the initial-state geometry substantially impacts the development of charm-hadron flow in heavy ion collisions. A model calculation that explores the thermalization and collective motion of $ \mathrm{D^0} $ mesons and charged particles is compared to the experimental results. | ||
| Links: e-print arXiv:2607.11017 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
An example of the fit to the invariant mass spectrum in the centrality class 40--50% and for the $ \mathrm{D^0} p_{\mathrm{T}} $ range 4--6 GeV. |
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Figure 2:
Dependence of the $ \mathrm{D^0} $ meson (upper row) and the charged particle (lower row) $ v_2 $ values on $ q_2 $. The $ \mathrm{D^0} $ mesons have 2 $ < p_{\mathrm{T}} < $ 4 GeV and $ |y| < $ 1. The inclusive charged particles have 1 $ < p_{\mathrm{T}} < $ 3 GeV and $ |\eta| < $ 1. The plots are shown for events in the centrality ranges of 10--20, 20--30, 30--40 and 40--50%. The vertical lines represent the statistical uncertainties and the boxes represent the systematic uncertainties. |
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Figure 3:
Scatter plots of the $ \mathrm{D^0} $ meson $ v_2 $ vs. charged particle $ v_2 $ values measured in common $ q_2 $ intervals. The $ \mathrm{D^0} $ mesons have 2 $ < p_{\mathrm{T}} < $ 4 GeV and $ |y| < $ 1. The inclusive charged particles have 1 $ < p_{\mathrm{T}} < $ 3 GeV and $ |\eta| < $ 1. The vertical lines represent the statistical uncertainties, and the boxes represent the systematic uncertainties associated with the $ \mathrm{D^0} $ meson $ v_2 $. The errors associated with the charged particle $ v_2 $ are smaller than the markers. The centrality classes 10--20% (upper left), 20--30% (upper right), 30--40% (lower left), and 40--50% (lower right) are shown. The red lines are linear fits to the experimental results based on the statistical uncertainties of the data, with the shaded red band corresponding to a one standard deviation uncertainty. The PHSD model [46,47] predictions are also shown in the plots. |
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Figure 3-a:
Scatter plots of the $ \mathrm{D^0} $ meson $ v_2 $ vs. charged particle $ v_2 $ values measured in common $ q_2 $ intervals. The $ \mathrm{D^0} $ mesons have 2 $ < p_{\mathrm{T}} < $ 4 GeV and $ |y| < $ 1. The inclusive charged particles have 1 $ < p_{\mathrm{T}} < $ 3 GeV and $ |\eta| < $ 1. The vertical lines represent the statistical uncertainties, and the boxes represent the systematic uncertainties associated with the $ \mathrm{D^0} $ meson $ v_2 $. The errors associated with the charged particle $ v_2 $ are smaller than the markers. The centrality classes 10--20% (upper left), 20--30% (upper right), 30--40% (lower left), and 40--50% (lower right) are shown. The red lines are linear fits to the experimental results based on the statistical uncertainties of the data, with the shaded red band corresponding to a one standard deviation uncertainty. The PHSD model [46,47] predictions are also shown in the plots. |
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Figure 3-b:
Scatter plots of the $ \mathrm{D^0} $ meson $ v_2 $ vs. charged particle $ v_2 $ values measured in common $ q_2 $ intervals. The $ \mathrm{D^0} $ mesons have 2 $ < p_{\mathrm{T}} < $ 4 GeV and $ |y| < $ 1. The inclusive charged particles have 1 $ < p_{\mathrm{T}} < $ 3 GeV and $ |\eta| < $ 1. The vertical lines represent the statistical uncertainties, and the boxes represent the systematic uncertainties associated with the $ \mathrm{D^0} $ meson $ v_2 $. The errors associated with the charged particle $ v_2 $ are smaller than the markers. The centrality classes 10--20% (upper left), 20--30% (upper right), 30--40% (lower left), and 40--50% (lower right) are shown. The red lines are linear fits to the experimental results based on the statistical uncertainties of the data, with the shaded red band corresponding to a one standard deviation uncertainty. The PHSD model [46,47] predictions are also shown in the plots. |
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Figure 3-c:
Scatter plots of the $ \mathrm{D^0} $ meson $ v_2 $ vs. charged particle $ v_2 $ values measured in common $ q_2 $ intervals. The $ \mathrm{D^0} $ mesons have 2 $ < p_{\mathrm{T}} < $ 4 GeV and $ |y| < $ 1. The inclusive charged particles have 1 $ < p_{\mathrm{T}} < $ 3 GeV and $ |\eta| < $ 1. The vertical lines represent the statistical uncertainties, and the boxes represent the systematic uncertainties associated with the $ \mathrm{D^0} $ meson $ v_2 $. The errors associated with the charged particle $ v_2 $ are smaller than the markers. The centrality classes 10--20% (upper left), 20--30% (upper right), 30--40% (lower left), and 40--50% (lower right) are shown. The red lines are linear fits to the experimental results based on the statistical uncertainties of the data, with the shaded red band corresponding to a one standard deviation uncertainty. The PHSD model [46,47] predictions are also shown in the plots. |
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Figure 3-d:
Scatter plots of the $ \mathrm{D^0} $ meson $ v_2 $ vs. charged particle $ v_2 $ values measured in common $ q_2 $ intervals. The $ \mathrm{D^0} $ mesons have 2 $ < p_{\mathrm{T}} < $ 4 GeV and $ |y| < $ 1. The inclusive charged particles have 1 $ < p_{\mathrm{T}} < $ 3 GeV and $ |\eta| < $ 1. The vertical lines represent the statistical uncertainties, and the boxes represent the systematic uncertainties associated with the $ \mathrm{D^0} $ meson $ v_2 $. The errors associated with the charged particle $ v_2 $ are smaller than the markers. The centrality classes 10--20% (upper left), 20--30% (upper right), 30--40% (lower left), and 40--50% (lower right) are shown. The red lines are linear fits to the experimental results based on the statistical uncertainties of the data, with the shaded red band corresponding to a one standard deviation uncertainty. The PHSD model [46,47] predictions are also shown in the plots. |
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Figure 4:
The Pearson correlation coefficients ($ r $) obtained from the scatter plots of the prompt $ \mathrm{D^0} $ meson $ v_2 $ vs. charged particle $ v_2 $ values for the indicated $ p_{\mathrm{T}} $ and centrality classes. The vertical lines correspond to the statistical uncertainties and the vertical bands correspond to the systematic uncertainties added in quadrature. The open symbols show the PHSD predictions in the $ \mathrm{D^0} $ meson $ p_{\mathrm{T}} $ range 2--10 GeV, with the symbols shifted along the $ p_{\mathrm{T}} $ axis for better visibility. |
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Figure 5:
Slopes (upper row) and intercepts (lower row) obtained from the fits of the prompt $ \mathrm{D^0} $ meson $ \mbox{\textsl{vs.}} $ charged particle $ v_2 $ values for each $ p_{\mathrm{T}} $ and centrality class. The $ \mathrm{D^0} $ meson and charged particle $ v_2 $ values in each $ q_2 $ interval are normalized by the corresponding $ q_2 $-inclusive $ v_2 $ value in the same $ p_{\mathrm{T}} $ and centrality class. The vertical lines correspond to the statistical uncertainties and the vertical bands correspond to the systematic uncertainties added in quadrature. The open symbols show the PHSD predictions in the $ \mathrm{D^0} $ meson $ p_{\mathrm{T}} $ range 2--10 GeV, with the symbols shifted along the $ p_{\mathrm{T}} $ axis for better visibility. |
png pdf |
Figure 6:
Scatter plots of the $ \mathrm{D^0} $ meson $ v_2 $ vs. charged particle $ v_2 $ values measured in common $ q_2 $ intervals. The inclusive charged particles have 1 $ < p_{\mathrm{T}} < $ 3 GeV and $ |\eta| < $ 1. The vertical lines represent the statistical uncertainties, and the boxes represent the systematic uncertainties associated with the $ \mathrm{D^0} $ meson $ v_2 $ values. The uncertainties associated with the inclusive charged particle $ v_2 $ values are smaller than the markers. The $ \mathrm{D^0} $ meson $ p_{\mathrm{T}} $ ranges 2--4 GeV (upper left), 4--6 GeV (upper right), 6--10 GeV (lower left), and 10--30 GeV (lower right) for the 0--10% centrality class are shown. The red lines are linear fits to the experimental results based on the statistical uncertainties of the data, with the shaded red band corresponding to a one standard deviation uncertainty. The PHSD model [46,47] predictions are also shown in the plots. |
png pdf |
Figure 6-a:
Scatter plots of the $ \mathrm{D^0} $ meson $ v_2 $ vs. charged particle $ v_2 $ values measured in common $ q_2 $ intervals. The inclusive charged particles have 1 $ < p_{\mathrm{T}} < $ 3 GeV and $ |\eta| < $ 1. The vertical lines represent the statistical uncertainties, and the boxes represent the systematic uncertainties associated with the $ \mathrm{D^0} $ meson $ v_2 $ values. The uncertainties associated with the inclusive charged particle $ v_2 $ values are smaller than the markers. The $ \mathrm{D^0} $ meson $ p_{\mathrm{T}} $ ranges 2--4 GeV (upper left), 4--6 GeV (upper right), 6--10 GeV (lower left), and 10--30 GeV (lower right) for the 0--10% centrality class are shown. The red lines are linear fits to the experimental results based on the statistical uncertainties of the data, with the shaded red band corresponding to a one standard deviation uncertainty. The PHSD model [46,47] predictions are also shown in the plots. |
png pdf |
Figure 6-b:
Scatter plots of the $ \mathrm{D^0} $ meson $ v_2 $ vs. charged particle $ v_2 $ values measured in common $ q_2 $ intervals. The inclusive charged particles have 1 $ < p_{\mathrm{T}} < $ 3 GeV and $ |\eta| < $ 1. The vertical lines represent the statistical uncertainties, and the boxes represent the systematic uncertainties associated with the $ \mathrm{D^0} $ meson $ v_2 $ values. The uncertainties associated with the inclusive charged particle $ v_2 $ values are smaller than the markers. The $ \mathrm{D^0} $ meson $ p_{\mathrm{T}} $ ranges 2--4 GeV (upper left), 4--6 GeV (upper right), 6--10 GeV (lower left), and 10--30 GeV (lower right) for the 0--10% centrality class are shown. The red lines are linear fits to the experimental results based on the statistical uncertainties of the data, with the shaded red band corresponding to a one standard deviation uncertainty. The PHSD model [46,47] predictions are also shown in the plots. |
png pdf |
Figure 6-c:
Scatter plots of the $ \mathrm{D^0} $ meson $ v_2 $ vs. charged particle $ v_2 $ values measured in common $ q_2 $ intervals. The inclusive charged particles have 1 $ < p_{\mathrm{T}} < $ 3 GeV and $ |\eta| < $ 1. The vertical lines represent the statistical uncertainties, and the boxes represent the systematic uncertainties associated with the $ \mathrm{D^0} $ meson $ v_2 $ values. The uncertainties associated with the inclusive charged particle $ v_2 $ values are smaller than the markers. The $ \mathrm{D^0} $ meson $ p_{\mathrm{T}} $ ranges 2--4 GeV (upper left), 4--6 GeV (upper right), 6--10 GeV (lower left), and 10--30 GeV (lower right) for the 0--10% centrality class are shown. The red lines are linear fits to the experimental results based on the statistical uncertainties of the data, with the shaded red band corresponding to a one standard deviation uncertainty. The PHSD model [46,47] predictions are also shown in the plots. |
png pdf |
Figure 6-d:
Scatter plots of the $ \mathrm{D^0} $ meson $ v_2 $ vs. charged particle $ v_2 $ values measured in common $ q_2 $ intervals. The inclusive charged particles have 1 $ < p_{\mathrm{T}} < $ 3 GeV and $ |\eta| < $ 1. The vertical lines represent the statistical uncertainties, and the boxes represent the systematic uncertainties associated with the $ \mathrm{D^0} $ meson $ v_2 $ values. The uncertainties associated with the inclusive charged particle $ v_2 $ values are smaller than the markers. The $ \mathrm{D^0} $ meson $ p_{\mathrm{T}} $ ranges 2--4 GeV (upper left), 4--6 GeV (upper right), 6--10 GeV (lower left), and 10--30 GeV (lower right) for the 0--10% centrality class are shown. The red lines are linear fits to the experimental results based on the statistical uncertainties of the data, with the shaded red band corresponding to a one standard deviation uncertainty. The PHSD model [46,47] predictions are also shown in the plots. |
png pdf |
Figure 7:
The same scatter plots as Fig. 6, but for the $ \mathrm{D^0} $ mesons with 10 $ < p_{\mathrm{T}} < $ 30 GeV in the 10--20, 20--30, 30--40, and 40--50% centrality classes. All other explanation for the plots are the same as in Fig. 6. |
png pdf |
Figure 7-a:
The same scatter plots as Fig. 6, but for the $ \mathrm{D^0} $ mesons with 10 $ < p_{\mathrm{T}} < $ 30 GeV in the 10--20, 20--30, 30--40, and 40--50% centrality classes. All other explanation for the plots are the same as in Fig. 6. |
png pdf |
Figure 7-b:
The same scatter plots as Fig. 6, but for the $ \mathrm{D^0} $ mesons with 10 $ < p_{\mathrm{T}} < $ 30 GeV in the 10--20, 20--30, 30--40, and 40--50% centrality classes. All other explanation for the plots are the same as in Fig. 6. |
png pdf |
Figure 7-c:
The same scatter plots as Fig. 6, but for the $ \mathrm{D^0} $ mesons with 10 $ < p_{\mathrm{T}} < $ 30 GeV in the 10--20, 20--30, 30--40, and 40--50% centrality classes. All other explanation for the plots are the same as in Fig. 6. |
png pdf |
Figure 7-d:
The same scatter plots as Fig. 6, but for the $ \mathrm{D^0} $ mesons with 10 $ < p_{\mathrm{T}} < $ 30 GeV in the 10--20, 20--30, 30--40, and 40--50% centrality classes. All other explanation for the plots are the same as in Fig. 6. |
| Tables | |
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Table 1:
Summary of systematic uncertainties in the absolute differences between the nominal and the alternative analyses for the $ \mathrm{D^0} $ meson $ v_2 $ values, slope, and intercept of the scatter plots. |
| Summary |
| The elliptic-flow $ v_2 $ Fourier coefficient is measured for $ \mathrm{D^0} $ mesons using an event-shape engineering technique. The data sample consists of lead-lead collisions measured with the CMS detector at the CERN LHC at a center-of-mass energy per nucleon pair of 5.02 TeV and with an integrated luminosity of 0.607$ \text{nb}^{-1}$. The azimuthal asymmetry of energy deposits in a forward-rapidity calorimeter is characterized by a $ q_2 $ parameter that can be related to the initial collision geometry. A strong linear correlation is found between this parameter and the corresponding $ v_2 $ values for inclusive charged particles measured in the pseudorapidity ($ \eta $) and transverse momentum ($ p_{\mathrm{T}} $) ranges of $ |\eta| < $ 1 and 1 $ < p_{\mathrm{T}} < $ 3 GeV, respectively. The variation between $ \mathrm{D^0} $ meson and inclusive charged particle $ v_2 $ values obtained at common $ q_2 $ intervals is then explored. A strong linear correlation is found over the centrality range of 10--40%, as binned in 10% classes, for $ \mathrm{D^0} $ mesons at low $ p_{\mathrm{T}} $ (2--10 GeV). A weaker linear correlation is observed for centrality ranges of 0--10 and 40--50%. The parton-hadron-string-dynamics model is compared to the experimental results and found to underestimate the degree of charm quark thermalization in the quark-gluon plasma at $ p_{\mathrm{T}} < $ 4 GeV. These findings provide compelling evidence for the importance of the initial-state geometry in determining the collective flow of heavy quarks within the quark-gluon plasma created in heavy ion collisions. |
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