Hydrodynamic Flow Fluctuations in $\sqrt{s_{\rm NN}}=5.02$ TeV PbPb Collisions

The collective, anisotropic expansion of the medium created in ultrarelativistic heavy-ion collisions, known as flow, is characterized through a Fourier expansion of the final-state azimuthal particle density. In the Fourier expansion, flow harmonic coefficients $v_n$ correspond to shape components in the final-state particle density and are related to spatial anisotropies in the initial-state transverse energy density of a collision. Flow harmonic fluctuations are studied for PbPb collisions at $\sqrt{s_{\rm NN}} = 5.02$~TeV using the CMS detector at the CERN LHC. Flow harmonic probability distributions $p(v_n)$ are obtained using particles with $0.3 < p_{\rm T} < 3.0$ GeV/$c$ and $\lvert \eta \rvert < 1.0$ by removing finite-multiplicity resolution effects from the observed azimuthal particle density through an unfolding procedure. Cumulant elliptic flow harmonics ($n=2$) are determined from the moments of the unfolded $p(v_2)$ distributions and used to construct observables in $5\%$ wide centrality bins up to $60\%$ that relate to the initial-state spatial anisotropy. Hydrodynamic models predict that fluctuations in the initial-state transverse energy density will lead to a non-Gaussian component in the elliptic flow probability distributions that manifests as a negative skewness. A statistically significant negative skewness is observed for all centrality bins as evidenced by a splitting between the higher-order cumulant elliptic flow harmonics. The unfolded $p(v_2)$ distributions are transformed assuming a linear relationship between the initial-state spatial anisotropy and final-state flow and are fitted with elliptic power law and Bessel Gaussian parametrizations to infer information on the nature of initial-state fluctuations. The elliptic power law parametrization is found to provide a more accurate description of the fluctuations than the Bessel-Gaussian parametrization. In addition, the event-shape engineering technique, where events are further divided into classes based on an observed ellipticity, is used to study fluctuation-driven differences in the initial-state spatial anisotropy for a given collision centrality that would otherwise be destroyed by event-averaging techniques. Correlations between the first and second moments of $p(v_n)$ distributions and event ellipticity are measured for harmonic orders $n=2-4$ by coupling event-shape engineering to the unfolding technique.