CMS-PAS-HIN-16-019 | ||

Measurement of the skewness of elliptic flow fluctuations in PbPb collisions at $\sqrt{s_{\mathrm{NN}}} = $ 5.02 TeV | ||

CMS Collaboration | ||

February 2017 | ||

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Abstract:
Event-by-event flow harmonics are studied for PbPb collisions at $\sqrt{s_{\mathrm{NN}}} = $ 5.02 TeV using the CMS detector at the LHC. Flow harmonic probability distributions $p(v_2)$ are obtained using particles of 0.3 $ \leq p_{\mathrm{T}} \leq $ 3.0 GeV/$c$ and $|\eta| \leq $ 1.0 and are unfolded to remove smearing effects from observed azimuthal particle distributions. Cumulant flow harmonics are determined from the moments of $p(v_2)$ and used to estimate the standardized elliptic flow skewness in 5% wide centrality bins up to 60%. Hydrodynamic models predict that flow fluctuations will lead to a non-Gaussian component in the flow distributions with a negative skew with respect to the reaction plane. A significant negative skewness is observed for all centrality bins as evidenced by a splitting between $v_2\{4\}$ and $v_2\{6\}$ cumulants. In addition, elliptic power law distribution fits are made to the $p(v_2)$ distributions to infer information on the nature of initial-state eccentricity distributions. The elliptic power law parametrization is found to provide a more accurate description of the fluctuations than the Bessel-Gaussian parametrization.
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Links:
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These preliminary results are superseded in this paper, PLB 789 (2019) 643.The superseded preliminary plots can be found here. |

Figures | |

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Figure 1:
Fit performance of a Gaussian and Student's t-distribution to the rescaled subevent difference distributions for events in the 5-10% (top row) and 55-60% centrality classes (bottom row). Central events have a large number of tracks in each subevent, thus the Gaussian and Student's t-functions both describe the data well. The difference in fit performance is more pronounced in peripheral events where the small number of tracks per event is in the regime where the Student's t-function is relevant. |

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Figure 2:
Cumulant values extracted from the unfolded $p ( v_2 )$ distributions exhibiting the expected $v_2\{2\} > v_2\{4\} \approx v_2\{6\} \approx v_2\{8\}$ behavior. Both statistical and systematic uncertainties are shown. A fine-level splitting of the higher-order cumulants becomes more pronounced in peripheral bins. |

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Figure 3:
Ratios of higher-order cumulants with values obtained from the moments of the unfolded $p ( v_2 )$ distributions. Both statistical and systematic uncertainties are shown. Hydrodynamic predictions for 2.76 TeV from Ref. [28] are presented as a colored band and are compared to the measured ratio $v_{2}\{6\}/v_2\{4\}$. Theory predictions are consistent to the measurement within uncertainties. |

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Figure 4:
The estimated skewness for the unfolded $p ( v_2 )$ as determined from its cumulant flow harmonics with Eq. 10. Both statistical and systematic uncertainties are shown. Hydrodynamic predictions for 2.76 TeV from Ref. [28] are presented as a colored band and are compared to the measured skewness. Theory predictions are consistent to the measurement within uncertainties. |

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Figure 5:
Ratios of higher-order cumulants with values obtained from the moments of the unfolded $p ( v_2 )$ distributions measured by CMS compared to those measured by ATLAS in Ref. [27]. Both statistical and systematic uncertainties are shown for CMS as error bars and bands respectively. ATLAS uncertainties are presented as statistical and systematic added in quadrature. |

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Figure 6:
Elliptic power law (Eq. 19) and Bessel-Gaussian (Eq. 5) parametrizations fitted to unfolded $p(v_2)$ distributions. Parameters extracted from each fit are provided in each panel with respective statistical uncertainties. All parameters except $\alpha $ are reported as percentages. Fit performance, as measured by the smeared-space $\chi ^2/$NDF goodness-of-fit, is presented as a function of centrality for each parametrization. |

Summary |

In summary, non-Gaussian behavior in the fluctuations of $v_2$ coefficients has been observed in PbPb collisions at $\sqrt{s_{\mathrm{NN}}} = $ 5.02 TeV. This observation was made by unfolding the statistical smearing effects in observed flow harmonic distributions to obtain the underlying event-by-event flow distributions for 5% wide centrality bins up to 60%. Cumulant flow harmonics were calculated from the moments of the underlying distributions and a fine-structure splitting was observed between $v_2\{4\}$, $v_2\{6\}$, and $v_2\{8\}$. In addition, the standardized skewness with respect to the reaction plane was estimated using the cumulants and was found to have a non-zero value, whose magnitude increases with centrality. Both measurements are consistent with a breakdown in the Gaussian model of elliptic flow fluctuations. In addition, Bessel-Gaussian and elliptic power law parametrizations were fitted to the unfolded $p(v_2)$ distributions to gain further insight as to the nature of the initial-state fluctuations. Both parametrizations assume a linear response between eccentricity and flow, but only the elliptic power law contains the physical constraint $\varepsilon_{2} < $ 1. This constraint naturally incorporates skewness and allows the elliptic power law parametrization to provide a more accurate description of $p(v_2)$ (and ultimately $p(\varepsilon_2)$) than the Bessel-Gaussian parametrization. |

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